2025

Branches

This is a kind of polytempic work in the sense of Peter Thoegersen (well, if he thinks so).  The whol time span gets divided into 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610 equal parts with each tempo supporting a layer consisting of only 7th chords that have one particular root.  Since I make chords in the slower tempi sound louder, the interaction of dynamics and periodicity tends to balance the importance of all the different roots.  With the next slower layer always carrying the given layers dominant, a certain amount of root progression emerges.  But it's complicated!

Those Fibonacci Fractal Four-Chord False Relation Blues, for piano four hands

Said the poet: "Euclid alone has looked on Beauty bare."

Push back on "alone" if you like, but beauty may dwell in the immaterial, and from thus the possibility of art formed purely out of ideas. Or not purely: a sensual experience may, by its structure, simultaneously carry ideas. Two art objects, one immersive, the other cognitive, can simultaneously inhabit the same experience.

Varèse framed music as "structured sound," and I would add, alternatively, "sonified structure." Mathematics is the science of structure, so, if you like, the part of music theory robust (to some extent) against the contingencies of sonic materials. I have a long interest both in bringing to my composition ready-made mathematical objects and mathematical phenomena, and in letting the same emerge from sonic considerations themselves. But truly to infuse music with at least the ghost of "Beauty bare" requires evoking mathematical argument.

So consider communicating something by drumming. Fix a small unit of time. Now say you decide to work with only two durations between strikes, namely 2 units and 3 units. Even with the best coding, that choice limits your bandwidth—limits the rate at which you can transmit information.  Now one can quantify this in a sophisticated way with information theory, but we don't need to get into that now. But here's an interesting and not quite trivial fact: if your durations are 1 unit and 5 units, then you have exactly the same bandwidth as with 2 and 3 units! 

A long and short duration might remind you of Morse code. Well, if you "glue" the "dash", the long duration, of the 2–3 system to the following duration, you will get a drumming pattern in a 2–5–6 system. And that translation is reversible. But if you glue the "dot" of the 1–5 system to the following duration, then you also get a pattern in the 2–5–6 system, and also in a reversible way. So you can get from 2–3 to 1–5 via the trick of interpolating between them with another system you might not originally have thought to consider. There's an episode in the piece that makes precisely this transition/translation audible.

But it doesn't stop there! All the following systems also have the same bandwidth as the three mentioned above:
                                                                1–6–11–16–20, 
                                                                1–6–10, 
                                                                1–7–10–12–16, 
                                                                2–6–7–10–11, 
                                                                3–4–5, 
                                                                3–4–8–9–10, 
                                                                3–5–7–8–9, 
                                                                4–5–6–7–8.
Now hopefully the required "bridge" between, say, 1–6–11–16–20 and 3–4–8–9–10 doesn't seem obvious at all! Nevertheless one will experience it if one attends very closely to the sonic details of the piece.

Yes, you can forget all this and you still have an intense experience reminiscent of ritual drumming, albeit without any periodic underpinning. By the way, he piano part works just as the drums do, but also correlates pitches to the durations.

The title: if you wish to transmit a long random "message" in the 2-3-system, a certain ratio between the frequency of 2's and 3's will emerge.  The famous golden ratio would emerge from the 1-2-system and goes by the name "phi."  Hence "high phi" as one old and mostly forgotten proposal for a name of our ratio here.

High Phi, for drums and piano obbligato

Imagine being in the jungles of myanmar and coming across the rare saber-toothed tiger of the jungles near the Naf River

poly etude 19

Microtonal Computer Music Etude w drums #20

The music can speak for itself, sonically, if you prefer.

But if you care to understand what's going on, here it is in brief.  The durations in the cello are 2, 4, and 8 8th notes; the durations in the bass line of the piano part are 3,5,6, and 7 8th notes.  Any rhythm of any duration of the former sort admits a translation into a rhythm of the latter sort, and vice-versa, indeed a translation that preserves the overall duration (to within a fixed few beats anyway).   I expect that this fact hardly seems obvious!  But the violin part is the intermediary, along with the other voices in the piano part.   Attend to the relationship between cello and violin; and between piano and violin, and, with some concentration, the logic indeed reveals itself.

Elegy for Piano Trio (High Phi II)

In both movements of this quartet, each instrument gets assigned a repeating rhythmic pattern—sequences of notes and rests of equal length (say, all eighth notes). 

The first violin plays a pattern of 11 beats (6 notes, 5 rests), the second violin a 7-beat pattern (4 notes, 3 rests), the viola 6 (3+3), and the cello 5 (3+2). These patterns cycle independently.

One full cycle  takes 2310 beats—the least common multiple of 11, 7, 6, and 5.

But—crucially—beat durations vary.

Indeed, the duration of a beat depends on its density—meaning how many instruments are sounding at that moment (0 through 4). Each density appears a fixed number of times within the full cycle, independent of pattern contents assuming the constraints above. 

The twist: beat durations get adjusted so that each density—whether a silence, solo, duo, trio, or a full quartet—occupies exactly one-fifth of the total time of the movement. Rare textures are stretched, common ones compressed.

Thus the interaction of the parts effects an emergent large-scale rhythm.

Out of millions of possible combinations of patterns, one movement employs the set that yields the most unpredictable overall rhythm (in a precisely defined mathematical sense). The other, the most predictable.

As for pitch: each instrument traces a fragment of the cycle of fifths—in near standard tuning. The quartet plays 17TET, so with the octave divided into 17 equal steps, which makes a "perfect" fifth span 10 steps. Each instrument repeatedly travels through this cycle fragment, alternating between octaves. Individually, the lines sound diatonic; together, they form unfamiliar and highly dissonant verticalities—often stranger than even the most dissonant music in 12-tone systems.

Despite this microtonality, no specialized technique is required. If each player tunes their instrument to a slightly different “A,” then standard fingerings suffice—as long as they resist the instinct to tune to one another.

Waves, Winds, Mind - Mvt. II

Waves, Winds, Mind - Mvt. I

This, my second mixed Trio in poly, features 17-19-21-23-25-28-31 seven note scale in the cello, that loops 6X against two polyrhythmic contrapuntal 24 unequal Pythagorean scale of al Farabi in the piano, and Ben Johnston's 6th Prime row of 25 unequal per octave, in the Clarinet. The interplay is finely thought out and responsorial. The poly trio is a new form I am experimenting with for more transparency for the contrapuntal interplay between the instruments in polymicrotonality. 2025

Mixed Trio in Polytempic Polymicrotonality #2

Twist

This piece is an outgrowth of the previous sextet that is now a NONET, with English Horn, C Trumpet, violin, viola, cello, 2 marimbas, guitar and piano. This is fully polytempic, but is only standard tuned, no microtones. (unless of course 12tet in-itself is already microtuned as it deviates from just overtones) . This piece is sprightly and alive, quite the opposite of its composer, so that remains an enigma. 

Just Shut the Fuck UP, it's a Beautiful Day Outside and I have a Boner, so don't ruin it.

Like a wild Klezmer orchestra, everyone is going dixieland Mad with pdlytempo and polymicrotonality, for piano, guitar, violin, viola, cello, 2 marimbas, English horn and Trumpet. It's a mad drunken bar fight but, fun, a fun mad drinking bar fight. No one lives! Composed today and all week. This is related to the Boner happy day piece. You're welcome. 

Polymicrotonal Nonet I

This music is about how we are all fucked and Trump will destroy the Earth, as I've been fucking telling you idiots for the last ten fucking goddamned years and you just sat on your ass doing nothing. Happy Death. 2025

Nonet in Polytempic 12tet, updated version, for English Horn, Trumpet, Violin, Viola, Cello, two Marimbae, Piano and Guitar

Music for English horn, trumpet, violin, viola, cello, two vibraphones, guitar and piano. Tunings will be discussed later. Working on score, still. This piece is constantly evolving. 2025

Polymicrotonal Nonet, without Polytempo, version 2, for Violin, Viola, Cello, English Horn, Trumpet, 2 Vibraphones, Guitar and Just Piano

Totally synthesized version of nonet for acoustic instruments, all with samplers. Relax and enjoy, or I'll kick your fucking ass. 

Nonet synthesized, Version III

2 Trumpets, Horn in F, Trombone, Tuba in 99-98-97-96-95 ratio tempi relationships with "large" quarter and eighth tone modulations. Quasi tripartite form in a Schoenbergian sense in that there is no tonic-dominant axis for formal constraints, yet the microtonal modulations act in place to delineate form. Simple retrograde is employed to a general singular "diatonic" line multiplied and displaced by the pdlytempo. This is not phase music. This is still polytempo but at micro rhythmic gradations. Each tempo is marked by a .5 beat difference between the five parts. There is no convergence, only separation, like our country. Frankly, like the world today.

Polytempic Polymicrotonal Brass Quintet

Composer, mathematician, visual artist. 
Seeks collaboration with performers and choreographers.

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Branches

David Victor Feldman

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