In the Artist’s Own Words

For as long as I can remember, I’ve been fascinated by the idea of free improvisation: that it’s possible to create an entire piece of music, never-before heard, in the moment, out of nothing. Growing up as a jazz pianist, I learned to improvise over pre-determined harmonic progressions, but I yearned for a greater freedom: not only to improvise within a given structure, but to improvise the structure itself. As an adult, I’ve slowly learned the discipline necessary to doing this in a way that feels meaningful — alone at the piano (on my recent album Inventions / Reinventions, for example) or with a big-eared collaborator (Lee Konitz, memorably). But it’s only recently that I’ve begun to wonder: what could free improvisation look like with an orchestra?

In 2010, I composed my first piano concerto, and left substantial room for improvisation in the piano part. The orchestra parts, however, were written out in the conventional way. At the same time, I began to bring my childhood love of computer programming into my music. I wrote algorithms — systems of musical rules — which could improvise with me in real time, expressing themselves acoustically through the Yamaha Disklavier player piano. This led to my 2019 album Natural Machines, where I explore the intersection of natural (intuitive, emotional) and mechanical (logical, rule-based) processes in music, doing free improvisation with an algorithm as creative partner. 

It’s worth remembering that many of the greatest musical minds were just as concerned with the rules that structured their music as with the emotion that made it soar. This is certainly true of Bach, and also of John Coltrane. I believe it’s when these two great forces meet — the algorithmic and the spiritual — that art is at its strongest.

In 2022, the Eugene Symphony approached me about writing a new piano concerto. I imagined composing in the conventional way at first. Then the symphony’s conductor, Francesco Lecce-Chong, suggested I incorporate elements from Natural Machines, in particular the live visual representations of the music I’d created. 

Over the last three years, this idea slowly percolated in me — of striking some balance between traditional notation and computer-augmented free improvisation. Then, in mid 2024, on the tail end of two large conventional composition projects, I suddenly felt like doing something radical: what if the entire orchestra, along with myself as the soloist, could enter the stage not knowing what was going to happen? What if we created the music together, in the moment? Wouldn’t that be exciting?

I devised a way to send musical notation in real-time to each member of the orchestra, on mobile devices they could easily set on their music stands. I started to think about the piano somewhat like an organ, with the ability to pull organ stops (or their digital equivalent on my iPad) to select different collections of sounds. I designed and built a system of foot pedals that enabled me to use my feet as much as my hands. I’ve personally labored over every line of code — from the ones that create the network of devices to those responsible for the real-time visuals — just as much as I’ve labored in the past over the individual notes of a composition.

The difference here, of course, is that every time this “piece” — or this process for a piece — is performed, it will sound different. Yet, there is a theme that will carry through the evening: the notion of harmony, in its broadest sense, from the delicious interactions of sound frequencies to the relative motions of orbiting planets, and perhaps most of all, to the hope that we — along with the orchestra, taken as a microcosm for society — may live in spontaneous, harmonious balance with one another. 

Technical note

By character, I’ve always liked to approach problems from the ground up. There’s something about being present in every aspect of how something works, from the smallest details to the overall structure, that feels right to me. For Natural Machines 2.0, I’ve taken this approach as far as I ever have, building my own gear, custom code libraries, and even learning to create my own integrated circuits. 

Thankfully, I didn’t have to create the instrument at the heart of it all. I’m performing on a Yamaha Disklavier CFX, a real acoustic piano that communicates every key and pedal movement to my computer via MIDI, and which has the magical ability to play by itself. The Disklavier allows me to play naturally while the computer listens, analyzing and responding to my playing with both visuals and sound. In Natural Machines 1.0, the computer expressed itself by playing the same piano I play; in 2.0, it can also play the orchestra.

To control the many layers of the system while performing, I built several interfaces. Beneath the piano keyboard, to the right, sits an adapted organ pedalboard with MIDI output. This pedalboard doesn’t only play notes: each pedal has a small display above it that shows its current function, for example “↑ m3” if that pedal transposes a musical voice up a minor third. The functions of the pedals can change depending on context, and the displays update dynamically as the computer sends them new instructions. 

On the floor to my left sits an array of twelve pedals, each with its own display and all connected to a microcontroller that communicates pedal presses to the computer via MIDI. These pedals can trigger all kinds of real-time transformations: switching instrument assignments, changing articulations, freezing loops: anything you can imagine. The device also supports expression pedals that continuously transmit data, allowing me to shape parameters fluidly with my feet while keeping both hands on the piano. I designed and had manufactured the integrated circuits in green, and couldn’t resist decorating them with stencils of my TriadSculptures.

Two iPads complete the control setup. The first functions as an instrument selector, akin to the stops used by organists. At any given moment, the music I play or which my algorithms generate can be routed to any of eight “voices” — conceptual layers within the music — and each voice can be assigned to one or more orchestral instruments. The iPad lets me choose which instruments are active in the current voice, and its layout can change when the musical algorithm changes to offer context-specific controls.

The second iPad lets me shape dynamics and other performance parameters in real time. Here I can limit or expand the volume range of each voice, trigger or stop loops, and split the piano so that only a portion of the keyboard feeds data to the computer. This iPad also lets me choose the current visual mode, altering how the music is represented on the projection screen.

What to do with all this input? At the center of the system is a laptop running three programs. The first, written in SuperCollider, acts as the central brain of the project. It receives data from all the input devices — the Disklavier, the pedalboards, the iPads, microphones — and processes that information to generate musical output, organized into independent voices. Each voice carries notes, dynamics, and articulations, as well as its own selection of orchestral instruments. This musical data gets sent out from SuperCollider to be represented and played.

The second program, written in Processing, translates the musical data into real-time visuals, to be projected on a screen behind the musicians. It receives information from SuperCollider via the OSC protocol, and displays the notes played by the orchestra and myself, with each voice represented visually in distinct and expressive ways. The projection system must be low-latency so that the imagery, which is so intimately linked to the notes being played, feels organically connected to the sound.

The third program, written in JavaScript, serves a web interface to each orchestral musician over a closed network, created with a specialized Wi-Fi router of the kind used by hotels and airports. Every player connects their phone or tablet to the network, opens a browser, and visits a local website. There, they select their instrument, and a notation display appears. The page shows a traditional five-line staff, automatically switching clefs for multi-clef instruments like cello or bassoon, and applying appropriate transpositions for instruments like French horn or clarinet. When I send commands to the JavaScript program from SuperCollider, notes, dynamics, and articulations specific to this instrument appear on the staff for the musician to play.

In this way, every musician receives live notation generated by what I’m playing at the piano and the algorithms I’ve designed, while the audience sees a parallel visual interpretation projected above the stage. 

It’s all a genuinely wild experiment — the fruit of some crazy dream. The notion of being able to improvise with an orchestra seemed irresistible to me, and I couldn’t exactly tell you why. I simply felt compelled to venture down this road, to see what was possible. I thank you, and the musicians with me on stage tonight, for coming along for the ride. 

There’s a corollary, albeit distant, between this joke and what A.I. is doing to our communication. It used to be that one would proofread a letter or an email before sending, in the understanding that a well-written, typo-free message showed care on the part of the writer towards the reader. Receiving a well-written note felt like a gift — someone had taken the time to make themselves understood to us in the clearest way they could.

Now, with people more and more frequently using A.I. to write their emails, their papers, even their books, we may be entering a phase where the greatest sign of care, on receiving a message, may be in typos, awkward turns of phrase, and other imperfections that indicate that the writer took the time to write it themselves.

A bit like a home-cooked meal, perhaps: there is a point of dry perfection beyond which one is tempted to wonder if the host had the meal catered.

Of course, A.I. is perfectly capable of injecting deliberate mistakes, or writing in all lowercase, if we ask it to. Here’s what ChatGPT returned when I asked it to “write four paragraphs commenting on how it may now be a sign of care, on the part of the writer, to include mistakes in their writing, since ubiquitous AI now makes clear, dry, correct writing the norm — and on the contrary, messages written entirely by hand become rarer and rarer. Include a few typos, and make it all lowercase, in order to appear human.”

it used to be that correctness was the mark of care in writing. people proofread their letters and emails, polishing away small mistakes to show that they had put in effort. but now, with ai everywhere, the opposite has begun to feel true. anyone can push a button and get a flawless block of text, shiny and impersonal. so a stray typo, a clumsy turn of phrase, or an extra space can start to look like a little flare of humanity. it says: i wrote this, me, not a machine.

handwriting, too, has almost dissapeared from everyday life. we still get the occasional note on paper, but most communication happens on screens, smoothed over by predictive text and spellcheck. so when you see a crooked line of handwriting, even messy, the ink smudged, you feel the presence of the person who held the pen. in the same way, a sentence with a small error in an email or message might now be read as a gesture of closeness. it’s not sloppiness; it’s proof of touch.

ironically, what machines are best at—consistency, clarity, grammar—is becoming less valuable as a signal of care. after all, machines don’t tire, they don’t stumble, they don’t write “hte” instead of “the.” so when a person lets a mistake stand, it can suggest they’re not outsourcing their voice. they’re showing you something real. the text is less polished, but it carries more warmth.

of course, this doesn’t mean we should abandon all standards. there’s a difference between a message dashed off with no thought and one that bears the quirks of human fingers on a keyboard. maybe the future of writing will hold a new etiquette: to sprinkle in just enough imperfection so the reader knows you’re there. a little unevenness, a missplaced comma, a word repeated twice—small flaws as a quiet way of saying, “i care enough to show up myself.”

That A.I. can do this — understand the relatively subtle intent of my prompt and expand on it quite competently — is still utterly amazing to me (not to mention scary). If you had told me ten years ago that we’d be here today, I wouldn’t have believed you, and this is coming from someone who’s been following A.I. for a long time and has innovators in the field for friends. And ChatGPT did include a few typos in addition to the obvious “hte” (did you catch them?). Not only that, but its first sentence, “it used to be that correctness was the mark of care in writing”, eerily echoes the second sentence of the second paragraph of my hand-written text, “It used to be that one would proofread a letter or an email before sending”, even though I didn’t share the text with ChatGPT, only the prompt.

Yet the writing somehow still feels lifeless to me. The cadence is flat, too smooth. It lacks rhythm. And there remains something a little cloying about it, too eager to please, a solicitousness that remains a mark of large-language-model chatbots. Or am I just imagining things? Would I have said the same had I been presented with this text as having been written by a person? I believe so, but only double-blind testing can tell.

As of now, I can’t imagine getting A.I. to write an email to anyone I respect. If I can’t take the time to write it, how can I expect my recipient to devote their precious time and attention to reading it? In the early days of the pandemic, I was asked to do an interview with someone I knew. When it came time to schedule the meeting, a message arrived from his email address. The writer identified itself as an automated bot and offered possible times for the meeting. This felt insulting. If he couldn’t take the time to engage at the human level, even on this smallest of exchanges, why should I? I never responded. Eventually he wrote by hand, and we did the interview.

I’m learning, however, in conversations with friends, that more and more people are using A.I. to write their emails, and without any caveats whatsoever. The message is presented as coming from them, in their voice, even though it would be impossible to learn anything about who they are from the subtleties of the writing, beyond its explicit bullet-point intents. Removing the minute particulars of written communication, like this, is as if we talked to someone without being able to hear their tone of voice, or shook their hand without being able to gage their temperature.

There’s a precedent to this, of course: many people throughout history have had secretaries write their replies. And when it comes to A.I. writing books, many people have hired unacknowledged ghostwriters. Is this any different? I think so. The only real currency in this world is time, and its close derivative, attention. Communication is a two-way street, and if I received a response written by a secretary or read a book written by a ghostwriter, I’d know, at the very least, that a human being, albeit not the one I might have wished, had spent their time and attention on the text. This, in turn, meant that if I reciprocated mine in reading it, I wasn’t alone.

Because this, in the end, is the real danger of A.I.: that it leave us increasingly alone, emitting increasingly impersonal communications read by no-one, all while gradually losing the ability to produce them, from the heart, ourselves.

***

PS: a few months after posting this, I started getting comments on the post that seemed a little off. I quickly realized that they were AI-generated, made to masquerade as real comments so that I would accept them. The point of these is to generate links to some other website, which increases search ranking, but that’s beside the point. The interesting thing here is how thoughtful the comments seem, how well they seem to understand what I’ve written. We’re fast approaching a world where the AI will generate the content, the AI will read the content and respond to it, and we humans won’t be needed at all. Here’s one of the comments, which of course I didn’t publish as actual comments on this post:

I love how you flipped the sunglasses joke on its head—it perfectly captures how performative gestures can flip meaning entirely depending on context. The parallel to AI-written emails is sharp too; there’s something genuinely lost when a polished message no longer signals that someone actually cared enough to sit down and think through what they wanted to say. It makes me wonder if we’re heading toward a world where typos and rough drafts become the new markers of authenticity.

And another:

The jazz sunglasses analogy is perfect—I’ve been getting emails lately that are so flawlessly structured they feel hollow, like the writer outsourced the human touch. It’s strange to miss the occasional typo that used to signal someone actually cared enough to send it themselves.

And another (the irony of an AI pointing out the laziness of “letting an AI draft” a message for you isn’t lost on me):

This is a sharp observation about how AI is flipping the social signals around communication quality. The sunglasses joke perfectly captures that ironic reversal—what used to signal dedication (a carefully proofread email) now risks signaling laziness (letting an AI draft it for you). I wonder if we’ll eventually develop new norms that distinguish between thoughtful human writing and AI-assisted text, or if the distinction will just fade into irrelevance as AI becomes ubiquitous.

And yet another (I’m getting more and more of these):

That jazz analogy is perfect—it really captures how the same surface-level behavior can mean the opposite depending on context. I love the point about well-written notes feeling like a “gift” of care; now I find myself wondering if someone actually composed their message or just asked ChatGPT to clean it up, which oddly makes me trust *good* writing a little less.

The sad thing about these posts is that in a way, they are the dream comment: respectful, clearly cognizant of the intention of my writing, thoughtful. To realize they are a naked attempt to increase Google search rankings is to realize a particularly skilled conman is trying to do his number on me.

How to tell a story in music? How to improvise one? As a child, I loved to sit at the piano and improvise from nothing. I would start in one place, then follow my nose to the next, then again to the next, until an ending suggested itself. It was fun, but I always felt a little unsatisfied. I’d gone from A to B to C, yes, but how were those ideas connected? How did the ending relate to the beginning? When I watched a movie or read a novel, the story made sense. The action progressed from one moment to the next, but crucially, there was also an overarching unity to it all. The ending resolved tensions that emerged during the course of the story. The way it was told made me want to know what was going to happen next. It made me care. How could I create something similar in wordless music?

There’s an argument to be made that storytelling is what defines us as humans. We have a capacity to believe in shared fictions, like gods, institutions, and money, to such an extent that they become functionally real. Our societies, in many ways, are built on stories. As a result, people have gotten very good at telling them, and have long considered the elements that make them tick. It’s helpful, first of all, to have a central character to care about: a protagonist. Second, something interesting needs to happen to our protagonist; otherwise, why tell the story? In classical narrative structure, we first meet our hero at home, in a position of comfort and security; then, an event takes place that thrusts them into the unknown. At this moment, our natural response is to be concerned for their future. Will they make it back home? Will they be okay? A good story makes you wait for the answer, as our hero is faced with one obstacle after another on their homebound quest. Finally, like a rubber-band returning to its initial form after having been stretched, our hero returns to safety, transformed by the adventure they’ve taken.

In 2011, I recorded Goldberg Variations / Variations, in which I follow each of Bach’s variations with an improvised one of my own. In the Goldbergs, Bach uses the same harmonic structure — that of the opening and closing Aria — as the frame for every variation, similarly to how Jazz musicians improvise over the repeating chord structures of Jazz standards. Theme and variations form is an effective way to tell a story, but it’s one in which the map of the adventure is known in advance, a little like watching an alpinist repeatedly climb a mountain following a known route. Many aspects of their climb — their exact path, their speed, tools, and mood, as well as the weather — can vary widely from one time to the next, but the direction and destination of their journey is known. In the Goldbergs, it’s from the aggregate of thirty different voyages taken through the same terrain that the story emerges. As someone who always thought of himself as a Jazz musician, but who grew up playing Bach, it made sense to me to add improvisations, over the same chord structure, to the sequence. I didn’t worry too much about storytelling, because I was piggy-backing on Bach’s already riveting narrative. I was simply adding my own commentary to a preexisting journey. But as I began to tour this project around the world, the difficulties of Bach’s music made me realize that I needed to better understand how it functioned, and I dove into a renewed study of harmony and counterpoint that eventually led me back to the Inventions, which, like many pianists, I’d studied as a child.

Completed three centuries ago, in 1723, the Inventions are study pieces, intended, as Bach explains on the title page, to teach the student to “play two voices clearly” and “at the same time to obtain not only good ideas, but also to carry them out well”, as a “foretaste of composition”. Bach’s use of the word “invention” to name these pieces is interesting in and of itself. He meant it not in our modern understanding of the word, but as it is understood in rhetoric, where, coming from the Latin inventio, it refers to the subject matter of an argument, the idea that we wish to put forward. As Bach points out, finding an idea is only the first stage; the second, elaboratio, is knowing how to carry it out. And indeed, the Inventions show, exquisitely, how to elaborate simple ideas into complete compositions. But, to me, the analogy to rhetoric only goes so far. In each of the Inventions, we are first introduced to a musical idea, often a short melody, in a known place of comfort: the home key. We get to know it well enough, through repeated exposure, that we identify it as a central character: a protagonist. Then, suddenly, our theme is thrust into a new key, often the dominant or relative major, and I’m convinced that in that moment, we unconsciously ask ourselves whether it will ever make it back home. Like any good storyteller, Bach makes us wait for the answer, taking his theme on an arresting adventure to foreign lands as represented by a series of disparate but related keys, full of dramatic tension and release, before finally returning home. Each of the Inventions, I realized, is a brilliant miniature demonstration of classical narrative form in music, carried out in under two minutes. (The Invention in C minor, with its long canonic subject, is an outlier, but still fits the bill).

When I first noticed this analogy with storytelling, it felt like an epiphany, and it made me wonder if I could use these ideas improvisationally. Of course, I can come up with a musical theme to serve as a protagonist. And I can give this theme quirks — maybe a touch of dissonance, or an insolence in its rhythm — that give it character and make it more than two-dimensional. But it’s not quite as simple as coming up with a melody and sticking with it. One crucial aspect of a good story is believability. Even in a sci-fi film, we object strongly to plot holes. If our hero is faced with a challenge, it needs to make sense within the world in which the story unfolds. But what makes a musical adventure believable? What makes the difference between a development that we accept, and one that feels arbitrary? I’ve found it useful to think of this through the lens of landscape. As we’ve discussed, in the Inventions, our hero’s journey is primarily harmonic. There is a constellation of keys around the home key, each with its own flavor, and our hero is free, through modulation, to visit these and the chords they contain. But these keys aren’t random. They’re related to the home key. They’re places that our protagonist can see, as it were, from where they’re standing. The keys are part of the existing landscape. And when we move to one of them, it doesn’t feel random or like a special effect; it feels real.

In Jazz, we spend our lives perfecting the art of improvising ideas within a given harmonic framework. We practice moving around within a pre-existing landscape, be it that of All the Things You Are or Giant Steps, and exploring its nooks and crannies. What I wanted to do now was improvise the landscape itself, and I didn’t find it easy. Given a certain starting point, say the key of Eb minor, I had to be able to see the geography around it clearly and quickly, and to be able to skillfully move the action to different places within it at will, without losing sight of my protagonist or the emotional charge of the story as it developed. And it’s not only the landscape, but also the arrows that point at destinations within it — what music theory calls secondary dominants — that needed to feel like second nature to me. No-one had ever told me to work on this before. It took me years of practice, a slow but persistent rewiring of my brain, to start to feel comfortable improvising in this way. And then, one day, it was suddenly… exhilaratingly fun. I found myself in a playground with infinite choices, but where every choice made sense. Harmonic destinations, when finally arrived at after being circled around through the same modulatory principles Bach used, felt deliciously gratifying, because they were earned and called for. Individual notes had more substance than in any free improvisation I’d done before, because they belonged to something larger. Rather than standing for themselves, they pointed at the mechanisms below. While my free improvisations used to be primarily concerned with the surface of the music, I now focused my attention on what was taking place underground, and the surface seemed to take care of itself. I was creating the fishbowl, and the fish seemed to show up spontaneously. I loved it.

It was unclear to me, at first, how to present this approach. During the Covid pandemic, I regularly asked the audience during livestream performances for melodies, keys, and time signatures, which I would use to improvise musical narratives in much the same way that a spontaneous storyteller might ask their audience for a character and setting with which to make up a fable. But I wanted to integrate these improvisations with the Inventions that inspired them. And it struck me that Bach had left open a window. Even though there are twenty-four possible major and minor keys, he wrote only fifteen Inventions. For pedagogical reasons, he focused on the most commonly used keys, leaving the more exotic ones to his Well-Tempered Clavier, which, composed around the same time, covers the keys exhaustively. 

So I landed on the structure you find in this recording, where I perform the Inventions as Bach wrote them, and, for the nine missing keys, improvise my own inventions. Not in Bach’s style, of course, but in my own voice. I close my eyes, listen inside for a fragment of melody, then take the melody on an adventure, trying hard to stay true both to the principles we’ve discussed here and to the intuition of my heart. Unlike my improvised variations in Goldberg Variations / Variations, each of which was a direct reaction to the movement that preceded it, my improvisations here stand on their own. They don’t react directly to Bach’s miniatures; instead, they react to the abstract and general structural concept that supports them. 

It’s worth remembering that Bach was most known in his lifetime as an improviser. People travelled long distances, often by foot, to hear him extemporize at the organ or harpsichord. Despite the perfect compositions he left behind, in which it’s difficult to imagine changing a single note, improvisation was at the core of his being. And I hope, three hundred years after he composed these pieces for his children and students, that Bach wouldn’t be too offended by a modern improviser making up some new musical stories in the windows he left open.

—Dan Tepfer, Brooklyn, December 2022

Introduction to the print edition

What follows is the entirety of Bach’s Goldberg Variations, published in 1741 under the title Aria mit verschiedenen Veränderungen, but with a transformation: every note of the original text has been chromatically inverted about the E/F axis. In addition, the ornaments that appear in the original as symbols have been written out. 

What does this mean? Inversion is an age-old musical process in which musical material is turned upside-down, similarly to the reflected text on the title page of this edition. It does not mean that the music is played backwards, which is a different process called retrograde. With inversion, the arrow of time still points forward, but any motion upwards is reflected to a motion downwards, and vice-versa. 

Diatonic inversion

There are two ways of inverting: diatonically and chromatically. In diatonic inversion, the transformation occurs within the frame of a key or scale. We find this type of inversion throughout the original text of the Goldberg Variations. For example, Variations 12 and 15, titled Canon at the Fourth and Canon at the Fifth respectively, are in fact inverted canons. In these two outliers among the nine canons of the Goldbergs, the melody of the initial voice gets inverted diatonically before its repetition in the second voice. In Variation 12, the axis of inversion is between the E and F at the bottom of the treble staff, causing the G at the bottom of the staff to invert to the D a fourth below:

In Variation 15, the axis of inversion is between the Bb and B in the middle of the treble staff:

In both these canons, only the G at the bottom of the treble staff — and no other note — generates a response the appropriate distance away (a fourth in Variation 12, a fifth in 15), which makes one wonder whether the titles of these variations are entirely earned. But it’s not only in these two movements that we encounter inversion. It’s ubiquitous in the work, albeit in a less systematic way. In Variation 26, for example, the 16^th-note runs that begin the first and second halves of the movement are mirror-images of each other:

And in variation 27, to choose just one more example among many, the opening canonic voice reappears in inverted form at the beginning of the variation’s second half:

Chromatic inversion

With diatonic inversion, intervals invert to the same interval, but the quality of that interval is allowed to change to fit the local tonality. A major third, for example, may invert to a minor third; a minor second to a major second, as can be seen in the examples above. In contrast, the process of chromatic inversion preserves every interval completely, all the way down to its quality: a minor second always inverts to a minor second, a major third to a major third, a perfect fourth to a perfect fourth, and so on. 

Chromatic inversion operates outside of the confines of tonality; it’s a strict mirroring process with no adjustment for musical context. As we’ll see, there’s no way to preserve the key quality. However, if we choose our axis of inversion carefully, it is possible to retain our tonal center. The Goldberg Variations are in G Major, except for Variations 15, 21 and 25, which are in g minor. Let’s consider our tonic chord, G Major. If we choose to invert chromatically around the Bb/B axis, at the exact midpoint between G and D, then G inverts to D, B to Bb, and D to G. Our G Major triad inverts to g minor:

This isn’t just true for the tonic triad, however. It’s true for the entire key, as can be seen by inverting the G Major scale:

As a result, all twenty-seven variations originally in G major end up in g minor when inverted:

The Goldberg bass line

The Goldberg Variations are built on the bass line and harmonic form of the opening Aria, which itself is an expansion to 32 bars of an eight-bar bass line used by Handel for a set of 64 variations he published in 1733. Bach took Handel’s short phrase and added three repetitions of it, modifying it as he went to move through the related keys of D Major, the dominant, and e minor, the relative minor, before returning to the tonic:

Let’s look at what this becomes when inverted:

The original bass line now finds itself in the treble, supporting the work from above rather than from below. The three modulations structuring each variation’s harmonic form become modulations to the minor subdominant (c minor), then to the relative Major (Bb Major), and finally back to the tonic (g minor). More generally, the inversion process turns perfect cadences into plagal ones, and vice versa. The entire flavor of the work is transformed, even as we maintain every detail of its internal structure.

From minor to Major

So far, I’ve shown the inversion process going one way, from Major to minor. But the same transformation applies in reverse, of course. Hence, if the major-key variations end up in the parallel minor, the three minor ones are recast to Major. But it’s a very complex type of Major, one with much more chromaticism than we’re used to. Indeed, when Bach and his contemporaries thought of minor keys, they considered both the ascending and descending melodic minor modes to simultaneously belong to the key. This results in the highly chromatic composite mode that gives Bach’s minor-key music its darkness and complexity:

When we invert this mode, we get a version of G Major with maximal chromaticism in the upper portion of the mode:

This chromatic mode forms the backbone of Variations 15, 21, and 25, the only movements to find themselves in the major key when inverted. On the other hand, the remaining major-key variations, originally in G Major and inverted to g minor in this edition, find themselves in a much simpler flavor of minor than we’re accustomed to from Bach, with just seven diatonic notes, the notes of G aeolian, and much less chromaticism. There is a joyful lightness to them as a result.

Axes and tessitura

We’ve shown that by inverting chromatically about the Bb/B axis, we maintain our key center of G, although we change its quality. But the same is true if we choose the E/F axis, a tritone away from Bb/B, the only difference being one of register:

This is the axis that I have chosen for this edition, for the simple reason that it’s close to the middle of the keyboard, producing an inversion that maintains most of the tessitura of the original, all while preserving its key center.

One final note on inversion: Bach very often ends his pieces with both the soprano and bass voices on the tonic, which gives a satisfying sense of finality. As we’ve noted, however, in the key of G, the tonic G inverts to the dominant D. Moreover, with inversion, the treble ends up in the bass, and vice versa. So, this final G of the original text, in the soprano voice, becomes a D in the bass voice when inverted. This gives many of the endings here the feeling of asking a question rather than of answering one. One exception is the close of Variation 15, where in the original, the soprano line ends on a high D, with an implication of unfinished business. In the inversion, instead, this high D becomes a low G that gives Variation 15 a rare sense of conclusion, right at the halfway mark of the work.

Ornamentation

And what about ornaments? They’re essential to baroque music, and we find them throughout the Goldberg Variations. To be true to Bach’s careful use of ornaments, which goes beyond mere decoration and often takes on a functional role, it’s essential to invert them along with the rest of the music. To help with this somewhat challenging task, this edition features a written-out realization of the ornaments. A companion edition features the text with the original ornament symbols instead, along with an explanation for how they should be performed.

Counterpoint

What happens to counterpoint when you turn it upside down? Counterpoint is the art of balancing the horizontal with the vertical. The horizontal, in this image, is the movement of notes through time; the vertical refers to the harmonic relationships between notes that sound at the same time. In other words, it’s the art of writing melodies that stand on their own while also functioning well together. In the centuries leading up to Bach’s time, counterpoint became a science, with a system of rules that classified which intervals between notes were desirable (consonances), which weren’t (dissonances), and how one could move elegantly between them. 

An essential aspect of counterpoint, from a vertical standpoint, is that it’s primarily concerned with intervals. As we’ve noted, the process of chromatic inversion preserves intervals exactly. Hence, if the rules of counterpoint have deemed a certain passage acceptable, then it should find its chromatic inversion acceptable as well. There is one exception to this, which is that suspensions — notes carried over from a previous consonance which become dissonances when the surrounding notes change — are traditionally only allowed to resolve downwards by step, a kind of acknowledgement of gravity. In the inversion, they resolve upwards instead, in an escape from that downwards pull. 

As for the horizontal, consider that it is generally true that a strong melody remains strong when inverted, even though it may be unrecognizable to most ears, and we begin to understand why Bach’s music sounds so surprisingly good when turned on its head: its underpinnings — the forces that make it tick — are impervious to inversion. 

Perspective

Why do this at all? Aside from how strangely wonderful it sounds, I believe that hearing this music upside-down reveals something profound about the work. For one thing, it allows us to hear it as if for the first time, a gift when you consider how many times an average music lover has heard the Goldbergs. It’s important to remember that we really are hearing the original work here, in the same way that we are still seeing an original Da Vinci or Picasso if we hang it upside down. It’s only our vantage point that’s changed. It’s easy, for example, to become somewhat blasé regarding the chromaticism of Variation 25 when you’ve heard it many times. But play or listen to it upside down, and you’ll be reminded that this is music that stretches the limits of dissonance in tonality like little else. 

Hearing the music this way also allows us to attend to aspects of the music that may have remained hidden to us until now. Bass lines, for example, have a tendency to play a supporting role in our ears. When inverted, they become the main event, the high voice, and as we instinctively bring our attention to them, we are reminded of how much care Bach put into every single one of his melodies, whether hidden or exposed. This is an essential factor in the success of these upside-down Goldbergs: Bach creates all voices equal, with an exceptional symmetry and balance that is undisturbed by inversion. More broadly speaking, it’s a testament to the soundness of his underlying compositional structures that they can withstand this kind of transformation so well. 

When I play the music in these pages, it’s striking to me how simultaneously familiar and foreign it sounds. There’s no doubt that it’s Bach we’re hearing, but it’s as if he’d been born not on Earth, but on another planet. Mars, perhaps.

Dan Tepfer, December 2021, Brooklyn, NY

It all started on April 16th. In the afternoon, I biked to pianist Simone Dinnerstein’s house, in Park Slope, to play some of Bach’s Goldberg Variations for her. She generously shared her insights into the piece, and I came away feeling inspired. It was a gorgeous day. I took the most direct route home afterwards, through Prospect Park, on my bike. In the middle of the park, there’s a narrow, paved trail that cuts through the woods and connects the western and eastern sides. It rises from the Park Slope side, and then plunges steeply down to the Flatbush side. 

As I reached the top of the ridge, right before the descent, I spotted a small animal by the side of the trail. I was biking slowly, and the strange thing was that as I approached, the animal — a squirrel, I could see now — didn’t run away. It almost seemed to come towards me. I put my bike down. As I approached on foot, it looked up at me and took a shy step in my direction. I couldn’t believe it. I slowly put my hand down to touch it, and it didn’t budge, instead looking up at me with huge eyes, eyes that belonged to a very young squirrel. 

Not a baby, but an adolescent, perhaps. It wasn’t long before I picked him up. At that point, other passers-by were watching too. This little guy was disarmingly cute. He quickly found his way inside my loose-fitting sweater and wouldn’t come back out. It dawned on me that he might have been cold. I noticed after a few minutes that his muzzle was covered in something that looked like dried mud. Other than that, he seemed in good health. After a while, my friend Ruben called me on my cell phone. I told him what was going on and he asked “well, have you named him yet?” “No, I just found him five minutes ago!” I replied. “Well I think you should give him a nice Jewish name,” he said. Inspiration struck: “How about Ruben?” 

My newly-christened Ruben was becoming increasingly friendly, but I couldn’t keep him, obviously, and the sun was starting to get low. So I put him down. Only thing was, he wouldn’t leave. He came right back to my feet, put his paws on my shoes, and looked up imploringly. I started to wonder what I had gotten myself into. Clearly this was a young squirrel that had somehow lost its mother, and it had imprinted on me as a possible new protector. But I’m a touring musician! The last thing I can do is keep a squirrel. I called an animal rescue center in Brooklyn — it was right before 7pm. The guy on the other end said “put him back. He’s what we call a dumb baby: he hasn’t learned to be afraid of humans yet.” So I put him back again. But he kept coming back. 

The fact that he was utterly irresistible didn’t make this any easier. Other people came and went, giving their little pieces of advice: “if I were you I’d keep away from that animal — you never know what diseases it might be carrying”. A quick search on my phone gave the official word back: small rodents, in the United States, are not considered a rabies risk. One couple came by and the husband said he’d grown up on a farm and had had abandoned squirrel babies come up to him a number of times, but his dad usually forbade him to keep them. He had raised one or two, though, feeding them milk and — he said — cat food. The only essential thing, he said, was to keep the animal hydrated. Make sure it drinks, and it’ll live.

Again I tried to put Ruben back. This time, he climbed about 4 feet up the closest tree, but just as I thought our story might be ending, he turned around and ran right back to my feet. Again the imploring eyes; I picked him back up. I was alone and in a true quandary: I definitely, no way, could have a pet squirrel. I was a fiercely independent guy. I did manage to water my plants, and I did manage to keep the humidifier in my piano full most of the time, but other than that I had very few real responsibilities outside of my music. And I liked it that way. But this little guy just wouldn’t leave me alone, and the more time I spent with him — perhaps 45 minutes at this point —, the more I liked him. 

Just as I was standing there with Ruben in my arms, a woman about my age appeared. She was in running gear, staring up at a branch hanging in mid-air, suspended by some kind of string attached to a tree above. Some unknown sequence of events, perhaps involving a helium balloon, had led to this. I asked her if she knew anything about squirrels, which must have come across as an odd pick-up line, until she saw that I was actually holding a squirrel in my arms. No, she said. But her curiosity was piqued and she loved holding him. We started talking. After a while I asked her what she did for a job. “I’m an actress, she said, and I teach French”. “Ah, tu parles français?”, I asked. Her English had been totally unaccented till then.

She answered in perfect French, only one of perhaps five people I’ve met in my life who speaks unaccented English and French. It turned out that she had grown up in Paris, not too far from where I grew up, on the eastern side. Her dad was American, her mom French. And then there was this: we had both gone to the same high school, a big one on the eastern edge of Paris called Hélène Boucher, and — we disbelievingly realized — had actually overlapped there by one whole year. Her name was Justine.

This was just too much. Too many unlikely events for one day. It was dark by now. I needed to put Ruben back. So I climbed over the fence separating the trail from the woods, walked ten feet in, and put him down. I walked back to the trail. Ten seconds later he was at my feet again. “You’re going to have to take him home, you know”, said Justine. Let’s make sure he doesn’t want to stay here, I said. I climbed back over the fence, Justine handed Ruben to me, and I walked a good fifty feet into the woods. I walked back, fast, to the trail. But something made me want to make sure that he was going to be all right. If his mother had abandoned him, after all, if he had fallen out of his nest onto his nose (which would possibly explain the caked mud covering his muzzle), he might not make it alone. Justine and I waited for about a minute, and sure enough, there he was again. He had followed me back. 

“How about we have a drink while I decide what to do with this guy?” We walked to the east side of the park, to my neighborhood, Lefferts Gardens, and walked into Lincoln Park Tavern, with Ruben hidden under my sweater. As we sat down, I took him out and held him in my hands. He was incredibly docile. Truth is, he seemed exhausted. A waitress came over, saw the little animal and got the manager, who promptly shoed us out of the restaurant, explaining that the whole place could be shut down if a rodent were found inside. But she wouldn’t let us leave without having us take a picture of her with Ruben. Turns out she’d wanted to hold a squirrel in her hands since she was a little girl.

The only other option was my apartment. We stopped at the local bodega on the way and I bought an eye dropper and some cat food. At my place, I found a cardboard box full of packing paper and put him in there. Then I emptied the eye dropper, washed it out and filled it with water. Ruben was hesitant at first, but he drank, at least a little. He curled up into a ball and fell asleep. Over tea, Justine told me about her parents, both painters, now divorced with her dad in New York, her mom still in Paris, and she showed me their work online. Both heavyweights. Her younger brother, too, in art school in Chicago and doing some really compelling work. Some of his hand-drawn images looked algorithmic and reminded me of some of the math-based line-drawings I’d made with code.

Before long, it was time for Justine to leave. I walked her back through the park and brought Ruben with me. She said I had to keep him for at least one night. How many people get to say they brought a squirrel home? But I wanted to try putting him back one more time. I figured that if he scampered off, it meant that he knew he’d survive the night. Perhaps all he’d needed was a little warmth, and he was now okay. I walked Justine to the west side, and on my way back, tried to set Ruben free again, an act that felt like a well-rehearsed routine at this point. He wouldn’t have it. I brought him home again. 

I put him in the cardboard box, full of paper that he could burrow into, and put the box in the bathtub. Next to it, I put water, cat food, and peanuts. The next morning he seemed to be okay, although he hadn’t eaten any of the things I had left for him. I gave him more water from the eye dropper, then tried to feed him some cow milk I had in the refrigerator, but he was completely uninterested. I left him with some cut-up vegetables and went into Manhattan to take a lesson with Sophia Rosoff, my 92-year-old piano teacher. A couple of days prior, Lee Konitz, the great saxophonist I regularly played with, had expressed an interest in meeting her, and I had arranged a group lesson. It had been a long time since Lee, 85 years old, had been given advice by someone older than him, but he took it gracefully. It was fun. I balanced an egg on its end, something Sophia often had her students do to get them focused and, like the egg, balanced. 

On the way back I stopped at a pet store and bought Esbilac, special milk formula for puppies that the squirrel websites (of which there are many) had informed me would be good for Ruben, as well as a tiny milk bottle to feed him with, and a mix of nuts and other things especially made for small rodents. When I got back, Ruben drank the milk, which I had warmed-up first, like it was the best thing he’d ever come across. The contrast between his dislike for cow milk and his love for the Esbilac was dramatic. He knew what was good for him. 

In the following days, he kept drinking milk voraciously, and he also started eating the nut and dried fruit mix that I bought. Friends came by and invariably fell in love with him. Even my friend Mathilde, with her life-long phobia of animals brought on by a childhood dog attack, loved him from afar. She even began to carefully pet him after a while, a major breakthrough for her. Over the course of two days, the caked mud, or whatever it was, that had covered his muzzle when I found him, gradually came off. When I first found him, there had been so much that he couldn’t breathe through his nose and kept sneezing when he drank; then his nostrils cleared, and then big chunks of the gunk started coming off. I had tried cleaning it off myself before, but it was solidly attached, almost like a scab. Sometimes it’s best to let time do the work for you. 

On April 18th and 19th, I traveled to Boston with Ben Wendel for a duo gig. My friend Y-Lan, who I learned had loved squirrels since she was a child and had always longed to hold and play with one, came over regularly to feed him milk. She figured out that he liked licking the milk out of her hand even more than drinking it from the bottle. The feeling of his tongue against one’s skin was particularly lovely. 

As this little fairy tale was unfolding in my Brooklyn apartment, Boston was in a state of emergency — the marathon there had been attacked in the most vicious of ways, with two pressure cooker bombs right at the finish line, on Monday, the day before I found Ruben. Ben and I had considered cancelling our gig, but decided that playing music in the city, as well as we could, would be the most meaningful way for us to help. I tried to say a few words about that during the concert: in many ways, it wasn’t the casualties that were most appalling in the attack (three people died, a hundred were injured; small numbers compared to the number of people killed, for example, in car accidents every year) but rather the sheer evil of it: it was so hard to imagine why anyone would want to hurt people at something as peaceful as a foot race. It just seemed so gratuitous. And for it to follow, only a few months later and not so far away, the murders of twenty children by a lone gunman at Sandy Hook Elementary School, including the six-year-old daughter of jazz saxophonist Jimmy Greene, whom I’d played with not so long before… It was horrifying. Even though it was only a few people who were committing these crimes, it tested your faith in humanity. 

While Ben and I were playing that night, at a venue I often played when I lived in Boston called the Lily Pad, gun shots were fired on the MIT campus, only a few blocks away. We learned about this right after the gig, virtually as the audience was applauding. A cop had been murdered, one of the two young brothers who were the suspects in the bombing had been shot, and the other, all of nineteen years old, was on the run. After the gig, we moved to an Irish pub next door; an amazingly good traditional Irish band was playing, and after a while a young woman got up on a table and danced, quite beautifully. The strange thing was witnessing this intersection of art and violence: we all knew what was going on outside — perhaps the closest thing I’ve experienced to a war zone in my absurdly sheltered life — yet here we were, making music, listening to music, dancing. It gave me a hint of an inkling of a glimpse of what it might have been like to be living in London during the Second World War: people going about their daily business, still making music and dancing, as bombs rained down at regular intervals from German warplanes overhead. Not to speak of the too-many warzones still active around the world today. I suddenly realized, in a visceral way that put any intellectual understanding to shame, how much we in the rich West take our safety for granted. We feel entitled to be able to live our lives without constant threats of violence, but we entirely forget how much of a historical anomaly our extended period of peace — 75 years without war in Western Europe — has been. Four years earlier, I had played a series of solo concerts through the Republic of Georgia, including a gig — to which we had to be escorted by armored UN convoy — in Abkhazia, the separatist region in the Northwest of the country. Five short months after I’d been there, the whole country was at war again, Russia sending troops in to fuel the separatist flames. This peace we know isn’t normal, I realized; it’s a luxury. Above all, we’ve just been lucky.

Ben and I took a cab back to the house where we were staying; the city was eerily quiet. Sirens were blaring and we passed a gas station that had been entirely cordoned off with Do-Not-Cross police tape, on Memorial Drive. It turned out later that the police had surrounded an innocent man there.

Meanwhile, Ruben was safe and sound at home in Brooklyn, playing with friends and putting on weight. I stayed up late into the night checking the news; periodically, my friend Y-Lan, who had been watching over Ruben and is a fellow night-owl, would send me pictures and videos of him. I started to feel a new emotion: I realized that I cared about Ruben, I cared about his well-being in a way that went beyond the mere practicality of whether he would live or not, the mere sense of responsibility for another being: there was something fatherly at play, there was love. This took me completely by surprise. It felt like an important moment of self-discovery, one of those moments when we uncover something in ourselves that we didn’t know was there before. 

How often do those moments of introspection happen, nowadays? I’d recently returned from studying bata drums in Cuba, where internet access was scarce and my cell phone didn’t work. I remembered the static gradually leaving my mind as time wore on. The endless noise surrounding us in our normal lives, I realized, the myriad voices competing for our attention, kept us from finding the quiet within that was so important to actual self-discovery, in Art or otherwise. As human beings, or as animals for that matter, it was only natural that we be addicted to newness: things that are new could be essential to our survival, so if a noise came up behind us, or a friend shared a piece of information, it made sense that we would have evolved to pay attention. But the internet uses our tendency to attribute value to mere newness to trick us into paying attention to things that have no value at all. And as a result, by the time an inner epiphany might start to suggest itself, we’re unable to notice, because our hunger for discovery, by that point, has been used up. Somehow the arrival of Ruben in my life was centering, making me focus on more important things like the value of life, instead of my Twitter feed. 

The next morning, Boston was on lockdown, all mass transit cancelled. Ben and I got lucky, though: a friend drove us in his car to Providence, and we took a bus from there to New Haven, where we were scheduled to play at the concert space Firehouse 12. Leaving Boston was very strange. The police had told everyone to stay indoors, away from the windows. I’d never seen a city so quiet during daytime in my entire life, and wouldn’t again until the Covid-19 epidemic eight years later. That evening, as we were playing in New Haven, the second suspect was apprehended, lying near death under a tarp in a small boat in someone’s back yard in Watertown. 

Over the following days, Ruben kept growing at a surprising rate. He loved being in his cardboard box, and spent an amazing amount of time sleeping. But when I woke him, he was as playful as before, only with more and more energy. He started jumping, like squirrels do. I noticed how big his paws were. He could scamper up and down my whole body as if it were a tree, and as long as I had a T-shirt and jeans on, it didn’t hurt, his claws sharp and delicate at the same time, only digging in as much as they needed to support his light body.

He was mesmerized by music. I had friends come over a number of times to listen to musical works in progress, and as soon as the music started, he would almost freeze in place, fascinated. I grew up with chinchillas, and I remembered that they reacted to music in a similar way. He once hid inside my piano as I practiced.

About a week after I found him, Ruben started getting less interested in milk. He was getting weaned. He liked nuts more and more and I loved watching him snatch one from my fingers: as soon as he grabbed it, the nut would monopolize his entire attention, the rest of the world falling away.

He was becoming increasingly squirrelly, nervous and energetic. It didn’t bother me — in fact I enjoyed seeing him grow into an independently-minded adult, and he never put up a fight when I tried to pick him up — but it made my friend Y-Lan a little sad. I had a gig in Washington, DC on April 24^th with Allison Miller and Shane Endsley, and she volunteered to take care of him again. He had really changed from a week before, when he was as docile as could be, happily sleeping on her shoulder, his head hidden in her long dark hair, the tip of his nose peeking out. Now he was in constant movement, hard to pin down. One day I was walking in the park and saw an adult squirrel jump gracefully from a tree to another, tail perfectly counterbalancing his body, and I remembered where Ruben was meant to be. Squirrels make notoriously poor pets: they need space and become increasingly high-strung as they get older. They’re known to bite, hard. Ruben only nipped our fingers in a friendly way, never coming close to drawing blood, but I started to think about reintroduction. 

According to my internet rodent sources, rescued squirrels do a great job of readapting to life in the wild (or in a park) if they’re released right as they’re reaching adulthood. This is the moment when a squirrel starts to curve its tail up above its body, in that classic squirrel pose, instead of letting it hang limply behind as they do when they’re young.

As April drew to a close, I was scheduled to leave for Japan for a tour with Lee Konitz, and I started to wonder what I should do with Ruben. Right at this moment he started picking his tail up, and although he behaved as fondly towards me as ever, never leaving my body voluntarily once I picked him up, he was increasingly skittish with everyone else. It was time. My only concern was that he would refuse to return, as he had done when I had first met him in the park. 

The day before I was scheduled to leave for Japan, I walked through Prospect Park with Ruben tucked into my loose cardigan and a handful of nuts in my pocket. He showed absolutely no interest in leaving. He seemed to prefer, of all available options — including total freedom, which he could have chosen at any time —, the comfort of my warm body. The thought of leaving him forcefully, of running away, broke my heart. I hedged my bets: I called two old friends who had been coincidentally harboring a very young squirrel of their own — I had learned this online — and we arranged to meet the following morning in Prospect Park at the very place where I had initially found Ruben. If he still refused to leave, they would take him home and care for him while I was away. And if all went well and he returned home willingly, the experience would be a welcome preview, for my friends, of what was to come for them.

So it’s the morning of my flight to Japan. It’s bright, warm and clear, and Ruben is hiding underneath my T-shirt. I’m repeatedly trying, through laughter brought on by the tickle of his paws against my skin, to get him out and onto my hand. After what seems like a while, as my friends stand patiently watching, I finally coax him into sitting, upright, in the palm of my hand, and bring him slowly up against the very tree that he had momentarily climbed two weeks earlier before he had run back to me. Something’s changed. He’s intrigued — the situation seems to resonate with him in a way that the previous day’s walk hadn’t. He sniffs at the bark of the tree, and then nibbles at it. He cautiously puts a front paw against the bark, then two, then a hind paw. It looks unmistakably like a moment of recognition. I slowly pull my hand away, and suddenly off he goes, straight up the vertical wall of his natural habitat, in what can only be described as a joyously wiry scamper. 

And then he stops, and I’m concerned that he’ll change his mind. But it’s only to look back at me, to say goodbye — or so, at least, it feels. He stops for a few moments, looks back, then moves a few more paces up before stopping to look again. It’s me he’s staring at, not the ground, nor my friends, nor the next tree over. He does this three more times before vanishing for good into the spring foliage. It’s a beautiful day, and Ruben, this spark of life small enough to hold in your hand, who may never know anything outside of my apartment and Prospect Park even as I fly off to Tokyo, is back home. 

Thanks to JazzTimes for inviting me to write this memoriam. It appeared in their March 2021 issue commemorating lives lost to the pandemic. The photographs are by Josh Goleman, originally taken for our 2018 duo album on Verve, “Decade”.

As someone who likes to think of himself as rational, I can’t bring myself to believe in fate, yet Lee and I seemed destined to meet. Although piano’s been my instrument since I was a child, I had a sax in my teens, and I sound strangely like Lee on home recordings from the time even though I’d hardly listened to him. After I moved to New York in 2006, I put on my mentor Martial Solal’s duo record with Lee one day, Star Eyes, and, moved by a conviction I’ve seldom had before or since — that if I got to play with Lee, I would know what to do — I asked Martial if he would introduce us. Martial gave me his blessing, I went to Lee’s apartment on the Upper West Side, we hit it off immediately on both a personal and musical level, and thus began fourteen years of close friendship and collaboration.

Lee certainly changed my life, but he touched countless others as well during his 92 years on this planet. He influenced the direction of jazz, establishing early on an alternative to Charlie Parker’s brilliant path, even though Lee would be the first to mention that Parker was one of his greatest influences, along with Lester Young and his mentor Lennie Tristano. He studied and learned Parker’s solos, but, when asked how we was able to avoid imitating him and be so singularly himself, even as a 20-year-old in Claude Thornhill’s band, he would jokingly explain that he did in fact try to sound like Bird, but it was too hard.

There may be some truth to this, to the extent that Lee’s shy and sensitive personality was somewhat at odds with the exuberant fire of early bebop. But it obscures a deeper difference of philosophy, which is that Lee, for reasons that remained opaque even to him beyond a deep-seated natural inclination, valued spontaneity at all costs. It’s easy to underestimate how radical his position on this point was: to him, nothing was more important than finding the truth of the moment, and this meant that you couldn’t rely on pre-prepared licks or arrangements. As he travelled the world playing with long-term collaborators or pickup bands (he never hustled for gigs, so he accepted most that came his way), he liked to start from the quasi-blank slate that overplayed standards offered, so that he could jump straight into open-ended exploration. In the 144 or so public concerts I played with Lee all around the world, I must have played All The Things You Are at least that many times with him, but he never played it once the same, and he brought that same spirit of discovery to the free improvisations we recorded on our duo albums. He spoke in straight-forward, unpretentious terms even about profound matters, but he was well-read, and would sometimes quote Heraclitus: “Everything flows… When I step into the river the second time, neither I nor the river are the same.”

Lee’s devotion to personal truth was matched by a tremendous courage. He was unafraid of looking silly, and didn’t hide his vulnerability. Once, with the Thornhill band, he stood up to play a 32-bar solo, and, following his motto “listen is an anagram of silent”, he began by listening intently to the rhythm section to find the right moment to enter. But the rhythm section sounded so good that he didn’t feel the need to contribute anything, and at the end of his 32-bars, he simply sat down again, not having played a note.

Lee’s love of spontaneity manifested in his fondness for animals and little children, who always speak their truth. He would unabashedly greet both on the street, occasionally to the consternation of their minders. But he took music extraordinarily seriously and recognized that it was not enough to be spontaneous; one also had to learn to express oneself with clarity and meaning. “To really improvise, one must be prepared to be unprepared”, he would say. “And that takes a lot of preparation!” His life centered around the search for meaning, and he tried to only make a sound when he had something meaningful to express. In turn, he was an extraordinary listener, constantly searching for meaning in everything he heard from others. Asked if he believed in heaven, Lee said: “Heaven is here, there, anywhere that we can communicate”.

Lee received recognition throughout his career — he was named an NEA Jazz Master in the U.S., a Knight of the Order of Arts and Letters in France and had a street named after him in Italy — but he maintained a disarming humility to the end, never resting on his laurels. He appeared on over three hundred recordings and was loved and respected around the world, but there was never a feeling that he was “great” or that his next gig would be a knockout. Every moment had to be earned and fought for in the present, and failure was always on the table. Till the very end, he simply wanted to make music, and do so as truthfully as he could.

29.97 vs 30

For historical reasons (i.e. for reasons that probably could have been better dealt with at the time but were instead swept under the rug, having to do with the switch from B&W TV to color), for these purely historical reasons, in the parts of the world that use the NTSC standard, including North America, footage is recorded and played back (on TV at least) not at 30 frames per second (fps) but at an incredibly arcane 29.97 fps. This would be okay if that were always the case.

It’s not. For example, let’s say I filmed a concert at 29.97 fps but then create a Final Cut Pro project at 30 fps, because, believe it or not, lots of online footage is actually at 30 fps and not at 29.97 fps — perhaps because computer monitors actually refresh at 30 or 60 Hz, not at 29.97 or 59.94. I import my footage and place it in the timeline. Now, unbeknownst to me, Final Cut will actually play the whole thing imperceptibly faster than it happened in real life, including the audio, because the playback frame rate is now a smidgeon faster than the recorded frame rate.

If that were it — if we exported our project and uploaded now — all would be okay, no-one would ever notice, because the discrepancy is so small. But, say I also recorded the concert with external audio gear. I import the sound file and place it underneath the previously imported video. I try to sync it up with the existing audio. What I find now is that if I sync it in one spot, it will be out of sync in every other spot. It’s unusable. Why? Because Final Cut is actually playing this newly imported sound file back at the same speed as it was recorded, whereas it’s playing the video footage back slightly faster. This is an easily solvable problem — just make sure you start your FCP project at the correct frame rate. But it’s an example of the headaches this historical artifact can cause. I’ve done this by accident twice, and it took me a little while both times to figure out what was going on.

Much worse is what happened when I was making my Natural Machines album. I filmed it at 29.97 fps, only because my cameras can’t record at true 30 fps (note that they label this as 30 fps, not 29.97! You’re just supposed to know, it seems). While I improvised, programs I wrote on my computer answered me in real time, both by playing the Disklavier piano themselves, and by generating a visual representation of the music. I recorded the visual output by plugging an HDMI recorder into the output of my computer. But, lo and behold, when I tried to sync the footage of my live performance with the live visuals, they kept drifting out of sync. Lots of headaches later (I didn’t know anything about the NTSC / PAL wars at the time), I realized that my computer was outputting 30 fps footage over HDMI and not 29.97. Which makes sense, because again, computer monitors don’t refresh at 29.97 fps. They refresh at 30 fps or 60 fps (or higher) because, obviously, since alternating current oscillates at 60 Hz in North America, it would be INSANE for anything to oscillate at anything other than multiples of this number, right?

Now, you might think that I could just run my 30 fps footage through a converter to resample it to 29.97 fps. This is, in fact, possible, but it’s very slow and, more importantly, it looks terrible. And for good reason. With audio files, you’re dealing with tens of thousands of data points a second. Typical audio is recorded at 44.1, 48, 88.2 or 96 thousand data points per second. With that much density of data, it’s relatively straightforward to resample a file from 88.2 kHz, say, to 48 kHz (although there are subtleties to this, too, involving aliasing etc, but they won’t bite you nearly as hard as the video issues I’m talking about), because the data points can essentially be imagined to describe a continuous line, and you can choose how often you cut that line up into data points without affecting the continuous line too much.

But video happens incredibly slowly — over one thousand times more slowly, typically. Instead of 44,100 events per second, we’re dealing with 30. So there’s nothing continuous about it. Whereas the change in audio level from one data point to another at a normal sampling rate is minute, at 30 fps the change in the image from one frame to another can be huge. It simply can’t (without advanced A.I., that is, and that’s coming here) be imagined to be a continuous flow that you could choose to sample at whatever rate you wanted. Instead, resampling from 30 fps to 29.97 essentially involves removing frames here and there, or if you’re being sophisticated, blending two of them together now and then. The resulting jerks in the image are immediately discernible, and to me, really annoying.

The solution to this problem was to figure out (this was not easy and involved external software) how to get my computer to output 29.97 fps via HDMI rather than 30 fps. And just imagine! If the switch from B&W to color TV had been dealt with cleanly in North America when it happened, this absurd problem wouldn’t even exist in the first place!

Luminance ranging

Most video — and most computer graphics, too — is encoded with 8 bits per channel. What does this mean? Each pixel in a frame of video has a brightness value (its luminance) described by a number. The question is, in how much detail do you describe it? If you have 8 bits per channel, that means you have 256 different possible values for it. If you have 10 bits per channel, which is becoming common now in pro and even less-pro video, you have 1024 possible values. In theory, at least.

Because, as I’ve recently learned, for another seemingly insane historical reason (fight me on this), there is a convention in video that the bottom and top values not be used. So, instead of your values ranging from 0 to 255, with 0 as black and 255 as white, they’re supposed to range from only 16 to 235. What happens to the rest of those values? Anything below 16, as I understand it, is considered black, and anything above 235 is considered white. I can’t begin to imagine why anyone would want to throw away 14% of their dynamic range, but that’s that.

How has this affected me? Well, I film with Panasonic LUMIX GH4 cameras, which I love because they’re very cheap used (~$400) and make a beautiful 4K image. I bought them when I was making my Natural Machines album. The LUMIX gives you the option of recording your luminance values either as 0 – 255, 16 – 235, or 16 – 255. Being a reasonable man, I opted for 0 – 255, of course. Why would I throw away those extra bits?

Now, since I’ve been live streaming, I’ve noticed that the image I see on my computer, after it comes out of my cameras as HDMI, enters my Blackmagic ATEM Mini, and exits as USB, is noticeably higher in contrast than the image I see in my cameras’ viewfinders. This puzzled me until last night, when I dove down this rabbit hole and discovered that the ATEM Mini expects its video to be delivered as 16-235, which, I now understand, is the common video standard. So it’s natural that it was cutting off the bottom and top luminances of my image, making anything somber completely black, and anything light completely white. Again, why does this problem even exist in the first place? To an outsider, it’s patently absurd.

Lighting is everything

One joyous thing which I simply had no real appreciation of before, even though I’d heard it talked about, is that lighting is everything. Wow does lighting completely determine how your image looks! I know that sounds like a platitude, but it was very impressive to experience it first hand. I feel lucky that I was forced to deal with it: early in the pandemic, the Karajan Institute hired me to produce a 30-minute long video of myself performing my project Natural Machines for Austrian and German television. They partnered with Deutsche Telekom and a TV company to ensure the footage met professional TV standards. They asked me for some test footage before I filmed my set.

I got a call from a nice man named Daniel who told me “Dan, the sound you’re getting is top notch, the quality of the image is really nice too, we love your playing and the music, but… your lighting needs to be improved.” We talked about it for some time and he ultimately pointed me to a YouTube video which in turn pointed me to another, which I recommend to everyone: How To Make A $300 Camera Look Pro!

Follow these instructions and it will completely change how your video looks. For my first five or so livestreams after upgrading my lighting, I didn’t even have a real diffuser for my lights. I used a storage box that had a white, transparent bottom, and a vegetable bag. It still looked good.

Macs overheat

Streaming is really hard on computers. On Macs, at least. I stream with the free software OBS, and apparently, Apple has chosen not to participate in the project (read, I think: has chosen not to give the project money), and as a result, OBS for Mac doesn’t make efficient use of the hardware. So what happens? Macs get very, very hot when streaming, even new and powerful ones. At the beginning of the pandemic, this was okay because the weather was mild. But as summer rolled in, I started having strange episodes in my streams where my image would start to slide way behind my audio. Seconds behind. It took me a while to figure out that as my laptop got hot, the system throttled down the processes using the most energy to keep the processor from overheating, and as a result OBS could no longer encode the video fast enough. At one point, on a hunch inspired by the jet-engine-like sound my Mac’s fans were making, I ran to the fridge, grabbed a couple ice packs, and put them under the computer. Zap! The image snapped back into sync with the audio in about 5 seconds. I later learned that cooling a computer with ice is a very bad idea, because ice creates condensation, causing the air your computer cools itself with to be full of moisture, ultimately causing your computer’s components to corrode, rust, go bust, fall to ruin. The ultimate solution, which has worked well for me, was to buy a $35 cooling pad — essentially two big, quiet fans powered by USB — and set it under my laptop. I haven’t had a problem since, and these external fans are much quieter than the internal ones in my computer.

Logic is bad for live mixing

I’ve been happily using Apple’s Logic Pro for years to record, mix, and master. I’ve even made extended midi experiments with it. I’ve recorded all my albums myself since 2011, so I’ve put together some good gear over the years and have become fairly experienced with audio.

So, naturally, getting a good sound out of my piano was the easy part of figuring out how to livestream. I brought my mics (two DPA d:vote CORE 4099P mics which conveniently fit under the closed lid of my piano, keeping out street noise) into Logic via my Apogee Ensemble (the same one I used to record my last four albums) and some nice preamps, record-armed the tracks there, applied some plugins to mix the sound, and routed the mixed sound to OBS via an excellent little piece of software called Loopback Audio. This all worked great, except that sometimes, for completely inexplicable reasons, one of my mics would develop an echo. A very pronounced one, too, a with a delay of a couple seconds. A total dealbreaker. It tended to happen in my vocal mic, too, which made it even worse, because it meant people couldn’t understand what I was saying. Thank goodness for the feedback given by Facebook comments! People would let me know right away when it happened. I realized I could fix it during the stream by resetting the sample rate of the project, but even if I did that, it could reoccur again at any moment and was a constant source of worry, something I didn’t need more of.

So, what did I do? I switched from Logic to Reaper for my live mixing. Reaper is very cheap ($65, and you can just use it for free if you want), extremely streamlined (it weighs about 35 MB to Logic’s many GB), and has worked perfectly for me. I haven’t had one bad moment with it. It’s what they’d call robust. I’d recommend it for this purpose to anyone.

It’s really possible to play music over the internet, and it helps to have nice neighbors

One of the best things that’s happened to me during the pandemic is the discovery that playing with other musicians over the internet is, contrary to popular perception, totally possible, and in fact super fun! And I’m not talking about the kind of playing where you accept the huge (~1/2 sec) latency of Zoom or Skype or Facetime and make the best of it. I’m talking about ultra-low-latency, real playing together, in rhythm, as if you were in a recording studio together.

I won’t recount the details of my journey with the open-source software Jacktrip here, because NPR did an extraordinary job of telling the story and explaining the challenges involved, all narrated by the great Christian McBride:

One thing not in the video: after that initial test with Jorge Roeder, I quickly discovered that in order to do Jacktrip properly while livestreaming — i.e. doing a live performance over the internet and simultaneously broadcasting it to an audience — one needs two computers, and two independent internet connections. Fortunately, when I bought my new laptop last year, I kept my previous one, from 2015. I almost sold it and then reconsidered, on a hunch that it would be essential in the future. I realized that in order to get the very lowest latency possible on Jacktrip, it needs to be the only thing using your internet connection at that time. You certainly don’t want it to be in competition with, say, a program (like OBS) that’s constantly uploading large amounts of data to YouTube for your livestream. Jacktrip’s ability to send packets of information in the fastest possible amount of time is key to making these remote musical collaborations work.

So, what did I do? I borrowed my neighbor Carrie’s internet. She kindly agreed to let me string an ethernet cable from her apartment to mine, which has now been snaking along the side of our common hallway for months. And Jacktrip has worked like a charm. It’s taken time to get the most out of it, though. The trouble is that getting the lowest possible latency (which is important in order to play together in rhythm) is at odds with getting the best audio quality. I won’t go into the details, but if you’re going to start playing the packets of sound information you’ve received as soon as possible, there will probably be some, because of the vagaries of the internet, that won’t have arrived in time. And this causes glitches in the audio, very noticeable ones.

So, for a while, I was constantly trying to find the best compromise between latency and audio quality. Remember, I was livestreaming these remote collaborations, sometimes for paying customers (I’m now on my sixth ticketed livestream concert), so glitchy audio wouldn’t do!

I had an epiphany while setting up for a Jacktrip session with trombonist Ryan Keberle: I could have my cake and eat it too. I could set up not one, but two simultaneous connections with my duet partner. One would have the lowest latency possible, and have the massive audio glitches to show for it. I would play along with that one, sometimes having to reconstruct a note in my ear through the noise. The other would have high latency, and perfect audio, and that’s what I would send to the livestream audience, after delaying my own audio to match it.

This felt like finding the holy grail. And I realized that having the extra Jacktrip connection was in fact superfluous. What was really needed was to be able to extract two different latency feeds from one single connection — there was no need to receive the same data twice. I wrote to Chris Chafe, who co-wrote Jacktrip, explained the idea, and he said that he had thought of that years ago but had never implemented it. He called it “slipstream”. The idea is now in active development among the community of programmers (especially one in particular, Anton Runov, a brilliant coder from St Petersburg) that maintains and develops Jacktrip.

Live is sacred

One thing I never saw coming before I started doing livestreams is how authentically live a performance can feel over the internet. It was clear to me from the beginning that I needed to make it obvious — I would even say prove — to my audience that what they were hearing and seeing was live. One reason I felt this is that I knew that some presenters were asking musicians to pre-record performances of themselves, then presenting it to their audiences as if it were live. This is fraudulent, of course, but it’s also understandable at a time when doing things genuinely live comes with the risk of it all falling apart. Many livestreams never even start, many more disappear halfway through, others have no sound (surprisingly common), and yet others have sound that peaks the entire time. I’ve made every single one of these mistakes myself, and I’m more tech-oriented than many musicians.

So I felt that if I was to go to the trouble of actually doing it live, all of it, including the real-time Natural Machines graphics — which I eventually figured out how to superimpose over the main camera feed with transparency —, but also my live remote musical partners on Jacktrip, or my friend Kristin Berardi controlling my piano all the way from Australia, then I had better prove to my audience without a shadow of a doubt that it was truly live. And, of course, there’s a simple way of doing that, which is to interact strongly with the comments.

So, in my livestreams, I always take requests and questions. I’ll fix technical issues that people mention in the comments — for example, that my speaking mic is off, or that my video is no longer synched with my audio, problems that thankfully don’t happen often anymore — on the fly if I can. In many ways, experiencing unforeseen problems and solving them in the moment is the most direct way of recreating the feeling of live performance.

Because that’s what it’s all about, right? The feeling of live. The feeling of danger, of the possibility of things going wrong, and conversely, of them going gloriously right. It’s a sacred thing, this feeling, because it’s ultimately about reminding us all to dwell in the moment.

What I think has most surprised me about livestreaming, as someone who has lived and breathed live performance for most of his life, is how authentically live it feels to me as the performer. I feel the presence of the audience watching me through the ether. I feel their gaze, their judgement, and I swear I can feel their joy when I’m particularly in the zone and the music I’m making is really speaking from the heart. It sounds crazy, but the livestream experience has felt even more intimate to me at times than it has to play in a jazz club or a concert hall.

During one stream, I mentioned in between improvisations that I was reading Douglas Hofstadter’s book I Am a Strange Loop, because he had written me after the New York Times covered my #bachUpsideDown project, and because his classic Gödel, Escher, Bach had been a big influence on me in my early twenties. One person commented that they had an entire shelf of their library devoted to Hofstadter’s work. I talked a little about Gödel’s incompleteness theorem, and how it related to what I had just played, and another listener mentioned that she had just finished translating three hundred of his letters from German to English! She also corrected me on the pronunciation of his name. When has that kind of interaction been possible in a live performance? I never would have thought that it would be possible to foster a genuine sense of community in this format.

The great classical pianist Leon Fleisher died on August 2nd at the age of 92. On my regular Monday livestream August 3rd, one listener asked if I would play the jazz standard Someday My Prince Will Come, and immediately afterwards, someone else asked if I would play something with my left hand only as a tribute to Mr. Fleisher. One thing I’ve come to love doing during these streams is combining ideas from my audience. For example, one person provides a key, another a time signature, another a theme, and I play a freely improvised piece using those elements. In this case, I played a left-hand-only tribute to Mr. Fleisher, something that I never would have thought of doing without these serendipitous suggestions from the audience.

Here’s the Major Triad (ratios 4:5:6) in natural sandstone:

And here’s the Minor Triad, ratios 10:12:15 in the same material:

They will be 3-D printed on demand for you and can be ordered at my Shapeways.com shop, right here.

Augmented and Diminished triads are coming soon! Here’s a sneak peek at the augmented…

If you listen to it without knowing what it is, there’s something about the harmonic movement that might feel surprising. You can feel intuitively that it has a really solid structure, but at the same time, the chords don’t seem to move in a way that you would expect. There’s a reason for that: Back Attya, as the name cryptically suggests (ATTYA being an acronym), is an inversion of All The Things You Are, by Jerome Kern.

(An inversion, for our purposes here, is a chromatic inversion — a mirror image, with the mirror placed horizontally, where all the intervals are preserved exactly — not to be confused with a diatonic inversion. So if the original melody moves up by a major third, say, the inverted version moves down by a major third. A descending perfect fourth becomes an ascending perfect fourth, and so on. What note do you start on? More on that later.)

The bottom staff is a chromatic inversion of the top staff, with middle C as the axis of symmetry

The first question I usually get about it is: “my friend told me that this was an inversion of All The Things You Are, and I can see how that works with the melody, but what’s going on with the harmony? Why is the first chord B Major?” At this point I tell people to look up saxophonist/theorist Steve Coleman’s theory of negative harmony, because my transformation of ATTYA above is basically a textbook application of that concept.

(I attended a couple of Steve’s workshops at the Jazz Gallery when I first moved to New York in 2006, and I learned a lot from them. Steve is exceptionally generous with sharing his ideas — where many people would keep them to themselves, he wants you to know his secrets.)

More often than not, I then get another email saying the person still couldn’t figure it out. Which I can understand, to a certain extent, because Steve rarely lays anything out in writing in an easily digestible way — he always goes deep, exploring every possible ramification of a topic. So I thought I’d explain my understanding of his method in as clear a way as possible, since 1) it’s a technique that can give gorgeous results and 2) it’s actually an application of very old musical ideas to jazz.

Here’s how you do it — from first principles:

1. Find the key of the tune you want to invert. In the case of All The Things You Are, it’s Ab Major. The tonic of the song is Ab.

2. Determine the axis you’re going to use for the inversion. This will stay the same for the whole tune, even if the song temporarily modulates to another key. The axis is exactly half way between the tonic and the perfect fifth above it. In the case of ATTYA, half way between Ab and Eb puts the axis halfway between B and C:

Finding the axis for ATTYA

3. Invert the melody around the axis. In the case of ATTYA, the axis is between B and C, so B inverts to C, Bb to Db, A to D, etc — and vice-versa (C becomes B, Db becomes Bb, etc).

Inversion map for ATTYA

The first melody note of ATTYA is Ab, which gives us Eb (or D#). Next one is Db, which gives us Bb (or A#), and so on.

Inverting the first 4 bars of the ATTYA melody

4. Invert the harmony. This is a little more complicated but still pretty straightforward. The first chord of ATTYA is F minor — let’s ignore the 7th for now. F is the root of the chord. We invert this root around the axis to get F#, which we call the generator of the negative chord. Now, we recreate the original chord going down from this generator, rather than up. The notes of Fmin are F, Ab and C; moving up from the root, this is a minor third, then a major third. To get our inverted chord, we move down from the generator with the same sequence of intervals, first a minor third, then a major third. This gives us (reading downwards) F#, D# and B. We call this chord F# negative minor, or F#Nmin.

Fmin —> F#Nmin

Now what shall we call this chord so that people who don’t know about negative harmony can read it? How do we name it in the positive world? This is really the key of Steve’s approach: the root of the negative chord is always a perfect fifth below the generator. This bears repeating: the root of the negative chord is always a perfect fifth below the generator. So the root (in the positive world) of F#Nmin is a perfect fifth below F#, which is B. Looking at all the notes together (the root B, plus the notes we inverted — B, D# and F#), we see that we can simply call this B Major. This seems trivial in this case, but in other situations it’s not, as we’ll see.

Let’s look at the second chord of ATTYA, Bbmin7. Inverting around the B/C axis, as before, we get:

Bbmin7 —> C#Nmin7

We’d be tempted to call this chord D#min7, but that would be wrong. Remember: the root in the positive world is always a perfect 5th below the generator. So the root of this chord is a perfect fifth below C#, i.e. F#. We call this chord F#6.

We’re almost there. Things get a little more complicated with chords that don’t already have a perfect fifth in them. The last chord of the bridge of ATTYA, C augmented, is a good example. Inverting around the B/C axis, the notes C, E, G# become B, G, D#. The root of this chord is a perfect fifth below B, so it’s E, even though that note isn’t present in the inverted notes. Looking at the combined notes, B, G, D# with an E root, we see that it’s an Emin(maj7) chord.

5. That’s it. Now play through the gorgeous results. As long as you’ve picked a tune with strong structure to start with, the negative version should have equally strong structure, but will often be unrecognizable. It’s amazing how much this straightforward, linear transformation completely changes the affect of a tune.

Here’s how you do it — the fast and easy way:

If you play around with what I explained above for a while — and you should definitely do it this way for a few tunes, if you really want to understand how this works — you’ll soon discover that producing negative harmony this way is the long way around. There are shortcuts you can take. Here’s the fast way:

1. Find the axis of symmetry, which is always exactly halfway between the tonic of the song and the perfect fifth above that.

Here’s another way of looking at it using the circle of fifths, for the less piano-oriented. This is how my friend Ben Wendel likes to picture it:

2. Invert the melody around this axis, preserving all the intervals exactly (i.e. perform a chromatic inversion, not a diatonic one).

3. Find the chord roots for the inversion: invert the chord roots of the original song the same way as the melody, then transpose them all a perfect fifth down.

4. Notice that chord types always invert to the same chord type.

5. Fill in the blanks

6. Enjoy!

Dan Tepfer: Hi, McCoy. I should start by telling you that I’m a pianist. I’ve been playing with Lee Konitz for a few years now. It’s been very special for me to find myself on the bandstand with someone I’ve listened to since I was a teenager. Likewise, it’s very special for me to get to talk to you now, because I’ve been listening to you since I was a kid.

McCoy Tyner: Yeah, well, it’s the same for me. I’m happy to meet you young guys on the scene, and when they say ‘well look, I’ve been listening to you for a long time’, I never think about how old I am, but I think ‘wow, that’s good that I helped somebody’ or ‘my presence has a meaning’, you know. That kind of thing makes me feel good — I have a purpose in life. 

Q: You seem to have honored this sense of purpose to an extraordinary degree throughout your life.

A: I always had the idea that playing music is a great thing. I owe a lot to my mom. She really encouraged me a lot. She was a beautician and had a beauty shop and that’s where my piano went because that was the biggest room in the house. 

Q: In the beauty shop?

A: Yeah, in the beauty shop! We’d have jam sessions in the shop as I got into my teens. There’d be a saxophone player playing a solo next to a lady in the drier. 

Q: Did they applaud or was the music treated like background music?

A: Nah, it was treated like background music. My mother was pretty hip — she loved jazz. She knew Duke Ellington’s music. She was a very culturally-oriented lady. 

Q: So there was never any question in your family that pursuing music for your career wasn’t a great idea?

A: She thought it was a great idea. 

Q: How about your dad?

A: He didn’t mind. At first he wasn’t that eager to help me, because he worked manually. I used to go on Saturday and work with him. He didn’t consider playing music to be a regular job. But later on he woke up, he said ‘oh man, why not’, especially after he saw me in clubs. He was a convert. 

Q: He never put his foot down and said ‘you’ve got to get a real job’?

A: No, he never did that. He wasn’t artistically inclined, but he loved the music. He grew up with Duke Ellington, Woodie Herman, Count Basie. They were heroes to them, the big music stars.

Q: Who were your heroes growing up? 

A: What was really interesting was that Bud Powell moved right around the corner from me in Philadelphia. In my neighborhood. We had a heck of a scene in Philly, the cats were really practicing, jam sessions all the time. So I learned from the older musicians. And then Bud moved into the neighborhood, Bud used to be walking down the street and we would follow him. He was like in his own world. He was a genius, so I guess his mind was somewhere else. He would communicate, but only for short periods. The moments were very short. But he’d be walking and then he’d go back to his apartment, only a few blocks from where I lived. My hero was my neighbor.

Q: I remember reading a Monk quote where he said, about Bud: ‘he’s not crazy, he’s just doing that to attract attention! We taught him to do that’.

A: [laughs] Oh yeah? That could be! Well Monk was kind of… he wasn’t as extreme as Bud. But I remember meeting Thelonious because John [Coltrane] had played with Monk for a while. I was very fortunate to have been around when they were around, to have the chance to meet them personally. Monk liked John’s playing a lot so he would come around to hear the [John Coltrane] Quartet when we were in town.

Q: This was between 61 and 65 or so?

A: You’ve got the stats better than me, but it had to be about that time because that’s when the quartet was really happening. But I met John when I was a teenager, when he was with Miles. 

Q: John was a little older than you, right?

A: Yeah, he was more than a little older. He could have been my older brother. 

Q: Was that a situation where you were a big fan of his and suddenly you had the experience of ‘oh my god, here I am on the bandstand with him’, or did it feel more like a peer relationship?

A: He was someone I looked up to because his musicality was unmatched. And the thing is my girlfriend at the time, who became my wife, her older sister was a jazz singer and knew John’s wife Naima. He wrote that great song for her. She knew the family, so I knew her before I met John. So I knew him from the recordings that John did — with Miles and the later quartet stuff — but you know, I really got familiar with him through my association with her. It was a kind of big family thing around Philly. And then John left Miles — he tried quitting twice and left the second time — and I made some gigs with him in Philly. He treated me like a little brother. I studied some of his tunes — I knew Giant Steps, etc. 

Q: I don’t think there’s a recording of you playing Giant Steps with John. 

A: I think I recorded it solo, but not with John. I’m not sure — I’ve made more than fifty recordings in my life! But it was in my repertoire. He wrote some nice tunes: Giant Steps, Countdown, Mr P.C. — he wrote that one when he was with Miles, for Paul Chambers.

Q: I’ve been enjoying your recording of Mr P.C. on your new album, Guitars.

A: Oh yeah. Those are some great guys on there, some really nice guys. They’ve got their own style and they knew a lot of my songs and some of John’s. Bela Fleck was on My Favorite Things and Greensleeves. 

Q: How did your repertoire choices come about for the record?

A: They knew my songs. It was nice to see that they knew my repertoire, stuff that I had written. John Scofield was on Mr P.C. — I think Sco brought that up. Passion Dance is something that I wrote, and Mark Ribot — these guys, they knew what they wanted — they wanted to play. And they did a great job!

Q: Coming back to these Coltrane tunes, the ones with very dense changes. You were on the scene at the time when these tunes emerged. Was that a big shock to players at the time? Were people struggling to navigate John’s changes?

A: No, you know I used to practice all the time. I couldn’t wait to get home. Before my mother bought me a piano, she had three clients whose hair she used to do who had pianos. So I would alternate — I would go to one of my mother’s clients one day… I had three homes I could go to to play. Then she bought me a piano, a spinet. 

Q: How much did you practice a day?

A: It depended — I would try to get an hour in; sometimes it would run longer. An hour is a safe bet. 

Q: Did you study classical music?

A: I did, I had a great teacher. 

Q: What age did you start?

A: I was thirteen. I can’t believe it, I was thirteen — I once was thirteen! I formed an R&B band with a saxophone player who lived not far from me. I used to play with a lot of blues singers — they had the gigs! People would come and dance. 

Q: So your evolution really comes out of dance music and the blues, and classical music for the technique. 

A: Yeah, yeah. Also another thing: house rockin. Like blues, but with a backbeat. Like the shuffle. You’d rock the house with it. I played gigs in people’s houses, in my late teens. And then I met John [Coltrane] around that time. He came by the home twice. He was with Miles. Before he left Miles the second time, he told me ‘I’m leaving Miles and I want to have my own band’. He liked my playing. So I said ‘let me know whenever you’re ready’!

Q: When you joined that band, with John Coltrane, the rhythm section had one of the most incredible chemistries we’ve ever heard in jazz. Did that happen immediately, with Elvin Jones and Jimmy Garrison?

A: Pete La Roca played drums with us for a while. John told me: ‘I know this drummer in Detroit, named Elvin Jones’. The first time we hit, man, it was at a rehearsal, I couldn’t believe this guy. I said ‘wow’! He was incredible… but he’d listen! Because playing with Hank, who was his brother and played piano, he had a sympathy, he was empathizing with the piano. You know his brother Hank Jones was one of the greatest piano players in jazz. Elvin would pick up the brushes. A lot of people would say he was very loud and all, but he would pick up the brushes when I would take a solo, not all the time but a lot of the time, so people could hear the piano. It was great, man. He was so musical. When he and Jimmy hooked up it was amazing, those guys really locked in.

Q: I remember seeing a video of you with Jimmy Garrison and Elvin playing on an outdoor stage somewhere and the piano — a big concert grand — is literally rocking back and forth. The energy you guys had on stage was phenomenal.

A: [laughs] Yeah, yeah. It was a joy playing with them guys. The thing is with them, they were supportive. They were listening to each other. I listened to Elvin, Elvin’s listening to me, Jimmy’s right there. Jimmy had good time and he’d be locking in. We were like brothers. 

Q: So there was never a feeling being loud because you wanted to be loud, there was a feeling of the music just organically going there?

A: Yeah. It wasn’t… I know Elvin was a strong drummer, but he would pick up the brushes. He was very conscious of supporting — John would play a phrase and he would play a phrase that would complement the phrase that he was playing. 

Q: There was never a feeling of him overpowering anyone.

A: No, no. Unless there was something wrong with the sound system. And he would come down! He would come down to compensate for what was not happening sound-wise. 

Q: Before you were with Trane, you were part of the Jazztet. How did that happen?

A: I’ll tell you what happened. Benny Golson was from North Philly. I played a gig with him and he got a gig in San Francisco and he said man, would you like to go out with me and I said listen, I’ll go out with you but I’ve already promised John that I’d be in his band when he leaves Miles. He and Art Farmer hooked up and that’s when we put together the Jazztet. And that’s when we did Killer Joe and all those tunes. [Benny] and Art were playing in the band so I said okay, but I wanted to play with John. But every time John wanted to leave Miles he would always give him a raise and ask him to stay. John and Miles were pretty tight so it was hard for him to break away like that. But he had to do it and thank goodness because I was ready to join his band — we had a rapport, a good chemistry. It’s funny how things happen step by step, you know, one thing and you go from here to there and before you know it you complete a cycle and you’re in something else. You look back and it tells a story, I guess.

Q: You’ve done an incredible amount of work as a sideman and as a leader. I’m a young musician but I’ve had a taste of both sides, and there are differences. I remember coming across a quote of Joe Henderson’s, on the liner notes to Tetragon, I think, where he says: ‘My sole ambition when I’m a leader on a recording session is to completely forget that I’m a leader and feel like a sideman’.

A: Yeah, I can understand that. You don’t try to search for dominance, you know, because you’ve got other people and you want that chemistry. And that’s important. And that makes a record sound more harmonious. Makes it sound like you’re playing like a group. That happens when people are listening to each other, even if they haven’t been playing for that long.

Q: You’ve gone back and re-recorded tunes. You recorded Passion Dance on The Real McCoy, and then you have a record called Passion Dance that’s from 1978, 11 years later. 

A: Yeah — and I recorded it again with Mark Ribot on Guitars. 

Q: That must be an incredible thing to have a composition like Passion Dance that’s become such a staple that people want to hear it again and again. You’ve recorded it at all these different periods in your life, so it becomes a prism through which we can see your evolution as a musician. 

A: Duke Ellington was like that. He wrote a lot of tunes and he played them with his big band. And that’s good to play your music. Nothing wrong with that. You get better and better at composing. I can tell when I’ve written something that really strikes home, were you say ‘I’m really glad I wrote this’. And your feelings change, it depends on the time period when you wrote the song, what was going on in your life and whatever. 

Q: As you mature, do you feel that your outlook on music changes? Do you get more contemplative as you get older? 

A: Yeah, I think things change. And that’s good. But I think it’s better when you’re building on something. Make everything part of your development. Use everything that you’re exposed to in terms of your own musical personality, and build on it. Not to say you should play the same thing for ten or twenty years, but use that time period as a stepping stone towards where you’re going next. You build and build and you look back and say wow, that’s what I did ten years ago, how interesting. And sometimes you’re so busy moving ahead you don’t have time to do that, but you can hear it in the music. 

Q: That’s something that really fascinates me with your music. You’re someone who’s taken a germ of an idea and developed it over a long time. I’m speaking in particular of your use of chords built in fourths. Do you remember when you first came across those sounds?

A: I used to listen to a lot of different kinds of music. I played out of a book of different classics, a book of all the great European composers. But I knew that I had to have something that came from me. I kept that in mind. I always wanted to have my own feeling and my own sound. That’s what I think you have to do. You can’t forget that you’re the guy who’s really making this thing happen. I don’t care what you do; maybe you’re influenced by someone you like — Bud Powell moved into my neighborhood, Thelonious Monk I saw, a lot of great guys — I know Bill Evans was around, Herbie… everybody was looking for themselves. And I respected that. I realized when I was young: man, you’ve got something to offer. Why not let it happen?

Q: So you always had that feeling about yourself. And once you found something that felt distinctly your own, you just kept developing it. 

A: Yeah, you have to. I think it’s important. 

Q: As a pianist, I have to ask: these quartal sounds, how did you develop them? Did you create exercises for yourself?

A: No, just playing. Because you have to grow, and growing is by doing. It’s hard to practice something like that. Your sound is you, like the way you talk. Like if I have a couple conversations with you, next time you call I’ll say hey, what’s happening man? Your voice is your identity. It’s your signature. 

Q: Do you feel that that’s something that’s maybe been forgotten a little bit today, with younger musicians?

A: I can understand being influenced — I was influenced by Bud and Monk and what have you, but you have to find out who number one is and that’s you. I think it’s a different world now, the business is different. I think that record companies, I don’t know what they’re looking for. I think originality maybe is not in some cases valued as much. At least by some promoters. But the good ones exist — you have to find the right guy. 

Q: Another pianist question: you have one of the most physical approaches to the piano — you get this incredibly strong sound. I remember reading a quote of John’s about you: ‘beauty is exactly the word for McCoy’s playing, and it’s all of a piece because he lives like that too’. You manage to make a big, strong, loud sound that’s also beautiful, and that’s one of the hardest things to do as a pianist. 

A: I think what it is, is you have to utilize the pedals. Use a lot of pedal but don’t lay on it so stuff runs into other things. Knowing how to lift off to get the sound. Then come back on it and let it come up because otherwise it’ll all come together. It’s a technique you can use — open the dampers on the piano. 

Q: I wanted to ask you about your relationship to Africa. You have some beautiful albums, like Asante, which to me are some of the most successful integrations of African rhythms with jazz.

A: You know it’s really something, because I was always interested in African culture since I was a teenager. I used to play conga drums too. I stopped because it was making the joints of my fingers swell. I was hanging around with a guy who was a drummer who lived right up the street from me, Garvin [Masseaux]. He played trap drums and he played conga drums very well. 

Q: This was in Philly?

A: Yeah. We took dancing lessons too. One of my teachers in junior high, she knew this lady who had a dance troupe, and she said she needed some male dancers. And so I said maybe I’ll give it a shot — maybe I can learn how to dance. But I didn’t stop playing piano. I played a little piano there for some of the pieces that were choreographed by the teachers there. But I really got interested in the dancing. There was a guy named Saka Acquaye who came to teach African dance at the dance school. So we were hanging out with some guys from Africa and kind of caught on, you know. Actually Garvin [Masseaux] was really a good conga player and a guy named Bobby Crowder from Philly was also a great player. We had the fortune of having these African guys who played for the dance school. And the chance to really meet them. So it was a combination of a lot of things: cultural identification as well as actually getting your notes from people who were active in that area. 

Q: This was all when you were a teenager in Philly?

A: Yeah. Not many people know this, so I’m letting you in on a secret: I studied ballet and African dancing. 

Q: Wow. I studied ballet too when I was a kid, actually. 

A: Yeah, I studied ballet. I was a teenager. It was interesting because I heard a lot of different music. We danced to Stravinsky and some of the other composers and I played a lot of it. I was studying piano, had a great teacher and a book full of Chopin, Beethoven, Bach. They were real popular compositions that they had written back in the day. It was interesting, my teenage days. 

Q: Your teenage years were so culturally diverse: you had all of European culture from your classical piano studies and the ballet, you had all of contemporary African-American musical culture too — house rockin, jazz, blues, and now you’re telling me that you also had the whole African cultural upbringing through African drumming and African dancing. That’s really incredible. 

A: It’s amazing, isn’t it. Kind of covered the whole spectrum. 

Q: And that was all when you were a teenager. 

A: Yeah, because I enjoyed all the music. All the music I was studying out of my books.  And then I had a one on one experience playing congas; of course I had to stop because like I said it was hurting the joints of my fingers so I said stop this. But it was really interesting while I was involved. 

Q: Well, that certainly explains a lot of your later development. Tell me, if you would, a little more specifically about Asante. 

A: Yeah, I think it was something that sort of grew out of my experience of being a teenager. Those rhythms. That’s what I was exposed to — different rhythms, African rhythms. So I think it stayed with me. It was part of my exposure as a teenager, culturally. 

Q: Where would you say you get inspiration for composition?

A: I don’t know — it think it was a gift. I think it has something to do with the fact that studying piano and music itself — I studied theory as well. I was very fortunate — I was exposed to so many things, culturally. And for some reason — I had a band, too. Garvin [Masseaux] was playing not only congas but drums as well. And so I had a shot of that with some guys who I went to school with. A bass player and Garvin and some other people who were older than we were but that exposed us to different things as well. So it was a multitude of exposures.

Q: So that all informed your composing. What’s your creative process when you’re writing? Is it deadline-related? Or do you compose all the time?

A: Well yeah. I love to compose. When I do a recording, I always have to introduce some new material, some fresh stuff, something I just wrote. I don’t know why but I do. It’s good for me because if I have tunes of mine to perform, I think it’s directly because I’ve written a lot of those songs for recordings. I wanted to write something and I had a deadline — the date was set to record — and I had figured out the instrumentation I wanted to use, and I would write new songs. So a lot of my original material came from recording sessions. But a lot of my songs I wrote right before recording them. So I really got familiar with my music playing it on gigs. So sometimes I’m more familiar with my music after recording; when I’m doing club dates and concerts. Because tunes will grow and develop as you play them. 

Q: So you’re able to sit down at the piano with the intent to write a song and something pretty much always comes up?

A: Yeah, it comes up through the soul. With major preparation. It’s just something that — I’ll play a melody and embellish on that and before you know it there’s a beginning and a middle part and a repeat, usually — I’ll go back to the first part of the melody, so it has form. And I’ll figure out the harmonic concept I want to use. 

Q: Does that often come after the melody, for you? Or before?

A: Well, um, yeah. Sometimes the chords inspire the sound itself that I use. Inspires me to write a melody based on what sound I may run into at that time. Maybe ‘run into’ isn’t the best way to explain this…

Q: This stuff is difficult to explain.

A: Yeah — I’ve done a lot of music interviews over the years. And I do all right with explaining something but sometimes it’s hard to explain your style, because I know that a lot of pianists listen to my recordings and they learn more from that than they do from asking me questions. Because it’s hard for me to relate to what I’m doing by just talking about it. I mean I try to describe it — I do the best I can.

Q: I think you’re doing a great job. 

A: thanks, Dan, I’m glad somebody thinks so.

Q: Speaking of personal style, I remember years ago transcribing your solo off of Passion Dance, on The Real McCoy. In the majority of the solo you’re playing in this Fsus area and it struck me that you’re virtually not at all using the note D in your lines. You’re avoiding that note. Years later I came across the concept of hexatonics, scales of six notes. And so I wanted to hear your thoughts on that, how you came across that idea. 

A: For some reason I like that sound. You know, the fourths sound, the fifths. And rather than playing chords the way everybody else plays it, you know, and moving around. Once you set the root of the sound that the melody is based on, I usually try to keep the voicing open so I can move around. I can play an Eb seventh chord on top of an F or Ab, or B, all of that stuff¹. All of those sounds sort of connect. And I think that if you voice things properly you can go where you want to go. When you first start playing you play chords that are based on root, third, fifth, that sort of thing. But if you play the voicing open, you can move around because I think every chord is related to the other one, whatever chord you want to pick. It’s how you resolve things. I hope I’m making sense.

Q: You’re making a lot of sense. 

A: I know you know what I’m talking about. You play piano.

Q: Yeah, I totally hear you and I think the readers will love hearing this stuff too. I guess the point of interviews sometimes is to let the people who don’t play have a glimpse of what’s going on. 

A: Like a tapestry of sound. One sound is related to another. 

Q: For example, in that solo, the fact that you’re avoiding the note D — that’s part of your tapestry, that’s part of the creation of the color?

A: Yeah, that keeps me from being locked into that F sound so I can’t move. Not that I can’t move, but it suggests movement. 

Q: So leaving one note out makes it more open.

A: Yeah, you could say that. And then you resolve it. Once you establish the sound, maybe by leaving that D out, maybe in the melody or in the beginning of the solo, then you can move around, you can move the bass around, it’s all related. You can play Bb Ab B Db whatever you want to do you can move around, so long as you resolve things in a good way so it makes sense. To me, anyway. Everybody has a — if you talk to Cecil Taylor he probably has another idea of how it should go. And that’s great — that’s what it’s all about. 

Q: I remember reading a great quote of Art Tatum’s, where he says “there are no wrong notes, there are only wrong ways of leaving notes”.

A: Exactly. Exactly. It’s perfect. There are no wrong notes — it’s what you do with them, how you resolve them, how you move from one thing to another. It’s a resolution, I think. 

Q: You’ve made some great solo piano albums. How is playing solo piano different from playing in a band, for you?

A: I do things in contrast. If I do a quartet thing, then I might do something solo, then I might do something quintet, then in a sextet, then a big band. I try to make it so that if people buy my recordings they’ll have a little collections of different me’s in different settings. 

Q: That explains why you’ve worked with so many different people in your bands over the years. 

A: Yeah, you’re right. Just to add a little contrast to my performances. Just to give me something to do. Also when I play live. Sometimes, like, my big band — I’ve had some great guys in my big band — really nice guys.

Q: I love your album Uptown/Downtown.

A: Yeah yeah! Those guys are so nice, man. 

Q: Do you think you’ll have a big band again in the future?

A: Yeah, I’d like to tour with it. It’s an expensive process. I have to have a tour set up so that — you know, with more than one gig, so they don’t fly out and do only a couple gigs. It’s hard to do that because it’s so expensive. Everyone’s trying to get paid, then you got transportation, but the promoter usually pays for that — the transportation and the hotels. And so me and my agency take care of the salaries of the musicians. And usually the guys in my big band — they’re still a lot of guys around who play in my big band and they’re happy to see the band — they ask: ‘when are we going to play with the big band?’ It’s the chance to see some musical friends and sit next to guys with whom they’re familiar. It’s fun but it’s an expensive process. We went a lot of places with the big band. That’s a lot of fun. Then I’ll break down and do a trio tour or quintet or something else. Some violins — I had John Blake with me — so the recordings are comprised of a variety of musical settings. 

Q: I think I’ve covered what I wanted to ask you about, is there anything else you wanted to add to the interview?

A: Well, Dan, I wanted to tell you man, it’s been a pleasure to talk to you. 

Q: Oh it’s truly my pleasure, McCoy, you’re one of my heroes.

A: Really is. See, you’re a musician, that’s the difference. I mean, it’s good, there are guys who really know how to write articles in magazines and newspapers but when you talk to a musician it’s special. 

Q: Well it’s special for me, I’ll tell you. Thank you so much for taking the time to talk today.

These “dreams” could take the shape of memories (as they do in the novel) or ideas which suddenly (and perhaps inexplicably) seem important. While reading John Krakauer’s Under the Banner of Heaven earlier this year, I was struck by the fact that the Mormon fundamentalists he writes about seemed to be receiving messages and visions from a source remarkably similar to my own as an artist: they would close their eyes and listen inside. The only major difference is that they attributed this new information to a source outside of themselves: God. To me, because I am merely making art, the source of the message is secondary: what matters is that it’s personal, and that I like it. To them, the identity of the source is paramount: if it’s from God, a murder can be justified; if it’s from the realm of dreams, they are merely delusional killers.

Because a vision that comes from the realm of mystery doesn’t include within itself any information about its source, arguing about that is akin to arguing about what happened before the Big Bang. We will never know. The information is there, it’s new, it exists. And it didn’t before. The important question (and this is the same with the universe) is not where did this come from, but: what do we do with this now?

I like that the vision is portrayed in McCarthy’s book as a memory. Because of the narrator’s accident, he doesn’t know if what he’s seeing has actually happened or not. If feels like a memory to him, and it is richly detailed, but he can’t actually place it — and never does. To him the provenance is secondary: what matters is getting it exactly right. What I like about this is that it portrays the Visions (capitalized now) as inviolate, an ideal and unquestionable goal, which, regardless of whatever meaning or truth may or may not be contained in it, we must work our hardest to bring to life.

A dream doesn’t have to be a mere starting point: it can be a fully fledged destination, making the creative act not so much a question of, say, finding the notes that work best in a particular musical situation, but one of deepening one’s memory of an already extant vision: like the difference between creation and recreation. The creative act itself becomes opaque, a black box.

Take, for example, an idea I’ve had for a composition called “Levels”. It’s more than an idea. It’s a vision, a clear feeling. The question I’ve been asking, and which gets me nowhere, is: how can I express this idea in music? A better question might be: how is this music that I have imagined? How much of it, and how much of its detail, can I remember? I haven’t been digging deep enough into the murky source itself; I’ve only been skimming the surface of it and passing development onto my conscious mind. What if all the answers were already there and all I needed to do was remember them?

Of course this is precisely what Michelangelo said about sculpting: “I saw the angel in the marble and carved until I set him free.” The stone already contains the sculpture, the shape, and the artist’s job is merely to chip away the excess. The art itself already exists, inviolate, inviolable. Essence precedes existence. I realize as I write this that Tom McCarthy has drawn the parallel with sculpture nearly explicitly in the book, although he leaves the reader to make the connection, at the top of chapter 6:

In school, when I was maybe twelve, I had to do art. I wasn’t any good at it, but it was part of the syllabus: one hour and twenty minutes each week — a double period. For a few weeks we were taught sculpture. We were given these big blocks of stone, a chisel and a mallet, and we had to turn the blocks into something recognizable — a human figure or a building. The teacher had an effective way of making us understand what we were doing. The finished statue, he explained, was already there in front of us — right in the block that we were chiseling away at. “Your task isn’t to create the sculpture,” he said; “it’s to strip all the other stuff away, get rid of it. The surplus matter.”

Picasso, somewhat questionably it seems, is often reported to have said: “I do not seek, I find”. The idea, as I understand it, is that rather than creating by narrowly seeking a result that we already have in mind (essence preceding existence; or requiring of the physical world that it manifest a concept we’ve already defined in our mind), it may be better to go the other direction: to keep an open mind, allow experience to suggest things to us, and simply pick and choose without preconception, perhaps going solely on how much delight something brings us. (Of course, according to Picasso’s friend and chronicler Hélène Parmelin, it was entirely unclear whether Picasso had actually ever said “I don’t seek, I find”, and the opposite — “I don’t find, I seek” was just as true of his manner of working).

Whatever the case may be, this is a little different: in presenting the Vision as a memory, as McCarthy does, it becomes other from us, a command rather than a recommendation. There’s no longer any choice between seeking or finding; it just is (again, just like the Big Bang). The essence / existence question only comes into play when we decide to manifest this Vision in the physical world, in which case we have to ask ourselves whether its essence occurred first and we will make it exist in such a way as to be as true to its essence as possible, or whether we will, based on some sort of limited hunch, start it into existence and build it dynamically, defining its essence as we go.

Sartre, with his whole “existence precedes essence” thesis, was responding to millennia of God-oriented thinking in which God already had a plan in place for us at the moment of birth: who we were preceded what (in terms of matter) we were. No, he said: first we are matter, then we create who we are through our choices and actions. But that is obviously very tenuous: Schopenhauer’s quote, “A man can very well do what he wants, but he cannot will what he wants” points out that our deepest desires are largely out of our control: we don’t choose or create them. They create us. In fact most theories of so-called self-realization rest on the idea that there is a “self” to realize: that there already is a figure within the block of stone and we have only to get rid of the surplus matter, the “remainder”.

A closing thought: Remainder presents a nice allegory for why improvisation might matter. The narrator’s main obsession is with authenticity: he is drawn to things that have been made without a will, such as grease stains on the floor and actions taken by people without thinking — where the desire to act and acting on that desire are one, without interference from consciousness. It’s striking to observe how similar this is to the ideal expressed in Zen — “sleep when you’re tired, eat when you’re hungry”, without second-guessing yourself.

The narrator’s approach to authenticity is to rehearse an action over and over again, perfecting it until it has attained the appearance of unplanned ease — an approach very similar to that of a classical pianist, for example (there is, not coincidentally I’m sure, a classical pianist in the book). Yet the novel’s denouement reveals to the narrator that real fusion of action and desire for action can only be achieved when something truly unplanned happens: this is when the truth that he is after, the holy grail of authenticity, is revealed at its fullest. And this is improvisation, or at least, this is what improvisation should be: an opportunity to be truly authentic, in a way that acknowledges that no two moments are the same. Authenticity at one moment is not the same as authenticity at another. We can mask this fact with endless rehearsal, or we can embrace it, reveal it, by letting the unknown into our game.

No doubt about it: Lee Konitz does this, quite purposefully, every time the music starts to feel predictable. I’ve seen him do it. To find true authenticity, he might say, we must allow the moment to continuously surprise us, and if it ceases to surprise us (as it can with unimaginative sidemen, an uninspiring audience, or a somnolent self), we must find ways to force surprise back in: by playing something totally unexpected, for example, or — in the extreme scenario of obliviousness — by walking across the stage mid-performance and stomping on the pianist’s foot. Which happened once. To me.

But this leaves a question: what direction does the interval in each of the canons go? If Bach writes a “Canon at the Second,” there’s some crucial information missing, isn’t there? Is it a second above? Or below?

One might expect that Bach settled on one direction, and that all of his canons are at increasing intervals above, or below. This isn’t the case. The direction of the canons, in fact, keeps changing, and seems to be an important structural component of the Goldbergs. This is something I’ve been fascinated by for a while, and I haven’t seen it discussed anywhere else before. Let’s take a look:

Canon #1, Var 3: Canon at the Unison —> no direction

Canon #2, Var 6: Canon at the Second —> above

Canon #3, Var 9: Canon at the Third —> below

Canon #4, Var 12: Inverted canon at the fourth, with the axis of symmetry between the F and E above middle C, so that the G above middle C is transformed to the D above middle C, a fourth below. With this kind of canon, one can’t really talk about it being above or below, because anything written below the axis will have a response above it, and vice versa. However, simply because of where Bach decides to place the subject, in the 1st half, the subject is above the response, and in the second half, the subject is below the response. So I would rate this one as a “1st half below, 2nd half above” canon. Let’s also point out that it’s kind of funny to call this a “Canon at the Fourth” at all, since the only moment you get a fourth between subject and answer here is when you play a G or a D in the subject. Every other note will have a response that is not a fourth away.

Canon #5, Var 15: Inverted canon at the fifth, with the axis of symmetry between the Bb and B above middle C, so that the G above middle C is transformed to the D above that, a fifth above. The same observations apply here that applied to Var 12. In fact, the two variations are effectively the same canon, in that the same note names are transformed to the same note names in each one, the only difference being the octave in which they are placed (and the minor key of course). Simply because of where Bach decided to place the subject with respect to the axis of symmetry, the subject is 99% of the time below the response, so that I would rate this canon as belonging to the “above” category.

Canon #6, Var 18: Canon at the Sixth —> above

Canon #7, Var 21: Canon at the Seventh —> above

Canon #8, Var 24: Canon at the Octave
1st quarter —> below
2nd quarter —> above
3rd quarter —> above
4th quarter —> below
I love how he switches directions in this one! At the end of each quarter of the variation, the subject becomes non-melodic (the very rare time that this happens in the entire set), with either disconnected eighth notes on each beat, or (at the end of the 3rd quarter) silence. I believe Bach does this so that the change of direction isn’t jarring to the listener. Bach always gets his cake and eats it too — he adheres to the formal logic, but manages it so artfully that it never feels pedantic to the listener.

Canon #9, Var 27: Canon at the Ninth
1st half —> above
2nd half —> below

To sum up, we have:
canon 1: no direction
canon 2: above
canon 3: below
canon 4: below / above
canon 5: above
canon 6: above
canon 7: above
canon 8: below / above / above / below
canon 9: above / below

One observation here is that there are what I call “sister” variations. For example, if we ignore octave displacement, the canon at the 3rd is the same as the canon at the 6th, since the first is descending (e.g. G becomes E below) and the second is ascending (e.g. G becomes E above). I’ve already noted that the canons at the fourth and fifth, if we ignore octave displacement, apply the same transformation. We can also observe that the first half of the canon at the 9th applies the same transformation as the canon at the 2nd (G becomes A), and the second half the same as the canon at the 7th (G becomes F). Obviously the canon at the octave applies the same identity transformation as the canon at the unison, and its many switchings of direction seem to go out of their way to stress this point — almost as if Bach wanted to make sure we understood that, on average, this too is a canon at the unison.

So I would pair up the canons this way:

1 & 8: G becomes G
2 & 9: G becomes A
3 & 6: G becomes E
4 & 5: G becomes D
7 & 9: G becomes F

(The canon at the 9th does double sisterly duty. It’s the only canon where the switch of direction actually changes the transformation. This makes it special and, to me, in conjunction with its status as the only 2-voice canon, gives it an air of finality).

Hence the canons of the Goldbergs, ignoring octave displacement, feature not 9 different transformations — or the 7 that you might expect, since if we ignore octave displacement 7 is the maximum that we could have — but only 5. That’s the main point. There are really only five canonic strategies here. We never have a canon at the third above (G becomes B), nor do we have the fifth below or the fourth above (G becomes C). Two of the possible 7 transformations are missing.

Why?

“Am I putting up with anything right now? Is there something that I’m unhappy with that I haven’t addressed?”

For example, awkward posture, which looks uncomfortable, will make the audience uncomfortable too, because it shows the performer to be someone who is putting up with something rather than doing something about it. We want to see someone who is at peace, from head to toe.

Why do Belgians sleep with two water glasses by their bed, one full and one empty?

One is in case they wake up in the middle of the night feeling thirsty. The other is in case they wake up in the middle of the night not feeling thirsty.

Of the two, this is the one that usually gets at least a chuckle. The second is dirtier, but is almost guaranteed to get no laughs at all:

One guy says to another guy: “You know, when I fart it smells pretty bad but it doesn’t make any noise. Isn’t that interesting?”

The other responds: “Well, what a coincidence! When I fart it’s the exact opposite, it makes a ton of noise but doesn’t smell at all!”

At that moment one of them feels a tap on his shoulder from a stranger. “Excuse me, gentlemen, but I was just sitting over there and couldn’t help overhearing your conversation. I thought I should join in, because it just so happens that when I fart, it makes a lot of noise, and smells terrible! Isn’t that extraordinary?”

Out of nowhere, a weak little voice speaks up. Another stranger. “My friends, I’m so sorry to interrupt. I was just walking by and couldn’t avoid hearing your fascinating conversation. Please forgive the intrusion, but I just had to. You see, when I fart, it doesn’t smell in the least, and honestly makes no noise at all!”

To which the three other men turn around and ask, indignant: “So why do you fart, then?”

I love these jokes because they’re really dumb in appearance, but are in fact profound. To me they’re actually the very same joke, in that they both wrestle with whether it makes sense to have containers for nothingness. Is a fart a fart if it doesn’t smell or make noise? Is it brilliant to have an empty glass by your bedside table, or just plain stupid?

It took humans a long time to understand that it’s not as stupid as it sounds, and that it could be useful to have a container for nothingness — otherwise known, in math, as the number zero, the numerical equivalent of reaching for a number without actually wanting one. Several other cultures got there earlier, but in Europe it remained elusive well into the AD era. From Wikipedia:

The ancient Greeks had no symbol for zero (μηδέν), and did not use a digit placeholder for it. They seemed unsure about the status of zero as a number. They asked themselves, “How can nothing be something?”, leading to philosophical and, by the medieval period, religious arguments about the nature and existence of zero and the vacuum.

As both jokes make clear, it’s no simple thing to accept that an idea that seems absurd on its face — that nothing can indeed be something — could in fact prove to be tremendously useful. Math simply wouldn’t have gotten very far without it.

Contrast these profound jokes, lowbrow in appearance, with another joke, this one seemingly sophisticated, but depending solely on one of the dumbest puns out there:

René Descartes is finishing lunch in a Paris bistro. The server comes up to him and asks if he’d like a cup of coffee. Mr. Descartes ponders this for a moment, and responds: “I think not”. And with that, he vanishes!

The Natural Machines album is out today, Saturday October 27th. I’m bringing the project to Le Poisson Rouge in New York on October 30th. The fine folks there asked me some smart questions ahead of the gig. Thanks to John Ruscher for asking me to do this interview.

LPR: Can you summarize what Natural Machines is?

Dan Tepfer: It’s a project where I explore the intersection, in music, between natural and mechanical processes. I do free improvisation at the piano, and programs I’ve written on my computer interact with me in real time as I’m playing, both musically and visually. I love it because it feels like very new territory, and it’s exciting to be exploring it.

You’ve mentioned you had a background in computer programming and physics as well as music. Does a relationship exist between the hard sciences of computer science and physics and the art form of music, and if so, how would you describe that relationship?

All great music, and probably a fair amount of great art too, but definitely this is true of music — all of it exists at the intersection of the spiritual and the algorithmic, I think. Good music, like good architecture, has strong structure. It’s what keeps it from falling apart. So whereas the surface of music is often above all emotional / spiritual, in the best music this surface is supported by logical systems, of varying kinds; this is what gives the surface a feeling of depth and stability. Just as an example, I don’t think it’d be that far fetched to say the “art” of counterpoint is close to a hard science, in the sense that it offers quite definite right or wrong answers to certain musical problems, and counterpoint is the underpinning of much of the music of the last 500 years, so there’s no doubt there’s a relationship there.

What is it like to play with an automated instrument such as your piano? Do you find yourself reacting as if you were playing alongside a real person, or is it a different kind of feeling?

It’s a different kind of feeling, because the computer responds according to strict rules I’ve programmed into it, so it would be like playing with a person that has absolutely no feelings but, instead, an unbelievably virtuosic ability to calculate. When I play and the algorithms respond, it feels more like I’m playing alongside an idea than a person.

You cited the music of Bach as being an example of that combination. Where do you see both the spiritual and the algorithmic in Bach’s music? Has it affected how you play Bach, and how?

Bach is really the poster child for this idea. His music speaks so strongly to us at an emotional and intuitive level, and yet when you dig into it even a little, you realize that it’s all supported by a mastery of logical systems. Often his music has more than one algorithmic process behind it. For example, in every third variation of the Goldberg Variations, he’s using, on the one hand, the rules of counterpoint, which by his time had been pretty strongly codified, and on the other, he’s imposing on himself the rules of canonic writing, where one voice imitates the other a certain musical interval apart. What makes it algorithmic is that Bach never cheats on either one — once he’s set up rules for himself, they are as rigid as if they were being calculated by a computer, with very few exceptions. And those aren’t the only rules at play. He’s also following a set chord progression, the same one in each variation, as well as adhering to larger structural ideas that govern the whole work. It’s no coincidence, for example, that the theme of the Goldbergs has 32 bars, divided in two at the midpoint, and that the work as a whole has 32 movements, likewise divided in two at the midpoint. And yes, getting deeper and deeper into the analysis side of Bach has deepened my playing of his music, no doubt about it. And it’s definitely given the act of improvising off of his music, as I do in my Goldberg Variations / Variations project, greater substance. 

In this performance, you’re programming an object (the piano) to act based on algorithms you create, and then recording how that object behaves, which seems very much like a science project. But, you’re also performing and communicating with that object inside an art form, which is music. Is Natural Machines a science project, an art project, or something entirely different?

Well, that’s the thing: I firmly believe that’s a false dichotomy — great art is naturally both at once, not one or the other. No one who’s really studied Bach would deny the science aspect of his work. But that’s not true only of Bach; it’s also true of a composer like Ligeti, or Bartok, and definitely of John Coltrane and Steve Coleman, too. 

It’s easy to talk about the technological aspects of the Natural Machines project, because technology is something that naturally lends itself to being put into words, but my most important focus in this project is making sure that the music is strong on its own terms. I’ve spent 11 years playing with Lee Konitz, I’ve spent my life performing Bach and playing jazz standards, so there’s no way that I would be happy presenting something that is only a science project. However, if I can find something that is both at once, and strongly so — that’s something I can get excited about.

Does the performance incorporate improvisation at all, and what kind of improvisation?

The project is very much based around the idea of free improvisation, and specifically, how free improvisation butts up against constraints. It’s a little like pouring water into a receptacle — whether it likes it or not, the water, even though it’s free flowing, will take the shape of the receptacle. So what I’m doing is creating a world, with its own natural rules of physics, and then visiting that world as a free agent and trying to find a way to enjoy living in it, to dance. I’m improvising from scratch, but the computer’s response makes it so certain things work, and others don’t. It’s the vessel I pour my freedom into. It shapes my freedom.

By now, you’ve probably spent a lot of time making music with this specially programmed piano. Because you’ve spent so much time with it, are you ever able to predict what the piano is going to do, and are there some patterns that the piano tends to play more than others?

The piano doesn’t really play patterns unless I’m playing patterns myself, because its reaction is always some kind of transformation of what I play. So, if I find myself not being surprised, it’s really up to me, as a free improviser, to not be complacent, and immediately search for a fresh angle to explore. But this is true of any situation in which you’re improvising, whether or not there’s technology involved. Only the great masters, Lee Konitz being a great inspiration in this regard, manage to keep it fresh every single time. It’s really important to me, in this project especially, that I keep surprising myself, and I’ve found that there’s nothing like painting yourself into a corner to make that happen. And there’s nothing like a computer to paint you into a corner…

What was your reasoning behind incorporating virtual reality into the performance?

Over the last year and a half, I’ve been creating visualizations for the different musical processes, with the intent of revealing the underlying musical structure of each. At shows, I’ve been projecting them on a screen behind me as I play.  Some of them are three-dimensional worlds, with a strong feeling of depth. They feel like a space that it’d be fun to explore, move around in, so I’ve been thinking of trying to incorporate VR for some time. But there’s a big challenge as far as incorporating VR into this project is concerned, because everything I’m doing is being created in real time. None of the notes I’m going to play are known ahead of time, nor the computer’s response, and hence none of the visuals either — only the way these things work is known ahead of time. So the data needs to be sent to each audience member’s device right as I’m playing it at the piano, and right as the computer is responding, with as minimal lag as possible. I think I’ve finally worked it out — I programmed it so it’ll all happen in a smartphone’s browser. I just ordered $600 worth of Google Cardboard, one for every audience member, and bought a powerful wifi router that should be up to the task of sending data to everyone at once. It’s going to be really exciting to see if it works at LPR, where I’ll be trying it for the very first time on a couple of pieces.

Do you think that in the future we’ll see more and more interaction between the arts and the hard sciences? If so, what kind of interaction? 

Art reflects the times we live in, and the times we live in, for better or for worse, are increasingly technological. So art needs to deal with technology at some level, whether it be by incorporating it, or rejecting it, or some middle ground. Music has always had a close relationship to technology. The pipe organ was one of the most sophisticated machines of its time when it was being developed, and the same could be said of the piano. Now, in terms specifically of hard sciences, Spotify now has an entire research department devoted to applying A.I. to music (imagine the profits once you have a program that can crank out infinite numbers of royalty-free tracks that sound good enough for people to put them on as background music! This has already happened, by the way). Also, while I’m on the topic, the mathematical building blocks of musical harmony were laid down by Pythagoras, so there’s a long history of the hard sciences interacting with music, and I can only see that increasing as we go. 

However, and this is a big but, as I said earlier, it’s not art if it’s just science. Art has to, somehow, speak from the soul, it has to tell us something unutterable about the mysteries of existence, or it’s no good. So the more scientific it gets, the more, if we want to keep making art that makes a difference in the world, we’re going to have to dig deep within ourselves to satisfy the left side of the spiritual / algorithmic divide.

What do you hope the audience will gain from Natural Machines?

Most of all I hope it takes them on a journey. I want my music, and my shows, to be transportive — to pick you up, take you on a ride and gently put you down in a different place, hopefully changed. 

What do you think about potential applications for virtual reality in the arts? Do you have any future plans to incorporate virtual reality into your music making?  

Well, I’m excited to start exploring the possibilities at LPR. If it works, I’ll go from there. My default attitude towards new technology is to be skeptical, but to try it and see. When it really does make a difference, as I think what I’m doing with the piano and the visuals does, it feels really special, because in many ways you’re lucky if you find a way to incorporate technology into art in a way that genuinely transcends the gimmick. 

Do you think that it’s possible to use science to understand the arts better, and vice versa? If so, how can we go about that process? What are some ways that science has helped you understand music as an art and express yourself through it?

I think we can use science to understand the science side of music better, for sure. To me it’s fascinating, for example, to understand the whole-number vibrational math behind just intonation, the ancient mathematical method for making sounds that work harmoniously together. But science can’t help us understand the spiritual side of music, no sir. For that, we just need to live our lives, feel things as deeply as we can, listen hard, and when we open our mouths, try to make sounds that matter.

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Listening to it today, I was reminded of Keith Jarrett’s solo version of Treasure Island, from The Bremen Concert, another piece notable for its unusual proportions. It’s a fairly conventional jazz song, with melody, lots of nice chords, a solo section, and then poof! 3 minutes and 8 seconds in (coincidence!), it suddenly turns into an aggressively minimalistic vamp, which vamp lasts for 7 minutes and 51 seconds with nary a change as far as the content is concerned (well, there’s a tiny bit of blowing at first, but by the 3:56 mark he’s all in). For seven solid minutes, we’re listening to Jarrett play the exact same 2 bars over and over again, the only change coming in the form of dynamic variation, both at macro (gradual or sudden changes in the overall dynamic) and micro scales (choosing to bring out different internal voices at different times).

(He also occasionally throws a high C in there). To me, there’s absolutely no doubt that Keith is testing us, and himself. He’s daring us to keep paying attention, and he’s daring himself to make the extremely limited material so compelling that we’ll be rewarded for our attention. And he wins, no doubt about it. The gamble is huge, because all it would take is one tiny stumble — one moment of inattention to touch, to groove, or even to the integrity of the natural dynamic development — for our suspension of disbelief to come crashing down.

The Beatles win too, of course. In both cases, the pairing down of the musical content is a way for the artists to remind their listeners that there’s a lot that happens in music beyond variation in notes, rhythm and harmony. You take away variation and the what of the music falls away, leaving you only with the how. The Beatles put the emphasis on orchestrational and energetic changes. Jarrett takes it to the extreme, showing us that micro-variations in touch and phrasing can keep our attention rapt if done with sufficient skill, patience and concentration.

I don’t know if anyone reads these blog posts anymore (it’s 2018), but if you do and you think of a song with similar architecture, please share in the comments below.

With most things, I’ve found, what’s most interesting isn’t the thing in itself, but rather how it relates to other things. In other words, everything is relative, which is why I was so excited to see the video below. It shows, using harmony, rhythm and visuals, the relationships between the orbits of the seven planets around TRAPPIST-1, a dwarf star about 40 light years away from us.

The video was made by astrophysicist Daniel Tamayo, who worked out the planets’ orbits, and Matt Russo, a fellow scientist who also plays jazz guitar. Musician Andrew Santaguida contributed as well.

What’s going on here? Why does it sound so good? How, in the first place, were these orbits figured out? It’s only in the past 25 years that we’ve been able to detect planets in orbit around stars other than our own. This is mainly done indirectly, by — for example — measuring faint dips in a star’s brightness as planets pass in front of it. In 2015, using this technique, three exoplanets, as planets outside of our Solar System are called, were discovered orbiting around TRAPPIST-1, a dwarf star about 40 light-years away from us in the Aquarius constellation. In February 2017, four more were discovered. The field of exoplanet detection has gotten so advanced that scientists are able to determine not only the size and mass of these planets, but also their orbital periods and — most amazingly — chemical composition. Three of TRAPPIST-1’s planets are considered to be within its habitable zone, where life could potentially be sustained, and some of the planets may even have liquid water on their surface.

Artist Impression of the TRAPPIST-1 system (NASA/JPL)

This is remarkable enough already. But what makes the TRAPPIST-1 system even more special is the relationships between its planets’ orbits. The farthest planet completes one orbit every 18 Earth days, and the next farthest once every 12. What’s 18 divided by 12? That’s 1.5, or 3/2. In other words, in the time it takes the farthest planet to go twice around the star, the next farthest has gone around three times.

We hear sound when the air around us vibrates and those vibrations reach our ears. Vibrations are a bit like orbits — they repeat at a certain frequency (the note A in the middle of a piano, for example, vibrates 440 times per second). What does it sound like when sounds vibrate in that same 3/2 ratio, one sound vibrating twice in the time it takes the other to vibrate three times? As Pythagoras discovered long ago, it sounds lovely. The musical interval which results, the so-called perfect fifth, is one of the fundamental building blocks of harmony — and not only Western harmony. It turns up in traditional music from all around the world, in every possible key. It sounds like this:

Now let’s look at the closest planet to TRAPPIST-1. It orbits the star in only 1.5 Earth days (these orbital periods are short because the system is very compact — all seven planets orbit the star much closer than Mercury orbits the Sun, and the star itself is only about the size of Jupiter). The next closest goes around once every 2.4 days, which gives their orbits a relationship of about 8/5. Now, if one sound vibrates eight times in the time it takes another to vibrate five, we get the interval of a minor sixth, which sounds like this:

This is a less basic interval than the perfect fifth, but it’s still part of the fundamental material of music. Like the perfect fifth, it’s a consonant interval, meaning its sounds seem to belong together; the relationship sounds harmonious to our ears. Let’s pause here for a moment to consider what we’re talking about: that some planets orbiting a star unfathomably far away from us are doing so in a way that sounds good to us. Isn’t that something?

What’s more, we’re capable of hearing relationships like 3/2 and 8/5 in other ways than through harmony. As I’ve written about before, pitch and rhythm are the same thing, expressed at different time scales. We can hear 8/5 as an interval between two pitches, and we can also hear it as a rhythm in which one sound is played eight times in the time the other is played five:

8 / 5 in musical notation

What does this rhythm sound like?

Pretty catchy, I would say! What’s important to appreciate is that this is exactly the same as hearing a minor sixth as harmony, only about 200 times slower. Pitch and rhythm are simply two different ways for us to perceive frequency relationships. It’s even possible to experience one turning into the other, and back again:

With the TRAPPIST-1 system, it’s not only the inner and outer two planets that orbit in a resonant harmonic relationships. All seven, surprisingly, do — the only planetary system discovered so far with such consistently resonant orbits. Their relationships, from inner to outer, are very nearly as follows: 8/5, 5/3, 3/2, 3/2, 4/3, and 3/2. This works out to a combined 2 / 3 / 4 / 6 / 9 / 15 / 24. Let’s hear all of these together, built up from the outermost planet to the innermost, in music:

Pretty, right? Now let’s hear these same relationships as rhythm, but instead of playing each note with a percussive sound as we did before with the minor sixth, let’s express each with the pitch that results from the orbital relationships. For fun, here it is in musical notation:

The TRAPPIST-1 system (2 / 3 / 4 / 6 / 9 / 15 / 24) in musical notation

And in sound:

We’re now hearing the TRAPPIST-1 system as pitch and rhythmic relationships, simultaneously. We’re experiencing the same thing in two different ways at once. As a friend of mine pointed out, it’s a bit like tasting roasted cauliflower next to a cauliflower gratin on a bed of cauliflower couscous.

Cauliflower gratin

But wait, something’s off — if you’re listening closely, you may have noticed that this is quite a bit more in tune and in time than the sounds and rhythms played in the video at top. This is because, although the TRAPPIST-1 system has relationships that are very close to whole numbers, they’re actually a little off. Nature is funny that way. The outermost planet doesn’t orbit in exactly 18 days but rather 18.766. The second farthest planet goes around in 12.353 days rather than 12. So their relationship isn’t quite 1.5, but rather 1.51918. We’ve been listening to an idealized version of the system so far. Let’s see what the real thing sounds like, with the most precise orbital periods plugged in, first as pitch, then as pitch and rhythm:

It still sounds quite harmonious, if a little sour (it’s worth comparing to the two previous recordings above). The discrepancies are particularly noticeable in the rhythm, which doesn’t line up quite as neatly as before. The intervals making up the harmonies aren’t as clean, either, but they still “work” — we still hear a clear, quite consonant chord (the history of tuning systems tells us that there is always a little lee-way with tuning). One result of recreating this rendering for myself was to notice that there is a wobble, or vibrato, in the piano-like sound that the TRAPPIST-1 physicists used in their video. To my ears, this causes the harmonies to sound a little further out of tune than they actually are. I’m using simpler, more stable sounds in my own rendering.

So — TRAPPIST-1 is remarkable. Without interfering with its orbits in any way, by just presenting the data scaled up to our range of hearing, we hear what we readily identify as harmonious music. But how special is it? To compare, I wanted to listen to our own Solar System. From Mercury’s 88-day orbit to Neptune’s 165-year one, our home planets take a lot longer to orbit the Sun than TRAPPIST-1’s do. But their relationships — Earth to Mars relate by about 17/9, for example — can be rendered in music just as well.

The Solar System (distances not to scale — WP)

The Solar System is so spread out that it helps to break it up. Let’s begin with the four inner planets, Mercury, Venus, Earth and Mars. Heard on their own, they spell out an eerie kind of Major 7th chord:

Meanwhile the outer planets Jupiter, Saturn, Uranus and Neptune together have something of a half-diminished color:

Now let’s try to hear these together. Because it is so compact, the planetary system of TRAPPIST-1 can fit neatly into the range of frequencies where we comfortably hear harmonies. Not so for the Solar System. TRAPPIST-1’s innermost planet makes only 12 orbits in the time the outermost makes 1, whereas Mercury makes 684 in the time Neptune makes 1, a vastly greater range that stretches our hearing to the limits. If I assign an extremely low note to Neptune, a low 23Hz rumble right at the bottom of our audible range, that puts Mercury’s sound right at the top of what we can hear, a mere dog whistle at 15,736Hz — which younger listeners will have more success hearing than older ones. Even if we’re able to hear this, we just don’t have the perceptual capacity to hear real harmonic relationships between tones spread that far apart.

For that reason, I’ve transposed the inner four planets down by 2 octaves, and the outer four up by 1 octave. As you’ll remember from music theory class, if you were there, this doesn’t alter the resulting harmony (think chord inversions) — it just allows us to hear it. Here is the sound of our Solar System, from Neptune through Mercury:

There’s no doubt when we hear this that the Solar System isn’t anywhere as harmonious as TRAPPIST-1. Not even in the same ballpark. I actually like the sound that results — it has a mystery that I find enticing — but it’s wildly dissonant. While there are some near-resonances in the Solar System — Uranus makes nearly two orbits in the time it takes Neptune to make one, for example — most of them are too far out of tune to qualify as harmonious.

The fact that the TRAPPIST-1 orbits are so obviously harmonious in comparison tells us something important about the physics of the system. The planets are so close together that they would collide with each other if they hadn’t settled into these resonant orbital relationships. Meanwhile, the planets of the Solar System are far enough apart that they face fewer demands on their orbits.

Kepler’s Harmonices Mundi

The great astronomer Johannes Kepler, in addition to contributing enormously to the field  of astronomy in the 17th century, was also something of an astrologer. He was particularly interested in how a planet’s speed varied during its orbit, which is what he rendered in musical notation in the figure above. He believed that the happiness of life on Earth depended on how harmoniously the orbits of the planets related to one another. He was following in the footsteps of the ancient Greeks, who advocated for a Harmony of the Spheres over 2,000 years ago. It turns out people have been trying to listen to planetary orbits for a very long time; it’s remarkable that we live in a time where we can accurately listen not only to our own, but to planets around other stars as well.

Aristotle and Kepler would have had to believe that life in the TRAPPIST-1 system, if indeed there any, is pretty dandy. It’s hard to imagine a system with more harmonious planets. Or is it? I’ll leave you with a sound rendering I made of the four Galilean Moons of Jupiter, both in pitch and rhythm. Io, Europa, Ganymede and Callisto have orbits that are perhaps even more harmonious than those of TRAPPIST-1, with a beautiful minor key sonority. Three of the moons are in quasi-perfect octaves, a 2 to 1 relationship that is the simplest there is. I guess life must be pretty good there, too.

Dan Tepfer interviewed by Gary Heimbauer
Jazz Inside Magazine, January 2010

Jazz Inside: Can you talk about how your unique childhood/young adulthood might have influenced your voice as a musician? You were born in Paris, France to American parents, got a degree in astrophysics in Edinburgh, Scotland and then moved here.

Dan Tepfer: I grew up in a way that doesn’t really give me any choice but to see the outside view, to see music as a pluralist art form. My grandfather was a jazz pianist on the West Coast. As a matter of fact, Nancy King, Ralph Towner and Glen Moore credit him with getting them into jazz. My mom is an opera singer. So I grew up hearing a lot of music, mainly jazz and classical, from before I was even born. I studied classical piano at one of the Paris conservatories through my childhood and teens, but somehow I always mainly considered myself an improviser. Knowing that my granddad improvised made it okay to do that in my mind, despite what my classical teacher would say. Playing classical music, even though I secretly really enjoyed it, and still do, was my work; improvising was my fun, so I ended up spending a lot of time at the piano making things up. And that’s basically how I learned jazz. I’m mainly self-taught except for a few lessons growing up and a two-year master’s degree in jazz from the New England Conservatory; but most of my foundation had already been set by then. So, because for most of my life nobody told me how to play jazz, it’s always felt natural to me to view it as just ‘improvisation’, to be really open-minded about it from a stylistic standpoint. Astrophysics is one of the most fascinating subjects there is to me, but I realized fairly quickly that as a full-time occupation, it wasn’t going to beat the combination of the visceral and intellectual involved in making music.

JI: How did music become such a big part of your life?

DT: I can’t ever remember it not being the biggest part of my life. It’s something that’s always been a given for me, for some reason. I’ve been passionate about other things — astrophysics, rock climbing, even computers, but music has always been the through-line, the wise friend with the unconditional love that I can always turn to. As I said before, my mom is an opera singer and for the nine months before I was born she was belting her lungs out five nights a week with me in her belly, so that might have something to do with it…

JI: What is your life like in New York? How do you make it all work in these expensive times?

DT: When I first moved to town I did all kinds of things to stay afloat. I taught French, I designed websites, I accompanied dance classes, I did voice-overs for language tapes, I taught three-year-olds piano, you name it. Then, starting in 2006, I got lucky and won some piano competitions, which gave me a little financial cushion to weather the lean times. It also allowed me to buy a piano. Since then I’ve been able to make a modest living playing music, which I’m extremely thankful for. My costs are low; I was recently joking to a friend that I have the least responsibilities I could possibly have in my life. I’m not married, don’t have any kids, don’t have a car, don’t own any property, don’t have any pets; my rent is pretty low and aside from watering a couple plants in my apartment, basically my only responsibilities are to myself and music. I live in Lefferts Gardens, in Brooklyn, on the East side of Prospect Park, an area that houses an astounding number of jazz musicians, and those two things —the Park and the creative stimulation all around — make my life a lot happier. When I’m not in New York I’m on tour as a leader — I have solo and trio projects that have been getting a nice amount of road time — or as a sideman.

JI: What motivates you and drives you forward on your journey?

DT: I don’t know. That’s perhaps the fundamental question about life, isn’t it? Why are we all doing it? Why are we even trying? In the end we’re all going to die anyway. And even if you believe in the importance of Humanity, beyond individuals, lasting into the future, you can’t ignore the fact that at some point down the line — okay, way down the line — the Sun is going to become a red giant and engulf the Earth. But that’s the rational mind talking. At an intuitive level I find myself thirsty for learning and expression. I’d love to find out how creative I can be. I also know that becoming an artist is essentially the process of getting to know yourself, of resolving, or at least becoming conscious of, your inner contradictions, and that’s a deeply attractive path to me. I don’t know why that is, and that’s kind of the beauty of it. I’m definitely at my most creative and free when I can manage to get a good grip on how futile the whole operation is anyway. It’s kind of a wonderful feeling, the realization that we’re really just doing it for the fun of it, because we feel like it. Art, to me, is fundamentally an expression of that, the mysterious human need to document our existence on Earth by leaving behind an expression of our own unique sensitivity: it has no justification but itself; we like it because we like it.

JI: Can you talk about the process of composing for you? How do you approach this task?

DT: That’s a tough one. Composing is hard for me, and I take comfort in knowing that it also is and was for some of the great musicians that I admire. One of the best ways for me to write is right before a jam session: I’ll sit down about an hour before the session is supposed to start with the simple goal of writing something down, whatever it may be, that we’ll be able to play together on the session. l’ve written some of my best tunes this way. It helps to know who I’m writing for. After more than fifteen years of composing, I finally feel like I have some kind of philosophical grip on what composition is: it’s the process of finding sounds that you like and writing them down so that you can remember them. *Like” is the important term here. Nothing else really matters — the theoretical constructs, etc., are nice for building an underlying architecture, but ultimately the only thing that matters is whether you dig it or not. So I try to stay really close to that feeling: if I’m writing and something pops into my head that sounds good to me, I rush to write it down before I second-guess it. And sometimes a tune just pops down, fully formed, from God-knows-where and you write it down. But you can’t count on that. Right now I’m writing a piano concerto for myself and the Prague Castle Guard orchestra in Czech Republic that we’ll premiere in May. It’s my first time writing for orchestra, and it’s daunting! But I love feeling challenged.

JI: What is it about musical improvisation that you find so valuable? What does it offer to you, your band-mates, and the listeners? What motivates you and drives you forward?

DT: That’s an excellent question. Why improvise? Why not just plan everything out ahead of time? Aside from the obvious answers — it’s less work, it makes it different every time, it’s more fun, etc. — I think it fundamentally has to do with desire. Desire in the sense that in all great music, there’s a palpable desire, a need, an intent, behind every note. With written music it takes a truly brilliant performer to be able to muster up that desire for every note when the notes were written by someone else. That’s what makes lesser performances of Bach so boring — all we hear is a bunch of notes. But when Glenn Gould played Bach, for example, he could somehow make it sound like he was creating the music as he was playing it. With improvisation, there’s no reason to play a note unless we deeply desire it. We can just lay out if we want to. So we have the opportunity to create music where every note we play comes from a clear intent — on a bluesy day we can play darkly, on the day we fall in love we can play with pure joy. When music has desire behind every note, it can be unbelievably powerful, and I think improvisation maximizes the possibility of that happening. This isn’t a guarantee, of course — even in improvisation, it’s perfectly possible and pretty common, especially since the advent of jazz education — to play superfluous notes… But at least the possibility is there.

JI: As an artist, your state of mind and ability to dig deep is important. Outside of playing, what do you do to re-center and find peace of mind? What do you do to break through all of the surface stress in our contemporary world? Or perhaps, you feel that angst is good for music?

DT: I think my single deepest source of perspective is Nature, mountains especially. I used to be a fairly dedicated rock climber and mountain climber; nowadays I don’t get out as much as I’d like but I did manage to climb Mount Rainier, outside of Seattle, this summer, with an old climbing buddy. We took a little-traveled route to the summit that really got us away from everything. There’s this completely obvious timelessness and majesty about mountains that you can’t possibly ignore, and there’s nothing like them, to me, if what you’re looking for is some perspective. It’s always a dance between spending time deeply involved in the Work of music to the point of creative exhaustion, then re-filling the tanks with the help of a wide-open view.

In one scene, Riggan Thomas (Michael Keaton), an aging Hollywood actor trying to make a grand artistic statement on Broadway, asks his daughter (Emma Stone) about the thousands of small dashes she’s been drawing on a roll of toilet paper. It’s a trick she learned in rehab, she explains, each of the dashes representing a thousand years, the entire roll representing the age of planet Earth (4.5 billion years), and the last toilet paper square standing for the amount of time (about 150,000 years) that modern humans have been around. The lesson: let’s step away from ourselves for a moment and contemplate how small we are. Let’s reevaluate. Riggan responds by absent-mindedly wiping the mustard off his mouth with the square representing humanity (the daughter: “You just wiped out the entire human race!”). Sure, we’re small and our selfish focus on our own small troubles looks ridiculous from any real perspective, but who cares, really, when it’s all that’s in front of your nose?

In another scene, our hero walks by a man on the street declaiming Macbeth:

[Life] is a tale
Told by an idiot, full of sound and fury,
Signifying nothing.

In the context of the movie, it’s easy to miss the fact that the choice of the excerpt here is important. I initially took it to be a scene about acting (which it also is), with a famous monologue thrown in for good measure. But it’s not just any old monologue; it’s the classic line in which Shakespeare makes his strongest statement about the absurdity of existence—or at least, how absurd it all seems if you believe in nothing. Riggan has a piece of paper taped to his dressing-room mirror that reads “A thing is just a thing, not what is said of that thing”—basically a Buddhist sentiment that we see Riggan trying to honor through meditation and breathing exercises. He tries hard to ignore the narcissistic voice in his head. And yet, in the ultimate irony, it’s a New York Times review, at the end of the movie, that settles the question of whether his play is any good or not. We have no idea until then one way or another, and no-one else seems to have any idea either. Perhaps the only important thing about a thing is what is said about it? It’s a messy world, folks.

Speaking of messy, how about the scene where the screenwriters bring two of the classic performer’s nightmares together? I’ve had both of them, many times: in the first, you know you’re supposed to be on stage but you can’t find it (see Spinal Tap—they had it too); in the second, you’re on stage and you realize you’re only wearing underwear. Riggan is subjected to both, in a plausible real life scenario, at once. Oh, the humiliation! And oh, the fine line between total embarrassment and greatness—there’s nothing more riveting than a human being doing all he can to transcend humiliation, specifically because we, who are watching, know that the success of the effort is entirely predicated on whether we feel it’s successful or not—i.e. on what we will say about it. It’s a moment of total power for the audience—the power of judgement. And perhaps this is what’s lacking from a lot of music I hear today, particularly in jazz—where is the risk? Where is the potential humiliation, to be battled with? And in the absence of the potential for total failure, what’s really in it for the audience? Shouldn’t every performance be a retelling of the story of Icarus (hopefully with a happier ending)?

Madness. What would we do without it? The film is quite clear on this point: people wouldn’t make much art. To make art is to believe that things matter; that we ourselves matter, when much around us is telling us the opposite (speck of dirt on rock around the Sun, etc). This recalls the great line from Moby Dick:

You is sharks, sartin; but if you gobern de shark in you, why den you be angel; for all angel is not’ing more dan de shark well goberned.

I.e. it’s not a matter of suppressing the shark within us, but a matter of managing its energies. In the same way, the schizophrenic voice in Riggan’s head seems to be the plague of his existence, but it’s ultimately what leads him to give a performance where he actually “risks all” (his life), and which lands him the all-vindicating New York Times rave. The last scene is particularly telling on this point: at first it seems that his near-death experience has enabled him to finally leave his narcissism behind, a shift visually represented in the film by Riggan’s ex-action-hero persona meekly sitting on the john. Our expectation, at this point, is that our hero has finally seen the light and will from now on live in the land of reality, not some desperate and self-destructive clinging to “being great.” Not so. The very end of the movie refuses to do away with madness, and in fact embraces it anew, and for the first time in a way that other characters in the movie can see as well. Perhaps Riggan has finally managed to make his madness his own—to govern his shark.

For life is ultimately absurd. If we know we’re going to die, then why live? Because we want to, that’s why. And there’s no explaining that desire, beyond the fact that eons of evolution have selected for the organisms that most want to survive. Schopenhauer* said

Man can do what he wills but he cannot will what he wills

and that is, to me, one of the most profound things that can be said about our existence. You can do what you want (if you’re lucky), but you can’t decide what you want. Somewhere in the mystery of our desires—of why we want certain things and not others—lives the concept of God. And Birdman, by exulting in the absurdity of our existence, manages to be one of the most profound movies I’ve seen.

It’s also very funny, viscerally compelling (I was on the edge of my seat for much of the movie), technically stunning (most of the film appears as a single long shot, although it’s not actually), and has great performances throughout. I loved the many abrupt shifts in tone as the movie progressed, many of them registering only as changes in an actor’s face. Most were overtly theatrical, perhaps even overdone by film standards, but this is a movie that is very much about theater. Early on, Riggan’s actress girlfriend breaks the fourth wall and summons us, the audience, into the play’s opening night in a way that directly recalls A Midsummer Night’s Dream‘s Puck. Shakespeare is never very far away here.

A word about the music. Aside from a few 19th-century orchestral excerpts, it’s all Antonio Sanchez playing drums, unaccompanied. Although that may sound unpromising on paper (unless you know Antonio’s playing—he’s one of the best jazz drummers around), it is highly effective film music. I wrote my first feature film score in early 2014 (for Alexis and Bodine Boling’s Movement And Location) and the first thing I learned was how powerful film music is. It can singlehandedly set the emotional tone of a scene. It was a revelation for me, because in the music I normally write, I think mostly about the structure and language of the music, not its affect, in much the same way that as I’m writing these words, I’m not thinking about how you, the reader, are going to feel while reading them—I’m only trying to convey some ideas. The emotion the music carries is something that emerges after the fact, on its own, not something I purposely craft. This is turned on its head in movie music, and that’s probably why most film scores are conservative from the perspective of their musical language: what’s essential is to convey emotion, so the most accessible language is often used to make the communication of that emotion as efficient as possible. What I was reminded of, watching and listening to Birdman, is how the emotional impact of music is itself a mysterious thing. How is it that Sanchez’s drums, those pitch-less hits and sizzles, can convey such a wide range of angst, anticipation, mulling, self-loathing, catharsis? How does that come through? It does, somehow. There’s no recipe for emotion in music. The surest bet is probably, if you’re the performer of the music, just to try to feel the emotion yourself, and trust that it will somehow be conveyed to the viewer—a process that sounds a lot like the work of an actor.

*the internet is great. I always thought that line was from Einstein, but looking it up just now, it turns out he was quoting Schopenhauer, whom I’ve never read, when he said it in a 1929 interview.

As I look back over the last ten years and the peculiar journey with J.S. Bach that the time represents for me, it’s sometimes hard to believe that I’m here, now, playing the Goldberg Variations from memory in their entirety, for sometimes sizeable audiences, well enough apparently to get enthusiastic approval from the classical section of the New York Times. I’m really a jazz pianist, after all, and the Goldbergs are hard. And the crazy thing is that I never set out to do this in the first place. How did I get here? The best answer I can give, to echo an experience many musicians have reported through the years, is that Bach taught me.

I grew up in Paris, France, in an American family, and started studying piano at the local conservatory when I was six. I was never asked what I wanted to play, as some of my friends in the US were—playing TV themes wasn’t on the radar. Mostly, I was made to play Bach, lots of it. At the same time, following the example of my grandfather, a jazz pianist on the West Coast, I started improvising, and that mode of music-making quickly took over my fledging artistic identity, even as I kept going through the classical repertoire with my teachers at the Conservatoire.

So I grew up with solid classical training paired with an all-out obsession with jazz and improvisation, which I mainly taught myself. In my early teens, I discovered the Goldberg Variations at a friend’s house in Paris, as recorded by Glenn Gould in 1981, and they took hold of me then like the most beautiful and tenacious earworm. Still, it was only in my early twenties, while studying jazz at the New England Conservatory, that I got a score, and even then, it took me a long time to look past the Aria. Slowly, out of what felt like simple curiosity, I started learning a Variation here and there, in breaks between practicing jazz scales. By the time I moved to New York, in ’06, I had learned the first five, at most. And yet, even as I put all my efforts into breaking into the New York jazz scene and developing a personal voice as an improviser, the Goldbergs stuck with me. I kept coming back to them, and found a classical teacher, Zitta Zohar, who convinced me they were somehow within reach.

The jazz pianist Fred Hersch, a long-time mentor of mine, recently reminded me that he had asked me, back then, why I was spending so much time learning the Variations, music that I would presumably never perform. Apparently I answered, “I don’t know—it just feels like something I have to do”. And so I soldiered on, slowly and not all that surely.

Meanwhile, my jazz career was developing. I got a boost from the American Pianists Association’s Cole Porter Fellowship, a competition prize that included a fair amount of touring. And so it was that I found myself backstage at a small concert hall in Czech Republic in early ‘08, fifteen concerts into a twenty-day solo tour, nearing creative exhaustion. I had decided for some reason that the gigs should be freely improvised, and I was starting to run out of ideas. So I decided to use the Goldbergs as inspiration: I played the first four or five, and followed each one with long, freeform improvisations that used the spirit of the preceding variation as a jumping-off point. The audience’s reaction surprised me—I walked off stage feeling that something special had happened. So I tried it again the next night. Bach’s genius suddenly struck me hard: instead of panning for gold dust in a cold and barren stream, which is how it increasingly felt to make improvisations up out of nothing, using the Goldbergs as inspiration was like starting with a giant gold nugget in my hand. Each one had such an utterly distinct identity. Suddenly my improvisations, though still totally speculative and fanciful, had as their subject something very specific, something rock-solid and strong.

And so my improvising started to teach me about Bach. Back home, as I turned to him again with renewed enthusiasm, I wanted to know why it was that each of his short pieces felt so entirely of a piece. The answer—Bach’s extreme compositional economy—took a long time to reveal itself to me; strangely, it didn’t jump out at me at all when I was just learning to play the pieces. And yet, to take an early and simple example, Variation 2 introduces a motive in its first half that gets repeated nearly verbatim in every single bar of the second half, this motive itself being derived from the oscillating bass-line figure that repeats throughout. I can only describe Bach’s strategy for saving the piece from predictability as sleight-of-hand: like a skilled magician, he continuously directs our attention away from the obvious. The clockwork machinery hides in plain sight.

He uses misdirection throughout the Goldbergs, in fact. Where a lesser artist might have wanted to make his achievement in devising a series of canons at every interval from the unison to the ninth clear to the listener, Bach often seems to do everything in his power to hide it, even as he never breaks from strict canonical form. Besides the continuous overlapping and crossing of voices, which is its own form of disguise, there’s a wonderful moment in Variation 12 where the third voice, which is free and not subject to canonical rules, steals the thunder from one of the 2^nd voice’s entrances by playing its melody a third away, a beat early.

Only the least pedantic composer would do such a thing. And this is in a canon at the inverted fourth, where a listener’s chances of anticipating the canonic response are even lower than in the non-inverted ones! An advanced volleyball-like fake-out is being deployed against an opponent who couldn’t possibly return the ball if he tried. Bach, I slowly realized, had his cake and ate it, too: his structures, if you look, are as plain as day and as solid as the steel skeleton of a modern building, and yet we rarely, if ever, notice them (as we often do, for example, in Handel). We only hear the incredibly expressive melodies, the rhythmic inventiveness, the continuous small surprises. Has a rule-follower ever been less boring than Bach?

By the summer of ’09, I had worked up enough courage to play eight of the Variations, followed by improvisations, at a small solo concert in Paris. I had been studying Zen philosophy and believed wholeheartedly that an improvisation should have integrity, as a piece of music, if I only put myself in an unobstructed frame of mind and let it flow, as it were, out of me. And the audience, for the most part, was convinced—it felt, again, like something special was happening, that I was exploring fertile ground.

But something started to gnaw at me: was it truly right, when Bach was being so phenomenally economical and elegant, to respond in such a freewheeling way? What would happen if I started to borrow some of his structure, too, beyond his emotional leads?

In the fall, I had a small solo tour through the Midwest, and played the Goldbergs on every gig. This strange idea—of following one of the most perfect works of art with quite imperfect improvisations—was starting to crystallize in my mind as something that had a certain legitimacy, partially as a result of personal conviction, but also because of the encouragement I was getting on the road. (I would later learn that the idea of improvising off of the Goldbergs wasn’t new: John Lewis and Uri Caine, among others, had recorded their own treatments of the theme in different ways.) Still, a year went by before I started thinking seriously of recording it. In early ’11, after releasing a jazz piano trio album of original material and writing a concerto for piano and wind symphony, I happened to meet Bonnie Barrett, the director of Yamaha Artist Services in New York. I became a Yamaha artist and saw an opportunity: if I brought in my own recording gear, I could use the Yamaha showroom in Midtown Manhattan to make my solo record with virtually unlimited studio time. As much as I’d been performing the music in public, a part of me realized there was still a lot of work to do. I just didn’t know quite how much.

To make a long story short, I recorded what eventually became Goldberg Variations / Variations three times. Once as I’d been performing it, with fewer than half the Variations and long, rambling improvisations. Then, when I realized presenting only part of a work so whole as the Goldbergs to the world would be an embarrassment, as a much-too-long and obscure investigation into all the Variations, with a non-linear structure and a speculative tone throughout. And finally, once I realized that the purity and coherence of the Goldbergs called out for the most simple and clear structure possible, the way it finally ended up, with each of the 30 movements alternating with an improvisation of similar length, closely linked to the preceding Variation.

Since I essentially learned to play the second half of the Goldbergs while I was recording it, I started to think of the project less as a record of a live performance and more as a conceptual work that might end up only existing as a recording. There are, after all, many electronic and pop artists who never perform their work live. Recorded music can be a destination of its own.

The recording process was a powerful learning experience for me. Suddenly my weaknesses of articulation and phrasing, when I played Bach’s notes, couldn’t be ignored (as they could so easily when I practiced at home, or even when I performed). Alone in the Yamaha space, often late into the night, I recorded take after take of the Variations, and didn’t shy away from editing the best portions together. Glenn Gould did plenty of editing, I reasoned, so why couldn’t I? (I conveniently ignored the fact that he, at least, was more than capable of performing the work in front of an audience.) Similarly, the recording process brought out all the structural, emotional and technical faults of my improvisations. It became clear to me that the only way they could hope to stand up next to the beauty and perfection of the Variations was if they lost most of the indulgence I’d been allowing them to have. They needed to be concise and focused; they needed to get to the point, all while remaining personal. I started to develop explicit strategies. I realized, for example, that I was capable of improvising my own canons, as long as I kept them fairly rudimentary. I realized that many of the virtuosic Variations stemmed from a very restricted amount of material, and tried to find ways to improvise with a similarly limited set of ideas. I saw that Bach gave himself considerable license in the way he navigated the I-I-V || V-vi-I harmonic framework that all the Variations share, and let myself take my own varied pathways through the changes. I researched the last Variation, the Quodlibet, learned the words to the folk songs it uses as its melodic material, and substituted two jazz tunes I love as material for my improvised response. I gradually went from an implicit, alchemical relationship with the Variations to a much more precise and explicit one. And to my surprise, I gradually saw the project turn into something that felt like it had an integrity of its own.

It’s hard to record improvisations. There’s always the possibility that the next take will be better—it’s hard to stop. And yet as I recorded and re-recorded my responses to Bach, I began to recognize a flag that would occasionally go up in my mind, on good days, saying “this one’s good enough”. At first it was only one of my improvisations that felt that way, but I knew I had found a tone that rang true. My goal became to extend that tone, that feeling. I found it in another, then another, and later, in most of them (but not quite all). Saxophonist and producer Ben Wendel came in to help me choose the final takes, and suddenly I had a 62-track, 78-minute solo piano record that didn’t fit into any record-store genre category.

When it came out, at the end of 2011, I figured I would play a couple CD-release concerts and get back to touring with my trio or playing duo with saxophonist Lee Konitz, with whom my musical relationship had been growing. But to my surprise, critics either absolutely loved it (many of them) or loathed it with a passion (a few of them), and it started to take on a life of its own. After the Wall Street Journal ran a smart and generous feature, it even—surprisingly—started to sell.

For the album release, I played the full first half of the Variations for the first time, from memory, and it felt like the hardest thing I’d ever done in my life, like teetering on the edge of a precipice from beginning to end. I played the Paris CD-release gig at the Sunside, a small jazz club, and an agent heard me there who decided to take a chance on me. Soon he had booked a long fall tour for me in surprisingly large venues in France, and it dawned on me that it just wouldn’t be good enough to play only half of the record. I traveled to Cuba and for two and a half weeks studied percussion in the morning and memorized Goldbergs in the afternoons, away from cell phones, internet and acquaintances. An inexperienced performer of classical works, this was slow work for me, but I found it intensely rewarding. The act of memorizing forced me to make sense of the Variations, to organize them in my mind in a way that I hadn’t had to in the recording process. Bach’s economy became all the more apparent, as did the many-fold symmetries that govern the entire work, from the structural to the physical.

Bach was a lover of symmetry. If most of us can agree that symmetry is important in aesthetics—people tend to prefer symmetrical faces to asymmetrical ones—Bach took the idea to the extreme. At the physical level, in almost every variation as well as the majority of his other keyboard works, both hands get treated with exacting evenness, as if he wanted the interpreter of his music to fully appreciate the symmetry of the body, from the hands to the hemispheres of the brain. It’s not so much that the music is equally difficult for the left hand as it is for the right, although that’s part of it: it’s that to play Bach’s music well, one is obligated to bring the same amount of melodic consciousness to the left hand as the right. This is not the case in keyboard music by most other composers, which tends to heavily favor the higher register of the right hand. I’ve always resisted redistributing the voices of the Variations between the hands for this reason, even though it’s fairly common practice to do so in order to reduce hand crossing. To me, the feeling of bodily symmetry is an essential part of the experience of playing the piece.

At the structural level, the Goldbergs exhibit symmetries from the smallest to the largest scales. At the smallest, Bach is constantly playing with inversion, one example being the 16^th-note runs that begin the first and second halves of Variation 26 above, strict mirror-images of each other.

At mid-scale, the rising or falling direction of the canonic intervals offers its own symmetries. Variation 24, for example, starts as a canon at the falling octave, switches to a rising octave on either side of its middle, and ends at the falling octave again, showing palindromic symmetry in its structure.

At the largest scale, the I-V || V-I binary form of the Aria and the Variations, with its central axis of symmetry, reflects the symmetry of the whole work, which similarly starts and ends in the same place (the Aria) and is split at its midpoint in the silence between the 15^th variation and the 16^th variation, the only to be titled “Overture”—a new beginning. The division of the Aria into 32 bars similarly reflects the work’s division into 32 movements, connecting the part to the whole. It’s easy to see this as an analogy of our existences: from ashes to ashes, with life in between. No wonder, then, that the Goldbergs are often described as expressing every possible shade of human emotion.

By the fall of ’12, I had coerced so many friends into letting me run through the program for them at home in casual performances—always with their share of little disasters—that I was beginning to get an idea of what I was up against. Performing the Goldbergs in public is not only a musical and spiritual challenge; it’s a physical and mental marathon, too. There’s no place to hide in Bach’s limpid music—it will immediately reveal and magnify any lapses in concentration, any tightening up of the body, any fear. And alternating between my role as interpreter of the written text and my role as in-the-moment improviser only made the task harder, constantly jolting me out of the possibility of getting ‘in the zone’ as I switched between mental states. To say I was terrified is an understatement, but the truth is that I’ve always been a thrill-seeker, in sports just as much as in music. So the terror had its own attraction. My dad called me an adrenaline junkie. And I think it’s fair to say that it’s during the fall tour that I started to learn what it really means to perform the Goldbergs in front of an audience. The tour was well received, but after I came home to Brooklyn, I heard Piotr Anderszewski play Bach’s English and French Suites at Carnegie Hall and was struck with a mirror-neuron-like physical feeling for how direct and unencumbered his relationship to the piano was. I realized that I had only fleetingly truly relaxed my body into the keyboard when I was playing Bach’s music on the road. A number of people had noted, in fact, how different my body language was between the Variations and my improvisations. The fear of a memory slip or technical slip-up kept my body on edge.

Much of my work since then has been on diminishing the sensation of fear. I realized, for example, that focusing my attention on rhythm and how it manifested in my body was a big help. It gave the notes a context to sit in and directed my attention forward, slightly into the future and away from the paralyzing present. I also realized the obvious, which is that the more I deepened my knowledge of Bach’s text, the more confidence I had when presenting it to an audience. Weeks after a solo performance in Vancouver, on the tail end of a duo tour with Ben Wendel, with whom I had just released a duo record, I got a call from an accomplished baroque harpsichordist who specializes in Bach and had heard my concert there. While he wished me good luck, he told me in no uncertain terms that my performance of the canons needed work. Why would you only bring out the top voice, he asked, when they’re all equally important? I didn’t have the heart to explain that I’d bring them all out if I could—that I was holding on for dear life out there. But I did take his cue and returned to Bach’s score with increased humility, practicing singing the interior voices of the canons while I played the others on the piano, or at other times willing myself to transpose variations to foreign keys from memory, and again at others spending hours obsessing over the exact phrasing of one short melody. Every time I opened the score, I was reminded that there is always something further to discover in Bach’s music—that the more you seek, the more you find. One thing dawned on me: when you’re starting with material of this quality, you don’t need to add anything to it. Your job is to get out of the way, to solve your interpretive problems so as to reveal the work itself as clearly as possible, like scraping mud off a diamond. I’m grateful to the pianist Simone Dinnerstein, a masterful interpreter of the Goldbergs, for generously giving me encouragement and musical advice during this time.

In the fall of ’13, a short solo tour came together on the East Coast, culminating in a show at one of my favorite New York venues, Le Poisson Rouge, a place that will present just about any style of music, from Johnny Gandelsman on solo violin to Laura Mvula with full band, as long as it’s good. Something happened on the tour—something started to click emotionally. I stopped trying so hard, started to let things be, both in the Variations and my improvisations. “Don’t try to make the music beautiful – it is beautiful; just let it out”, the beloved piano guru Sophia Rosoff had told me, and I slowly began to understand what she meant. And after the gig at Le Poisson Rouge, a man introduced himself to me, warmly, as Anthony Tommasini of the New York Times. A day later there was a glowing review in the paper, and suddenly the record was selling better on Amazon than Justin Timberlake and Lady Gaga, if only for a brief while. In the following days I got calls from some of the best presenters and festivals in America inviting me to perform.

What astonishes me about this is that the same critic, a fierce and erudite expert on classical music, may very well have panned me if he had heard me two years earlier. It took me that long to even begin to understand what was at stake when performing this music in front of an audience. And in those two years, my rising standards for what makes an acceptable performance of Bach started to spread laterally to the other types of music I was making, from my composing to my improvising. Dealing with Bach so frequently and—it felt—so intimately made all but the most well structured and meaningful new music feel lacking in comparison.

Looking back, as I prepare for solo shows at the Ravinia Festival, SF Jazz Center and Wigmore Hall in London, I’m amazed any of this happened at all. From many perspectives, I’m sure it would seem that I developed my Goldberg Variations / Variations project exactly backwards. But I didn’t know any better, and that’s probably why it ended up coming into existence—I just followed my nose. Above all, I’m grateful for the opportunity, a truly unexpected one for me, to engage much more deeply than I thought I ever would with one of music’s greatest geniuses, and to let Bach teach me.

Lee Konitz will be turning 87 in October, and his long and distinguished career as one of the most singular saxophonists in jazz needs no introduction (but if you need one, it’s here). He is known in particular for his intense focus on improvisational integrity, a desire for each musical choice to reflect the present moment as much as possible instead of a pre-made plan or habit.

It’s easy to overlook how radical this position is. In many other styles of music, from classical to pop, the goal in live performance is the opposite: to reproduce a carefully thought-out plan as faithfully as possible. Even in jazz, it’s not uncommon for groups to take a hybrid approach where a good portion of the material, even outside of written sections, is predetermined. Despite all this, Lee has somehow stubbornly insisted on showing up to his concerts prepared to be unprepared, and has (mostly) delighted audiences in doing so.

In my seven years of playing with Lee in diverse contexts I’ve been able to observe his commitment to the moment firsthand, particularly in our duo playing. One direct result of his approach is that his music is rarely boring; audiences seem to intuitively understand that something unique is going on; they pay attention in the way that people do when they genuinely don’t know what’s going to happen next.

And yet it’s also become clear to me that our audience doesn’t always necessarily understand what’s at stake when we perform. In his commitment to true improvisation, Lee isn’t taking the easy road. Failure is very much an option. And success, in the form of authentic engagement with the truth of the moment, may not sound like success to a listener used to being wowed by virtuosic effects.

I was reminded of this a few months ago when Lee and I played a duo concert in the Belgrade Jazz Festival. During the afternoon before the concert, I conducted a workshop with young local musicians. A number of them were very talented, but—as is common with young musicians—they had a tendency to play predictable patterns that weren’t closely related to what else was going on. As a result, I spent a lot of the workshop talking about the importance of listening and the goal of reacting as genuinely as possible to what we heard, rather than rattling off what we already knew.

In the audience were a couple of guys in their mid-thirties listening intently. After the concert, one of them approached me and told me that he had loved the concert, but that he might not have if he hadn’t heard my workshop earlier in the day. He explained that if I hadn’t clarified that our main objective on stage was to be as spontaneous and authentic as possible, he might have interpreted the opening of our concert as timid, rather than as a committed search for communication, and walked out. He was an electronic pop composer, and his job was to blow a listener’s socks off as quickly and reliably as possible. But, now that he understood the rules of our game, he found himself intensely engrossed in our concert, bringing his attention to how the notes that we played seemed to accord themselves with the feeling in the room at that moment, and the quality of the listening and communication between us.

I realized then how elusive the concept of real improvisation is. It’s a subtle thing that’s not easy to explain. As a listener, one could even be forgiven for asking what the point of improvising is in the first place. In the following interview, which I conducted for Chamber Music America at the very end of 2012, Lee and I explore this thorny topic, among others. I learned a lot from the conversation.

Dec 4, 2012: Dan Tepfer interviews Lee Konitz

Hosted by Chamber Music America’s Talking Music series
Transcribed by Kevin Sun and edited for clarity by Dan Tepfer

I. Spontaneity

Dan Tepfer: There are a lot of reasons that I feel lucky to have gotten to know Lee over the last seven years.

Lee Konitz: Can you give me one good reason?

DT: Here’s maybe the biggest reason, or the biggest influence that Lee has had on me: we’re sitting here doing this interview, and instead of being very formal about it and, say, trying to adhere to the format of an interview, Lee comes in and he just—this is what he always does—he keeps it real. Janette, in her introduction, talks about mentorship; Lee talks about sex. Or he talks about his teeth falling out. The thing that I really love about Lee is that he’s always expressing his freedom. We talk like this, but he also plays like this, too.

LK: My teeth falling out!

DT: To look at it another way, I always think of Lee as a Zen master. Like there’s nothing keeping you from responding to what’s actually going on in the moment.

LK: Well, I appreciate your bringing that out, because I’m actually pretty shy. I think I have some of what we might call “ham” tendencies in front of an audience. I might figure I have to do something now in front of this audience; what am I going to do? Make a joke, or play a good phrase, or whatever. So usually some silly thing comes into my mind, and, as far as that, I love to hear people laughing.

DT: But you just wait for a silly thing to come to mind; you don’t plan it out.

LK: Oh, right. Well, you know, I memorize some of those lines [laughter].

DT: I just read a novel called Remainder. It’s a new novel by a young author named Tom McCarthy, and the main character is this kind of weirdo who starts to obsess—because his brain was damaged in an accident—over recreating everyday events. So, for example, he goes to a carwash and he gets very obsessed with the experience he had there, which to most people would seem perfectly ordinary. As a result of the accident he’s come into a lot of money, so he decides to hire actors to reenact exactly what happened when he got to the carwash, and he has them do it over and over and over thousands of times with him participating, his idea being to perfect this unremarkable little event. The novel is an exploration of the idea of spontaneity, I think, and what this character is looking for is a form of perfect spontaneity. By rehearsing it over and over again and fine-tuning details of it, he wants it to appear completely spontaneous, but the end of the novel is him realizing that true spontaneity can only happen when unpredictable things happen. And that really got me to think about improvisation, which is something that I’ve learned a lot about from you. So my question is: what is important about improvisation? In what way could improvisation be better than planning it all ahead, planning it all out ahead of time and getting it just right?

LK: Well, I think you could answer that question with a little bit of reflection because we have accomplished that a number of times on the stage. That is one of the miracles of playing this kind of music—that, all of a sudden, you’re in another time frame and another emotional setting and the whole thing feels like magic, and that’s the goal of this kind of playing. The other kind of playing is very valid, of course: being prepared, well prepared, and zipping on through what you know, and it’s certainly a major accomplishment, but compared to taking the chance of walking on the stage and not knowing the first note of what you’re going to play… I swear, considering I’ve been practicing for 65 years—boy, almost 75 years now, I’ve been practicing for a long time—I’ve got familiarity with the keyboard and its possibilities, but the idea for me is to be able to play from the first note whatever occurs to me at the moment. And the only way you can learn how to do that is to do it a lot, and I’ve been fortunate to be able to do that a lot, and I appreciate when other people join me to make it a conversation—a spontaneous conversation—which is very worth doing in front of people.

DT: If you’re on stage and you don’t know what you’re going to play, the experience is really fundamentally different from knowing what you’re going to play, and, for example, I do things where I play classical music where I know what I’m going to play and things where I improvise where I don’t, so it’s a really, really big difference in terms of mental process, but I wonder: does that difference really communicate to the audience?

LK: I think so. For people who are really looking, listening, they know that this isn’t a prepared situation somehow.

DT: There’s something they can feel about it?

LK: The actual movement, the sound projection, and the choice of notes—it doesn’t sound as slick or prepared somehow. Sometimes it’s positively clumsy, but with the right feeling you can get away with murder. I don’t mean murder…

DT: I always think of the greatest classical musicians who can somehow—or the greatest Shakespearean actors, for example—who can somehow put you in a state where you’re listening to them and you actually believe that they’re making up what they’re saying or playing in the moment, even though you know it’s preplanned.

LK: Yeah, but Laurence Olivier was scared to death of standing in the wings, as he was quoted saying. He was that well-prepared, and he still feared something spontaneous was going to happen. Couldn’t handle it maybe, or something like that.

DT: Do you remember if there was a specific time when you got a clear conviction that being spontaneous was a legitimate way of performing?

LK: Well, it was the result of playing a number of times. I then learned that this was honest, an honest endeavor, and it gave me great faith to spend the rest of my life trying to develop that technique.

DT: So that was 1947? Was that something that you realized immediately when you started playing, or did it take a while?

LK: No, I was very nervous at the beginning and just foomphing on through at some point or another without really knowing what I was doing, I think, and then gradually I got more familiar with what I was doing and how to play it out to the listeners without designing it specifically for them—just to do what I had to do and hope that they could experience it in some way, rather than, you know, preparing to hit a home run in front of the people and all those kinds of things, which I think most jazz musicians that I hear over these years do: prepare so that they have a clear effect on the audience.

DT: Now, if you heard a musician who comes across to you as having something prepared, but you heard him two nights in a row and he played completely different stuff from one night to the next, but still came across as being prepared, how would that affect you?

LK: That would affect me very positively, I think. Strangely enough, Charlie Parker, who I had heard before I came to New York on a 10-inch acetate record, sounded so knowing of what he was doing that when I went to the Three Deuces and heard him play, I said, “Wow, that sounded like the record.” So I realized then that he was really prepared, well-prepared, and listened to him that way and appreciated how well he did it—when he did it well—in the same way that you would appreciate a classical player. They talk about [Vladimir] Horowitz missing notes and [Arthur] Rubenstein missing notes and things like that, but we were left with the great feeling that they gave to that music.

DT: So Charlie Parker is obviously somebody that you admire, but also we’ve talked a lot about Lester Young—also somebody that you and the whole Tristano school greatly admire, and so I’ve heard you on the one hand talk about him as being one of your greatest influences, and on the other hand also acknowledge that on some of those classic solos of his early recordings it felt to you like it was probably fairly prepared.

LK: Well, I think so. Playing every night with a big band where you have a chance to play a 32-bar solo or less, you kind of, you know, end up with something similar each time. You anticipate the background coming in and things like that.

DT: You start to develop a feeling for what works and what doesn’t.

LK: You don’t have time to just stand there and relax; you just pump away. And he was, I think, in condition enough, psychologically and the other way…

DT: Physically?

LK: —smoking, getting stoned, so he just got right to the point.

DT: And what do you make of somebody like Stan Getz, who, from what I’ve heard even from guys who played with him, the first time he played a tune, he would really be improvising. Somebody would teach him a tune; they’d be there at the sound check, and he’d learn the tune by ear from somebody—he was really, really quick—and he’d play his first solo—brilliantly—and then the next night he would play another solo that was kind of closely related to the previous night, but pretty different. And the third night would be a mixture of those first two solos, and by the fourth night it would be starting to crystallize, and then by the fifth night he would have started to develop this very perfectly structured solo that would then become his fixed solo on that piece, and after a while he’d have to fire his band because they knew his solos too well! What do you think of that: somebody who has the ability to improvise but chooses not to?

LK: Well, it’s kind of the easy way out.

DT: Aha.

LK: He had perfect pitch, or perfect recollection or something. I believe he could repeat things the first time he heard them, but then he would be dependent on that.

DT: So this is what I’m so fascinated about. Faced with all these influences in your life—people whom you really respect who took what seems like a different approach—you still developed total conviction in the power of really starting fresh every night.

LK: Well, thank you for verbalizing that. That’s what I intended to do, but I’m very pleased that that’s happened as many times as it has over my playing career, so that it feels that real to me and not just an accident. I don’t get stoned anymore, so it’s not dependent on that or things like that.

DT: I talk to young guys sometimes—not that young, guys my age—

LK: Not very young anymore… [laughter]

DT: —and sometimes there’s almost a backlash against this kind of idea. I think one thing that’s happened—

LK: Do your improvising at home? Is that what you’re talking about? Go out in public and play what you know?

DT: —I think some people feel that the idea of valuing spontaneity very highly could actually be an excuse for laziness.

LK: Absolutely. I fought for that. [laughter] It’s a good opportunity to have a little nap or things like… No, I mean, it’s a specific discipline that requires specific attention and can be developed, I think.

DT: Well, that’s the thing, right? If you’re going to decide to take that route, you’re going to have to be really, really good at that, otherwise it sucks.

LK: Yeah, absolutely. See if anybody came in that didn’t hear that last word.

DT: For example, I was hanging out with a friend of mine a few months ago and he played me two takes of an Ahmad Jamal track—an early track—and they’re just two takes of the same track from a record date, and Ahmad plays pretty much the same solo on both takes. And my friend’s reaction was, “Isn’t this amazing? He cared so much that he developed his solo and wasn’t improvising!” To him, it was a very positive thing, and he also brought up Thelonious Monk, who would sit at home practicing one of his compositions over and over and over again until he kind of worked out what felt like the right thing to play to him—

LK: And he’d play it over and over again.

DT: —and that’s what he would play in public, maybe rearranging the order of the pieces of the jigsaw puzzle or whatever. But basically, to my friend who’s a musician I really respect, that was like, “Look how much these guys cared. They weren’t just going out there unprepared.” So this is the crux of the matter to me—why you’ve decided to take the approach you took. Because the thing is, when you, Lee, go out there unprepared, it’s pretty much always great. I don’t know how you do it.

LK: I’m not unprepared! I mean, I’ve been preparing for 70 years, but not in that specific a way, I presume.

DT: So how do you practice this?

LK: I just improvise. I just practice improvising, trying to stay in that frame of mind and remembering things that occur to me that are interesting and jot them down maybe, just to refer to them. And then I go on to the next thing.

DT: So maybe it’s about preparing your taste and not the actual specific information?

LK: It’s definitely taste first. The information is a result of that taste, I think.

DT: So if your goal is to go out on stage and be authentically in the moment, how strong is the influence of the players that you’re working with?

LK: Very strong. It depends entirely on their response, or else I’m playing by myself. It’s easier with only one other person. As soon as you add a third voice and a fourth voice, even though they’re bass and drums usually, you’re responsible for hearing all of that and using it in some way and relating to it in some way, and that is, phew, that is difficult.

DT: And yet, in your career, you’ve toured all over the world—

LK: Not China!

DT: —and played with a lot of pickup bands.

LK: Yes, I have.

DT: So what do you do when you get on stage and you’re playing with people you’ve never played with before, and you realize, you know, three bars into the first tune that they’re not on the same wavelength, in terms of actually listening and trying to create fresh music.

LK: Well, if I continue to play during those few bars, and I obviously am not on the right wavelength to relate to them, then the first thing I have to do is cool it and listen to them—

DT: So you just stop playing.

LK: —and just be influenced by them. Whatever they’re playing can influence me in some way to some degree, and that is what I look forward to.

DT: So whomever you’re playing with, even if what they’re playing isn’t that inspiring, you have to say yes to it.

LK: Yeah, and if it’s not gonna work I’m going to know quickly enough and not do it again, you know.

DT: Now, is this search for spontaneity a reason that you’ve changed bands so much?

LK: No, it’s a result of being asked to do gigs by different people. I’ve never been a gig hunter, so I wouldn’t work if people didn’t invite me, and when I realized that all the guys knew how to play “All the Things You Are” to some extent, I knew I was kind of in business to that extent, since I just know about seven tunes, but I know mine in all keys and stuff like that.

DT: What about change in keys? I remember when we first started playing together we did a tour in Japan without a bassist, just with Richie Barshay on drums and me on piano, and somehow on that tour you were changing key and changing tempos all the time. Now, is that something you do, is that a technique to keep things fresh? Is that something you do when you’re feeling like something’s lacking?

LK: If I just feel like doing it and I’m not concerned that it’s going to upset anybody, really, I’ll do it. I’m not complaining; I’m just trying to stretch it out.

DT: So you’d only do that if it feels like the situation is right for it.

LK: Yeah, and in that particular situation there’s no problem with the drum notes, and I know I can depend on you, so that’s pretty safe territory for me.

DT: And is there ever a situation where you’d actually throw a wrench in the works?

LK: Uh, not voluntarily: just closing up in some way and not feeling compelled to keep going when I’m not listening.

II. Learning

DT: In the West there’s this whole tradition of learning in a classroom, so information is presented in an intellectual way. It’s on paper and you’re supposed to take it in, somehow make it your own, and then put it out in a way that doesn’t sound like you learned it academically. But in a lot of other cultures music is learned through an apprenticeship model.

For example, I was in Cuba earlier this year in April studying with the great percussionist Changuito. The way he teaches is, simply, that he shows you something and he stays with you long enough that you can do it, kind of, then he leaves the room and you work on it on your own until you get it right, and then he comes back and he listens and he plays with you as you play it, and if it feels like you’ve gotten it then he shows you the next thing. And that’s the way music is taught in a lot of parts of the world. There’s never necessarily a verbalization of anything; it’s really about the practice.

That’s what I feel like we’re missing a lot in the way that music is taught in the West, and that’s why I feel so lucky to get to play with somebody like you, because that’s one of the places where I get that direct experience of the history of jazz, beyond what can be put into words.

LK: I think that being able to express it in words is to some extent a newer thing that’s adding to the learning process—in this subject especially—and I think that’s welcome if it’s done in the right kind of spirit. If people actually measure specifically what that is, you know, why you use a metronome to do a certain time realization and somehow talking about the use of the scales, why you use this scale against this chord or whatever kind of analysis—that could help to be talked about to some extent.

DT: Do you see a danger in that?

LK: No.

DT: You’re saying that it has to be done—

LK: No, I’m saying that’s a welcome addition, I think.

DT: —but you said it has to be done in the right kind of spirit.

LK: Yeah, it should be done after the fact, after you’ve already realized it somehow through just trying it. Then you might gradually want to put it into words to someone else, maybe—to other players or something like that.

DT: So in other words, the information should really come to you through the music—

LK: I think so, first of all.

DT: —and then be verbalized.

LK: Yeah.

DT: I think that difference in order is something that we often get wrong.

LK: Yeah.

DT: For example, when you talk about transcribing, you say: first listen to the solo, then learn to sing it, then play it on your instrument, and finally, if you want, write it down so you won’t forget it, but that’s absolutely the last step. The first two steps are really aural, and they force you to organize the information in your own way, whereas I think a lot of people who transcribe actually do it backwards.

LK: Yeah, I think so.

DT: What’s the difference?

LK: Well, you know it, somehow, before you analyze it. I think it’s necessary to be able to hear internally, to be able to express it away from an instrument and then to be able to write it down. It’s like a new experience when you try to put it into notes.

DT: How does the knowing part feel to you?

LK: It means that I can express it by voice or whistling it or playing it before reading it, the finished product.

DT: A person could write down the notes without actually knowing it; they could write down the notes and still not know how to phrase it, or what the feeling is.

LK: Yeah. The Charlie Parker transcription books have a very limited effect because all you get is a litter of notes that could be anybody’s notes, almost. But to learn the solo by yourself makes it very much a part of you.

DT: It’s funny because you can almost think that you’re learning it by yourself if you write it down first, but somehow there’s something really different about using your memory and your intuition or whatever it is that’s happening when you do it without paper. I’m fascinated by how different that is and why it is so different.

LK: Well, it’s just a very specific process, composing a piece like that from learning by ear and then recomposing it, if you will, or transcribing it.

III. Originality

DT: How much do you value originality and did you ever consciously set out to be original?

LK: Not really, no. I was made aware that there are original players and copyists early on and…

DT: By whom?

LK: By colleagues around, you know, fellow musicians. I heard them copying Charlie Parker, basically, or Lester Young or some prominent players. They were using them as models, learning from them as models as young people sitting at the Metropolitan Museum copying Van Gogh learn that way, to know exactly how you do that. And since I couldn’t identify with Charlie Parker’s experience as a human being, so to speak, I was just going by the music, the notes, the way they were played and hoping that I didn’t try to copy him when I left the room and went out to play in public. I usually got away with that by telling people that it was too hard for me to imitate him [laughter]. And I ended up being one of the only alto players that didn’t try to play like him, even though I was copying all his solos and everything, and I found it difficult to play with that kind of energy and that kind of brilliance and all of those things, so I used what energy I got from that and whatever notes, construction of notes, and whatever good phrases and then I mashed it up, mixed it up myself into my way of playing. And all the guys put me down because I didn’t sound like Bird, and every time I met Charlie Parker he said, “Thank you for not trying to play like me.”

DT: I’ve heard you play Charlie Parker solos, even in the last few years.

LK: You mean parts of his phrases?

DT: Not on gigs, but I’ve heard you backstage.

LK: Going through specifically his solos.

DT: Going specifically through a Charlie Parker solo. And obviously you can play many of Lester Young’s solos. That’s interesting to me, because I think some younger players think, “I don’t want to sound like my model,” so they shy away from that kind of study. There might actually be a will to stay away from it, to keep away from directly transcribing. But you totally went there: you studied Charlie Parker as hard you could, you studied Lester Young as hard as you could, and yet you came out sounding like yourself, so there must have been a conscious awareness of the difference between copyists and creators, as you said earlier.

LK: I think Tristano helped make that real to me. First of all, it took me a long time to get around to studying Charlie Parker because of my relationship with Tristano—it felt like it was in another neighborhood. He suggested, certainly, to absorb: this is the master, absorb what you can and make it your own. And that’s pretty much the way I pursued it.

DT: I just love how mysterious these questions are. I mean, how would you go about telling somebody how to on the one hand study as much as they can of their models and on the other stay true to themselves?

LK: Yeah. Well, when I actually played one of his solos pretty precisely, I felt like someone else to some extent, and that was a little bit not comprehensible in some way—how I could change like that. And then I got stoned, and then that really changed, and boy, that was nice! I mean it was still incomprehensible to an extent, but phew, it was very nice terrain to try to traverse. But I somehow felt that I was going to live for a long time, so I thank you [knock on wood] very much for whoever you are up there for letting me stay around and try to get it right.

DT: You felt like you were going to live a long time when you were young?

LK: Oh, I don’t know that exactly, but I never planned on leaving.

DT: You didn’t like the storyline of burning out young?

LK: No, I saw too many of my colleagues dropping the thing way young—Charlie Parker at the age of 34, and Charlie Christian I think at 22, something like that—and it was a great loss, these very talented people.

DT: So the fact that you felt like you were going to be around for a long time was one reason why you felt like you could take your time with the music. You didn’t have to force a result, or…

LK: Well, I felt like I needed some extra incentive or work ethic to be able to practice my eight hours a day like Coltrane presumably did. If I got an hour and a half in, I felt like, “Oh good, I had a good day.” But, you know, I’m still around, so my hour and a half didn’t do me in completely, or something.

DT: So for you there’s always a very clear sense, when you’re playing, of whether you’re sounding like yourself or not.

LK: Yeah, in the sense that it feels like the music is available, that whatever I decide to do during those moments is feeling nice to me—feeling correct, if you will, or pleasant, or whatever. It feels like I’m doing what I enjoy doing most, and I just try to get into that place as much as possible, alone and then with varieties of people.

DT: So being yourself is the feeling of being able to do what you want.

LK: Of course.

DT: And if you’re playing pre-prepared music you can’t be doing what you want, because you prepared it at a different time when you presumably felt differently than you feel at that moment.

LK: Yeah, but that’s a whole different philosophical goal to reach: to play something prepared, you know, is a major achievement if it’s well done and well conceived.

DT: So one could find authenticity in that, too.

LK: Yeah, absolutely. I never feel superior in that sense; I just feel that I’m happy to have found a place to function to some extent.

DT: So it’s not a feeling that this is the only valid way there is, but a feeling of having found something that worked for you.

LK: Right.

IV. Drugs

DT: I’m curious if you feel like in your life the influence of the very limited amount of drug-taking you’ve done has been important, or whether basically your evolution as an artist would have been the same without it.

LK: I can’t answer that accurately, of course, but I know that at some point I felt like I knew that that was something that I loved to do, at best, and that I wanted to live my life without it. I felt a dependence—wanting to have a poke [smoke a joint] before I faced the audience and all that kind of stuff. And when I found out that I didn’t really need it, that was a great reward for me and it’s remained that way. I haven’t snuck a poke before a set since (that anybody knows about) [laughter].

DT: Occasionally you encounter musicians, very brilliant musicians, who will come to rehearsal and sound incredible in the rehearsal, playing very accurately, with great energy and investment, and sometimes—this has happened to me a few times—they’ll be very well-prepared, incredibly serious, and you’re very impressed. You’re thinking, “Wow, this is great, I’m so happy I have this guy here,” and then you get to the gig and they will have taken something that makes them really different. It can even get sloppy, and that’s so disappointing. You’ve seen that, right?

LK: Yeah, of course. Or just freezing up cold sober in front of the audience. Something can be turned off completely in that process for some people.

DT: You mean if you don’t take anything.

LK: Yeah, just the fear of functioning, of being that transparent or that naked in front of a bunch of people looking and listening. That’s very intimidating.

DT: So you were saying at the very beginning of this talk that you felt like you were a shy person, and so maybe in a way the biggest role of taking a poke or whatever was just to combat that rather than creative reasons?

LK: Well, sometimes after a poke I was more shy, so I had to be careful of that, too. More self-conscious, you know, “What am I doing?” and things like that.

DT: Well, that sounds like it hasn’t been entirely positive, then.

LK: No, and thankfully I didn’t have to get into all the heavy kinds of things. Pot was the only thing I liked; I didn’t like to drink or anything like that.

DT: Probably why you’re still around.

LK: Probably part of the reason, maybe. I know some 85-year-old guys who are stoned every day, and they know who they are, right there. [Laughter]

V. Competition

DT: In the book that you did with Andy Hamilton—this is a great book if you guys don’t know it, Conversations On the Improviser’s Art, a great book on jazz—Sonny Rollins challenges you to a duel because you were a little critical of him in a very respectful way, and so he said, “Well, we gotta work this out in a duel,” and first it’s with swords and then it’s with saxophones. What role has competition played in your evolution and do you think that’s important to the scene?

LK: I think that’s unfortunately important, and I’m not a strong challenger in that sense. I was very intimidated by the new guys who really knew what they were doing, so to speak. Trying to improvise in that context feels very, you know, you gotta start someplace and develop slowly. But the other way, [claps] you jump right in to it. You hit a home run and then you’re done or whatever, so I was very inhibited by that.

DT: Because your approach takes more time.

LK: Yeah, and it’s really different all the time. Sometimes it starts with a few spare notes; sometimes I can jump into it immediately. It all depends.

DT: You can’t count on it.

LK: But people who are prepared can count on it. That’s the idea, being prepared.

DT: And yet this is an idea that really interests me about your life. If you look at your career, starting when you’re 20 you’re totally at the top of the game—being hired for great gigs, being hired for great recordings. I mean, you’re really, really active. Maybe you had a less active period, but that was in the ’70s or ’80s. You were totally in demand for a long time without, as you say, being able to get up there and immediately blow everybody out of the water.

VI. Playing Sharp

LK: But part of my charm, if you will, was I played sharp frequently, which made a whole different tonal relationship between the rest of the instruments, which I call “antisocial” in some way, but whatever sound that I was able to produce on the instrument was what got me the job with Miles Davis’s Birth of the Cool because I fit into that ensemble according to Gil Evans and Gerry Mulligan and those guys, you know what I mean?

DT: I know what you mean, and this is something else that I love about you that I’ve observed over the years, which is: some people will say, “Oh, Lee Konitz plays sharp,” but, in fact, when you want to you’re able to play more in tune that anyone I’ve ever heard.

LK: Ah, look at that. Isn’t that a nice thing to say?

DT: No, but, I mean, it’s exactly what you just said: you will play sharp if you feel antisocial, but you’ll play perfectly in tune if you feel social, and I think that the expressivity of intonation is something that doesn’t get used enough.

LK: Well, that’s the fact, I think. Jackie McLean didn’t want to talk about it. I went into a club where he was playing with Cedar Walton’s trio and the pianist Larry Willis was sitting at the bar in front of me at the Village Vanguard, and Cedar played a couple tunes then called Jackie up, and Jackie was sharp! I mean, no playing around, he was sharp. And so after a little while Larry turned around to me and said, “He can push it in or pull it out, but don’t leave it where it is!” [laughter].

I kind of talked to Jackie afterwards and he didn’t want to talk about it. That was it, that was the way he heard it, and that’s the way I hear it. Sometimes it’s a little bit on the edge, but some so-called critic reviewing a record said, “I can’t stand listening to this man playing flat all the time” [Laughter]. Jesus Christ, what could he say about the music after that? So you can’t depend on those guys.

DT: So remember at the beginning of the conversation I was asking you what you do if you show up with a pickup band and you realize that somehow the musicians aren’t very inspiring, so you said, “Well, you stop playing and you listen and you try to respond, somehow,” so would being sharp be a response sometimes? A way of saying, “Hey! I don’t like you guys.”

LK: No, it’s not a deliberate thing. It’s the way I’m hearing it at the moment and it’s different every time, obviously, at the moment.

DT: I remember feeling like Paul Motian would do kind of the equivalent of that on the drums, which was he could play the most beautiful, meshing music with people if he felt good, and if he didn’t feel good he would let you know immediately.

LK: Bam!

DT: Bam bam! I think it was a very positive thing because it was his way of waking other people up and saying, “Hey, pay attention to the music,” but it also made his own unhappiness very clear. Sometimes I feel the intonation thing is that too.

LK: It could be.

DT: We’re supposed to wrap up, I’m being told. I feel like we’re just getting started here. Thank you very much, Lee.

Cross-posted from JazzSpeaks.org. Thanks to Kevin Sun for inviting me to write the above as a guest-blogger there and for transcribing the interview. Thanks also to Jeannette Vuocolo of Chamber Music America for inviting Lee and me to participate in the Talking Music series back in 2012.

I started hunting around the program for sounds. One of the big additions to Logic is that it now comes with a huge sample library. I focused on the orchestral samples, because I’ve never seriously tried to make a computer sound like a real orchestra before. The music I’ve made so far with sequencers, like my recent score for the film Movement & Location, is what we’d call electronic music: it purposely sounds machine-generated. There are people out there, particularly film composers, who are great at drawing acoustic-sounding music out of a computer, but it’s not a skill I’ve worked on before.

Logic now also has an advanced arpeggiator, which is something that was (amazingly) lacking in the old version — there were workarounds, but they weren’t pretty. In this context, arpeggiation means making melodies out of the notes in a chord by playing them sequentially instead of playing them all at once. Combine arpeggiation and some string samples, hold down a chord, and you might get something like this:

For a first try, right out of the box, that’s pretty cool! I found it exciting, at least. Another new feature of the program is something called Drummer, which tries to provide an electronic drummer that sounds like a human being instead of a machine. I asked it to give me a light groove in 5/4 for 4 bars, then to get heavier, adding toms, for 4 bars, with a few fills here and there. Logic has various drummer personalities you can dial up, who play with different time feels and different sounds. I chose one called “Aidan”:

Within limits, it does impressively well. I don’t see this kind of thing as taking work away from great drummers anytime soon — there’s no substitute for the decision-making, sound and time feel of a real, live musician — but it’s going to make a lot of demos sound vastly better.

Dylan’s All I Really Want To Do is all in one key, so I made a one-chord arpeggiated loop similar to the one above, but in 3/4, and I recorded myself singing the song over it. Then I took away the loop and started building an arrangement, gradually adding orchestral instruments, and before I knew it I was having such a good time that the better part of a day went by without me noticing. In the end it turned into some of the more straight-forwardly happy music I’ve made, by dint (I guess) of circumstance and, especially, the song itself. It’s an exuberantly positive song — on the original recording, Dylan laughs out loud towards the end of the track. With apologies to him, here’s my version. I wasn’t trying to do anything fancy or particularly sophisticated. Mainly, I was just having fun.

You can hear how the backbone of the track is provided by arpeggiation, with the instruments alternating by sections between strings, woodwinds, and brass. To that, I added other, non-arpeggiated layers as I went. Hear how the hand claps sound different every time they happen? That humanizing element is provided automatically by the Drummer module (with a little tweaking). The hi-hat pattern at the end is also something the module came up with — I didn’t have to place each one of those cymbal hits, nor did I have to use a pre-made, static loop. I asked for something, and this is what the program conjured up, on command. It’s remarkable, I think, that it’s possible to make something that sounds this realistic so quickly nowadays, with (in my case) very little prior experience dealing with these kinds of sounds. It’s a brave new world, folks.

* * *

But really… How about that song??? I’m blown away by the straight-forwardness of Dylan’s lyrics.

I ain’t lookin’ to compete with you
Beat or cheat or mistreat you
Simplify you, classify you
Deny, defy or crucify you
All I really want to do
Is, baby, be friends with you.

No, and I ain’t lookin’ to fight with you
Frighten you or uptighten you
Drag you down or drain you down
Chain you down or bring you down
All I really want to do
Is, baby, be friends with you.

I ain’t lookin’ to block you up
Shock or knock or lock you up
Analyze you, categorize you
Finalize you or advertise you
All I really want to do
Is, baby, be friends with you.

I don’t want to straight-face you
Race or chase you, track or trace you
Or disgrace you or displace you
Or define you or confine you
All I really want to do
Is, baby, be friends with you.

I don’t want to meet your kin
Make you spin or do you in
Or select you or dissect you
Or inspect you or reject you
All I really want to do
Is, baby, be friends with you.

I don’t want to fake you out
Take or shake or forsake you out
I ain’t lookin’ for you to feel like me
See like me or be like me
All I really want to do
Is, baby, be friends with you.

Has there ever been a more direct encapsulation of objectification, in all its forms? On first glance, Dylan is talking to a woman (“baby”), possibly reacting to a request from her to let her be the way she is, to stop trying to change her. But the lyric can be read at many other levels, too. What should we make of the line “I don’t want to meet your kin”, for example? If Dylan were talking to a love interest, presumably there’d be nothing wrong with wanting to meet her family. But when one talks about meeting someone’s kin, one is implicitly positioning the person as a member of a group, a part of something else. It’s a distancing thing to say, as if the person were a foreign species that we hoped to better understand by observing its interactions with other members of its group. Dylan is denouncing racism, among other things. He’s reminding us that the minute we position something, or someone, as the other, we’re losing out on one of the most beautiful experiences we can have, which is to know something for what it is. Yet Dylan offers an important caveat in the last verse: just as we should try not to place our interlocutor at an objectifying distance from us, we should also remember that we’re not the same. We’re separate beings and we can’t expect others to function the same way we do. It’s clearly a delicate balance. And what can possibly be gentler and more caring, if you’d like to get to know something or someone, than asking to be friends?

At a more abstract level, Dylan is reminding us to be careful not to get the signified and the signifier confused. Once we’ve named something, if we’re not careful it’s easy to stop considering its actual essence (the signified), and instead to get blinded by the name (the signifier) we’ve given it, as if the name could possibly sum up all the minute particulars of the thing itself. There’s a lovely book called Drawing on the Right Side of the Brain, by Betty Edwards, that makes the strong point that the reason so many people feel like they can’t draw is that when they try to draw an eye, say, they fail to actually look at the details of what makes up an eye, and instead draw an  idea they have in their head of what an “eye” is. It turns out that people who self-identify as not being able to draw, and who do a terrible job of copying a simple line-drawing, will often do quite well when asked to copy the same picture if it’s placed upside-down.

People have tried to address this pitfall for a long time, from the concept of duality in Buddhism to that of end gaining in the Alexander Technique. Here’s Taoist philosopher Chuang-Tzu on the matter:

That’s, to me, what Dylan is really talking about here: he’s reminding us, by making an exhaustive list of the ways we can fail to see what’s actually there, to keep paying attention.

* * *

Is it an act of objectification to make a piece of music digitally but endeavor to make it sound like it was performed by an orchestra? We’ve identified an end result (the sound of an orchestra) and divorced it from its organic integrity (the actual people and instruments and performance space that would come together in real, live performance). It’s a little like the man (we’ve all seen this) who has started seeing his wife as just a “wife”, and has forgotten that she is a person who just happens to have married him, no? At a certain level, the track is a simulacrum of the real thing, merely a signifier.

And yet… There’s an awful lot of detail in that simulacrum, isn’t there? It’s not just pointing to our memory of orchestral recordings, the way, say, the experience of a work of art in a dream can sometimes be a mere envelope for the work, empty of any specific content. There’s actual content here that goes beyond reference, even if it is masquerading as something that it is not. But then, is a recording of a real orchestra that contains 500 edits (a typical number nowadays for a classical recording) the real thing, or is it masquerading too, in its own way, for a live performance? Ultimately, you can only really trust a live show, and even then you’ve got to be on the lookout for lip synching.

How something is made really only matters insofar as it manifests itself in the end result (the expression “what you don’t know can’t hurt you” captures this nicely). If the 500 edits in the orchestral record suck the life out of the music, then the process has corrupted the result. If, like Glenn Gould, you manage to make great recordings this way, then more power to you. At the end of the day, the real barometer of music is: do we like it? Is it good? Does it move us? Do we really, baby, want to be friends with it? And it, with us?

Yesterday I was fooling around with it and suddenly realized that with SuperCollider, I could do something I’d been wanting to do for years, which is to make a recording of rhythm becoming pitch, and back again. You see, rhythm and pitch are exactly the same thing, only at very different speeds. How’s that, you ask? Well, let’s start with the harmonic series:

The harmonic series is what you get when you take a string, on a guitar, say, and start dividing it up. So let’s say you tune your string to a low C, the lowest note on the staff above. Then you divide it in two, so only half of the string is ringing. That note, as Pythagoras discovered a long time ago, sounds exactly an octave higher than the fundamental. Now you divide it in thirds, and you realize that that note is exactly an octave and a perfect fifth above the fundamental, a G. Now here’s the interesting part: the octave vibrates at exactly twice the frequency of the fundamental, and the octave + fifth vibrates at 3 times the frequency of the fundamental. In other words, divide a string in 2 and it vibrates twice as fast; in 3 and it vibrates 3 times as fast. And so on through the harmonic series — I’ve written down the first 8 notes of it above. The major third (E 2 octaves above the fundamental), for example, shows up when you divide the string in 5 and it vibrates 5 times as fast as the fundamental.

How does this relate to rhythm? Let’s think about the interval of an octave. If we play a low C and the C an octave above that at the same time, we’ll have one note vibrating at one frequency and the other vibrating 2 times as fast. If you looked at the sound waves next to each other, they would look like this:

Now consider just the crests of each wave, the moment where they reach their maximum. In the time between two crests of the bottom wave (the fundamental), the top one (the octave) crests twice. If we were to write this out in rhythmic notation, it would look like this:

Octave (2/1)

That’s a very simple rhythm: 2 for 1. Any child can tap it on her knees. But did you know that if you sped a recording of her tapping this rhythm on her knees up about a hundred times, you would actually hear two pitches an octave apart? Don’t take my word for it, check it out:

;

Pretty amazing, right? For most of us, this will be the first time we’ll have consciously witnessed rhythm turning into pitch, then turning back to rhythm. At the beginning, you can hear the “fundamental” in the left channel clicking away, and the “octave” in the right channel clicking twice as fast (2 clicks for every one in the left channel). Then, as it speeds up, there’s a period where you can’t really hear rhythm — the clicks start to blur into each other. Then something magical happens — you start to perceive pitch, first as a very low note, then as it speeds up, as a higher and higher note. Then the octave below starts to emerge as well. By the time we reach the highest point, the two notes are clear, the fundamental in the left channel and the octave in the right.

Why does this work? Well, it turns out that we have two systems for perceiving music. For slow things, our consciousness distinguishes individual events and interprets them as what we call “rhythm”, such as the child tapping on her knees. For very fast things (like when the taps get very close together), our consciousness isn’t fast enough to distinguish the individual events, and our pitch hearing kicks in, guided by those tiny hairs in our cochlea, each one specialized in resonating at a certain pitch.

That is, when rhythm is very fast, we hear it as pitch. In the same way that we can say one song is “faster” than another (and we could measure that difference in BPM), we can also say that one pitch is “higher” than another (and we could measure that difference as a musical interval). The thing that some people may not realize is that when we’re making those comparisons, we’re talking about the very same thing: a “high” pitch could also be called a “fast” pitch.

So here’s where it gets interesting. We just heard what an octave sounds like. That’s a very simple rhythm. How about a fifth? If you look back at the harmonic series diagram, you’ll see that if we want to listen to a perfect fifth (the first G from the bottom against the C right below it), we should be listening to two tones that vibrate in a 3 to 2 relationship — that is, the upper one vibrates 3 times in the time it takes the bottom one to vibrate twice:

Looking at the crests of the waves in musical notation gives us:

Perfect Fifth (3/2)

That’s a slightly more complicated rhythm, but kids can still do it with a little practice. Now hear it become pitch:

;

Again, I find the transition between our two systems of hearing fascinating — it’s as if you could see slow flashes of light speed up and gradually morph into a color (is that feasible? Not as far as I can tell). And it only gets more interesting as the rhythms get more complex. A perfect fourth is a 4 to 3 relationship,

Perfect Fourth (4/3)

and sounds like this:

;

My favorite is the major third, a 5 to 4 relationship that is an awesome rhythm (I use it all the time in my music) and also happens to be a lovely interval. Would you have guessed that such a consonant interval would have such a thorny rhythm behind it? Next time you tap it out on your knees, try to get your mind around the idea that you’re playing a really slow major third.

Major Third (5/4)

;

The minor third is great, too — a 6 to 5 relationship

Minor Third (6/5)

that sounds like this:

;

* * *

We could go on with these intervals — the major sixth, for example, a 5 to 3 relationship, is particularly nice — but what I really wanted to know as I experimented with this last night was: what does a triad sound like, rhythmically? Well here it is. Let’s look at a major triad first, which as you can easily figure out from the harmonic series diagram, is a 6 to 5 to 4 relationship:

Major Triad (6/5/4)

This isn’t a rhythm that you’re going to hear a kid tapping out, but a good drummer could work it up relatively quickly. The difficulty is in the way it mixes ternary (triplet) and binary divisions of the beat. Still, it’s pretty catchy. Here I’ve put the lowest note in the middle, the third in the left speaker, and the fifth in the right:

;

Pretty crazy, right? How an honest-to-goodness major triad could emerge out of that clicky mess? Now we’re left with the minor triad. Interestingly, even though we often think of a minor triad as a more complex sound than a major one (or at least, sadder) it’s a simpler rhythm in that it’s entirely made up of ternary divisions of the beat. But it also takes longer to resolve. So you could say it’s more in phase with itself, but also more ponderous; less cognitive dissonance, perhaps, but more internal debate.

Minor Triad (15/12/10)

It sounds like so:

;

If you’re wondering how I got those ratios (15 to 12 to 10), it’s like this: take the minor third from the harmonic series, between the E and G in the first diagram above. That’s a 6 to 5 relationship. Now we need the fifth, which we can get by multiplying the root note (the E) by 3/2, giving us 7.5. Now multiply all 3 numbers by 2 so that we can be dealing with whole numbers, and voilà: 15/12/10.

* * *

One last thing. The waves I’ve drawn for you here are sine waves, but if you know anything about sine waves, you’ll quickly realize that the sounds you’re hearing on these recordings, even when things are going very fast and you’re hearing clear pitches, aren’t sine waves. The clicks that you hear at the beginning and end of the tracks are what are called impulses, basically the quickest move the speaker can make. The wave for an impulse looks like this:

These sound like clicks when you hear them individually. But when they get very close together,

we stop hearing the clicking and instead, we hear the same pitch that we would hear if each impulse were the crest of a sine wave. Our ear can clearly tell the difference, though, by the timbre of the sound: the pitches made of impulses are aggressive and tinny to the ear, whereas ones made of sine waves are pleasant and full:

The difference in timbre is huge. Our sense of pitch, however, is activated just the same.

* * *

One very last bonus track: remember the major sixth I talked about earlier, the 5 to 3 relationship? That’s such a nice rhythm (my friend Gabriel Kahane, for one, uses it throughout his song Durrants) that I’ll give it to you here

Major Sixth (5/3)

in all its transformative glory:

* * *

Post-scriptum: thirteen years later, in December 2025, a reader asked for 5/2, which is another of my favorite rhythms. In the intervening time, for public presentations, I made a visualizer for these relationships. So now, for the first time here, here’s 5 against 2, first as rhythm, then as pitch (sounding like a Major tenth), in both sound and video:

1.

2.

3.

4. 

5.