My chamber music

Another hypercanon piece.  

This time, from the mathematical perspective, beats get filled when their beat number equals the sum of a square, a positive cube and 6th power.  

Because the powers vary, the music keeps the counts on different instruments. 

The numbers to square get heard on the piano (with 1 the top key and then descending chromatically).

The numbers to cube get heard on pizzicato strings tuned in 19-TET, using an ascending scale that divides three octaves into 19 equal intervals which sound as nearly 10:9 rations.

The numbers to raise to the 6th power, never more than 4, map to a small gamut of tuned drums.

The complexities of the sets of sums of just two kinds of powers asserts itself as the irregular staggered entrances of the canon on the instrument associated with other power.  

If this is too much information for you, the bottom line is an intense listen which, white it has a hypersimple underlying concept, also feature a rather complex surface regardless, and because of the density of the beat numbers with a "yes" answer, intense but also unfamiliar syncopation. 

Big thank you to Peter Thoegersen, who literally wrote the book on polymicrotonal (and polytempic) music.  He's a genius and you should check out his music.  While his music and also his working methods are quite different than mine, he has opened me up to one of his great discoveries, namely that the listening mind can instinctively decouple the layers of a complex music according to the tuning systems girding each layer (at a given moment).  The effect is like passing to an experience in a higher dimension, akin to the discovery of perspective in visual art.   I'm not sure Peter would even count this as "poly" since two of the layers are 12TET and my treatment of 19TET avoids actual microintervals.  But I'd never have come to this way of projecting my ideas without his influence.

Higher Powers, for Piano, Percussion and Pizzicato Strings

At first blush this music may seem to hearken back to the the Second Viennese School,  but stay with it for a few minutes and you will hear something altogether different.  This is actually as consonant as that music is dissonant.  The organization is more diatonic than serial though far more than twelve notes occupy each octave, and the harmonic universe slowly progresses through related keys like a symphonic development section does.

Trio for Strings

Six parts, each in a different meter, intertwining in a Brownian way.

Luctuosa desideria for piano, marimba, brass and cello

The 25 sections of this deliberately generic pointillistic music alternate between two types of pitch material:
1) atonal, actually simplistic serial using only untransposed prime form;
2) diatonic (in a sequence of keys that follows the row of 1)).

Babbitt famously described Arthur Berger's Duo for Cello and Piano as "diatonic Webern" (some say "white-note Webern").    If you have the ear for it, the "diatonic Darmstadt" sections will stand in stark contrast from the atonal sections.    Or maybe just in gentle contrast.  And doubtless some people won't detect the boundaries and others will start to hear the structure here only after repeated listenings.

My aesthetic object here really lies in the staged moment of awareness concerning the distinctions the brain can make (or not), that and awareness concerning how the meaning of a fixed sonic object varies with the listener.  "Experimental music" usually refers to an experiment designed by the composer, and executed by the performer, but here the listener experiments by reflecting inward on what they can hear and how it feels to hear it.

All that said, I hope you find the surface pleasant enough albeit, for me, not an end in itself.

Ishihara Test For The Ear (for piano and harp)

If a composer wishes to avoid tonality, wishes to avoid the monarchical tyranny of tonic, then a simple (but not sure-fire) recipe consists in working a symmetrical treatment of the totality of pitches (with said totality often going by the name "total chromatic," or more generally "aggregate," but aggregate can also mean a totality of anything).  The twelve-tone system treats pitch classes symmetrically by design, and aleatoric methods also prove quite effective.  Other tyrants can arise aside from tonics.  So if mezzo-forte, or the central octave, or the 16th-note should threaten domination, a composer can also serialize (or randomize) dynamics, tessitura, or duration, etc.  In practice, all this fair treatment of possibilities, all this fiat symmetry, can ironically make tyrants out of the relevant aggregates themselves, effectively replacing monarchy, one might say, by obsessive bureaucracy, with the ear experiencing concomitant fatigue (not necessarily a bad thing depending on the composer's artistic goal).  In any case the emergence of this irony perhaps explains the briefness for total serialism's vogue.  Long ago, atonal composers working more freely discovered the trick of "keeping a note in your pocket" only to pull it out again when you need it to sound fresh---and it will.  

This piece plies a latter-day total serialism (but a serialism not anchored in rows) which governs pitch, tessitura, rhythm, dynamics and articulation, but which has the note-in-the-pocket wisdom inscribed in its genetics.  The 81 sections survey all 80 hexachord-up-transposition classes (the final section reprising the first, a whole-tone scale), with each section signaled by the entrance of a single pocketed pitch class and less noticeably by the departure of another (so traversing a Hamiltonian circuit through hexachord space).  Likewise, a Hamiltonian circuit through time-point "hexachords" (a la Babbitt) characterizes the rhythm.  But then each hexachord gets developed by a special type of Hamiltonian circuit through all 20 of its own sub-trichords, with the instantiation of each trichord pulling a note of a shallower pocket. 

The spare texture of the present work pays homage to John Cage, specifically works from his Lou Harrison period, to Morton Feldman, specifically his late pattern pieces, to Jo Kondo, specifically his hockets, and to Jonathan Kramer, specifically his process pieces and works with restricted pitch sets.

The Note in Your Pocket (My Travels Through Hexachord Space), for two melody instruments

There are fundamentally 713 distinct ways to partition the aggregate (a.k.a chromatic scale)into four trichords.  Of these, 290 have no trichord type repeated and these I'm calling the tetra-trichords.  Call two tetra-trichords neighbors if they share at least three trichords types.  

This piece follows a loop, from neighbor-to-neighbor, through most of the space of tetra-trichords, 288 of them.  The two omitted tetra-trichords only neighbor one-another, so refuse to play along.  They deserve a piece all their own (I'll get to it!).

So this is fundamentally "twelve-tone" (but not row) music, as in all twelve tones are more or less constantly active and in equal proportions.  But thinking of the trichords as the-new-notes, the aggregate becomes a kind of super-chord, and the whole piece a super-four-part-chorale, with consecutive super-chords always sharing a common "tone" (actually, a common trichord) for good (super)-voice-leading.  

So this is twelve-tone music with no direct input from common practice, yet very audibly working with analogous ideas.

My Travels Through (Most of) Tetra-trichord Space, for flute, clarinet, bassoon and celesta

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

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Higher Powers, for Piano, Percussion and Pizzicato Strings

David Victor Feldman