The Pythagorean Tetractys, or how to build all of music with only the numbers 2 and 3

The Pythagorean Tetractys, or how multiplying by 2 & 3 gets you all the notes you need, with stops at the Pythagorean Comma and Equal Temperament along the way. Like my previous post, a deep rabbit hole, but — to me at least — a very rewarding one.

(Originally posted as part of #100daysofpractice 2023)

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Tonal Harmony in 3D

I sometimes disappear down a rabbit hole, and this one was deep. I wrote a program that generates a map of tonal harmony as I see it in my mind when I do free improvisation in a key, as on my album Inventions / Reinventions. Come for the pretty colors, stay for the nerdy explanations of secondary dominants. I coded all this from scratch, including the surface forming the landscape and its ripples, the diatonic chord spellings, the hierarchical positioning of the chords in space, the voice-leading in the chord player, the way the camera selects chords… These programming journeys can become all-consuming for me. Glad I got this one out of me.

(Originally posted as part of #100daysofpractice 2023)

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Inventions / Reinventions

Inventions / Reinventions, my new solo album, came out today on StorySound Records. Listen here (US & Canada) or here (Europe & UK). It’s also available in physical CD format here. What follows are my album liner notes.

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?

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#BachUpsideDown: Bach’s Goldberg Variations in chromatic inversion, explained

My first project of the 2020/21 pandemic was something I called #BachUpsideDown, an exploration of the sound of Bach’s music in chromatic inversion. During the early months of lockdown, I recorded myself performing the Goldberg Variations as written, and after each variation, I triggered a program I’d written on my computer that played back the notes I’d just performed upside-down. I fell in love with the strange and wonderful sound that results from this process, and decided to make a score so that other musicians could perform the music without the need for special technology. What follows is my introduction to the print edition, which is available for purchase here. You’ll find the YouTube playlist with all 30 variations here, and a May 2020 New York Times feature by Anthony Tommasini here.

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. 

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Ruben the Squirrel & the Boston Marathon bombing

Something extraordinary happened to me in the spring of 2013. I found a squirrel. Or rather, the squirrel found me. It’s not all that uncommon, it turns out, but it sure felt special at the time. 

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. 

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Lee Konitz, 1927 – 2020

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.

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A Few Things I’ve Learned About Livestreaming

“Thanks” to the pandemic, I’ve spent much more time figuring out how to deal with video and live streaming than I ever thought I would. It’s turned out to be a surprisingly rewarding experience. In no particular order, here are some things I’ve learned along the way.

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.

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TriadSculpture for sale

At long last, I’m now offering my triad sculptures — the ones that I created while developing my Natural Machines project — for sale.

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…

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Negative Harmony: a primer

Ever since Five Pedals Deep, my trio record with Thomas Morgan and Ted Poor, came out in 2010, I’ve gotten a steady trickle of emails asking about a particular tune on it called Back Attya.

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. Continue reading

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McCoy Tyner: dance, drums, beauty salons & fourths

The great McCoy Tyner, giant of jazz, huge influence on me and countless others, died a week ago, on March 6th 2020. Back in 2008, when I was 26, I had the privilege of interviewing him for French magazine Jazzman ahead of the release of his album Guitars. Now seems like an apt time to share the interview below, which — aside from the translated and much condensed version that appeared in the magazine at the time — has never been published. Thanks to then editor-in-chief Alex Dutilh for trusting my young self with this assignment and giving me the opportunity to talk to one of my heroes.

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. 

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Creativity and Its Sources / Tom McCarthy’s Remainder

Reading Tom McCarthy’s novel Remainder, which I love, I’m reminded of a realization I had a while ago: pure creativity is closely related to dreams — a mysterious place where new visions are somehow born. You dream, and you see something, and metaphorically speaking — because “dreams” can be taken to represent any information that comes from the unconscious mind — your conscious job as an artist is to reproduce this vision in real life as faithfully as possible.

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.

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Sister Canons in the Goldberg Variations

In Bach’s Goldberg Variations, every third variation is a canon at an increasing interval. The first (Variation 3) is at the unison (the canonic voice repeats the leading voice verbatim), the second (Variation 6) is at the second (the response repeats the subject a diatonic second away), and so on until Variation 27, which is a canon at the ninth. (Variation 30, the last of the set, where you would expect a canon at the tenth, is instead a Quodlibet).

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: Continue reading

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The question, when performing

The question, when performing, is:

“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.

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A Container for Nothingness

Two of my favorite jokes rarely get any laughs. I learned them both as a kid growing up in France. The first goes:

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: Continue reading

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Natural Machines

 

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. Continue reading

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Short songs with absurdly long codas

Form-wise, the Beatles’ Hey Jude is unusual. For 3 minutes and 8 seconds, it’s a conventional song, with melody, varying harmony, A and B sections that repeat in a predictable pattern — what you’d expect from a pop song. Then, for the remaining 3 minutes and 57 seconds, it’s something else entirely, a long vamp where the same static chord sequence repeats over and over again while the melody repeats with small variations and interjections. The proportion of these two parts feels like a bold move — there’s something about the length of the coda in relation to the body of the song that makes you question whether you just listened to a song or to… something else. Are we being tested? Are the Beatles daring us to walk away? If “art is what you can get away with” (Andy Warhol), are the Beatles pushing the limits? Continue reading

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The TRAPPIST-1 System: Listening to Planetary Orbits

(Cross-posted from WBGO.org. Thanks to Nate Chinen for inviting me to write this.)

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.

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Vancouver

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Interview: Improvisation, Mountain Climbing & the Meaning of Life

I’ve got a little time off from touring so I’m cleaning house. While sorting through old papers I came across the interview below. Most of these answers still ring true to me today. It’s fun to hear from past iterations of oneself, sometimes.

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. Continue reading

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Birdman! Absurdity, theater, music & the importance of madness

birdman-1000I left the movie theater last night, post-Birdman, intensely moved. Rarely has a film gotten to me so directly. Birdman is a wacky movie that seems to be asking a serious question: why live? What keeps us trucking on and floundering and trying as hard as we can to accomplish things, when we’re only specks of dust on a small rock orbiting around an average star, one of billions in a galaxy that itself is one of billions in the universe? How can you explain that we care so deeply about our shit? Our little troubles and tribulations? The movie has a simple answer: madness. That’s what explains it. And the beauty of it all is that madness is at once a curse and a necessity, without which, well, we might as well throw in the towel. Continue reading

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Doing It Bachwards: my unexpected Goldberg Variations

(Cross-posted from UCLA’s Ethnomusicological Review. Thanks to AJ Kluth for inviting me to write this piece for the journal.)

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. Continue reading

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Lee Konitz on Spontaneity, Originality, Drugs & Playing Sharp

Lee and Dan

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. Continue reading

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The New Logic, Objectification, & Bob Dylan

When I got back home to Brooklyn from tour a couple days ago, one of the things I did was buy Logic Pro X, a big update to a music production app I’ve used for a long time. To get a handle on it, I decided to make a track for a friend of mine. Earlier in the day I’d come across Bob Dylan’s All I Really Want To Do again, which, I was reminded, has got to be one of the most wonderfully simple and profound songs there is, and I thought it would do just fine.

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:

 

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Rhythm / Pitch Duality: hear rhythm become pitch before your ears

I just got home from a five-week tour in Europe and finally have some time to do what I call research. The way I see it, being a touring musician is a bit like being a scientist: you spend a bunch of time in the lab, and you find something that you’re excited about; then you have to go out and give a bunch of seminars to tell the world about it. But very soon you’re itching to get back to the lab, because you want to discover the next thing. So here I am, at home and doing research, which for me, right now, in between practicing piano and writing tunes, means getting into a computer music programming environment called SuperCollider.

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:

harmonic_series

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Long Island

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Normandy

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Algorithmic Art

My dirty little secret is that I can be a pretty serious nerd sometimes. While I was procrastinating from writing a piece for nonet a few months ago, I reopened a computer program I had started working on in 1998 (!) and modified it so that it would work on my current Mac. The idea is pretty basic: use lines and a little math to make pretty pictures. Although I didn’t know it at the time, it’s an example of what’s called algorithmic art. I remember being totally fascinated by this as a teenager: I would try things, almost at random, and these incredible shapes would appear. Fourteen years later, with a couple tweaks to the program, I still think there’s something really special about these images.

1.

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Questions from the Atlas

I’m bringing my trio with Ted Poor and Ben Street to the Atlas in Washington DC tomorrow night (Wednesday, May 30th, 8pm). Brad Linde, who curates the jazz series at the Atlas and is also a saxophonist/bandleader of renown on the DC scene, asked me a few questions ahead of the gig. (Cross-posted from the Atlas Arts Blog).

Brad: How does your approach to improvising/accompanying/etc change based on the different contexts you encounter?

Dan: The essence of improvisation is context. That’s what’s special about it. Since it’s happening in real time, since we’re actually making music up on the spot, at its deepest level it should reflect everything about the current moment. I’m not only talking about the note choices that my bandmates make, and that I respond to; I’m also talking about subtle things like the sound of the room we’re playing in, what we’ve eaten that day, how we’ve slept, and what the weather is like outside. In improvisation, we have the opportunity to take all this into account at an intuitive level. It’s exactly like having a conversation with a group of people: depending on how noisy the room is, how well you know the people, the general vibe, you’ll participate in a unique way — if you’re really listening, that is (we all know people who seem oblivious to context, interrupting and forcing their point across). So I see the challenge of improvisation as listening to the current context in as sensitive and authentic a way as possible, and letting myself respond. The other side of this challenge is to be able to find yourself in that context: not to give in to it completely but to find the balance between it and who you are. Continue reading

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Montana

 

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Konitz Playlist

A few months ago, JazzTimes asked me to choose ten tracks from Lee Konitz’ recorded work that stand out to me in his career. Here’s what I came up with.

Lee Konitz Playlist – Dan Tepfer

Lee Konitz started recording in 1945, and he’s still going strong today. He appears on hundreds of records, with an incredibly wide array of musical associates. Lee was unique from the get-go: his tone and phrasing are as instantly recognizable on his recordings from the forties as they are now. I’m fortunate that I’ve gotten to play regularly with Lee over the past four years; here are some tracks of his that have struck me along the way.

Marshmallow
Subconscious-Lee (Prestige) 1949
A classic cut of Lee and Warne Marsh tearing up a lightning-fast written line in close harmony, something they did peerlessly. This is Lee’s first session as a leader; he’s barely 21, and he plays a super-tight, blistering solo.

Odjenar
Conception (Prestige) 1951
I like this track because it shows Lee completely at ease in the modernist classically-influenced style that was coming into vogue at the time, two years after the Birth of the Cool sessions. The composition is by George Russell, and the interplay between Lee and Miles Davis is mysterious and fascinating. Continue reading

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