My solo music

2024

# 15

The aggregate contains six tritones, 0-6, 1-7, etc.
In 1-out-of-64 rows, the PCs of each tritone sound in just that order.
Then perhaps also the time-point gap between PCs 0 and 6 is smaller than the gap between 1 and 7, etc.  

This piece is made up all of the 957 rows that meet all these requirements.

Specifying the gaps between the tritones, one has a kind of jigsaw puzzle: to find a row with exactly those tritone time gaps.  

Sometimes such a puzzle has no solutions (for example when the sum of the gaps is odd).  

With gaps 1-2-3-4-5-7 one finds 38 solutions, the most, and these begin the piece; with gaps 1-3-5-7-9-11 one finds 1 solution, the least if not zero, and that row ends the piece.  Between, all the rows occur organized according to which puzzle they solve, the puzzles ordered so that the number of solutions weakly decreases.

With each statement, each tritone gets its own octave.

If one has the ear for it, one can attend to these details, or else just take in the energy of it all.  I would like this to looking at a descriptive picture either as a visit to a virtual 3D place (e.g. a fictive city street, mountainside room) or as a decorated planar region, typically bounded by a rectangle.  When musicians talk about "movement" and "line" and "implications," that's happening the musical equivalent of virtual space.  In reality, notes and sounds find all their places by compositional fiat and don't actually generate or cause one another.

The cover image more or less encodes the score.

Rational Exuberance (Not Your Grandparents' Twelve-Tone Music VI), for organ and piano

There are 362,797,056 ways to partition a three octave span into three aggregates.  Once you do so, reading each aggregate from low to high, you get three 12-tone rows.  If you further require that those rows feature at least 7 distinct interval classes, the 362,797,056 possibilities reduce to just 46.  One of those 46 possibilities plays the role here of a passacaglia-like chord progression.  

There are 144 ways to have three triads sit within the aggregate without any overlap.  Remarkably, one can cycle through those possibilities so that each step turns up just one new triad.  Such a cycle provides the figuration for the variations. 

The overall effect produces a counterpoint between two opposing notions of harmonic rhythm, one based on the cycle of aggregates, and one based on the the featured triads.

A Friendly Accord between Aggregates and Triads, for guitar

If a twelve-note chord features all the pitch classes, you can read it up to get a row. If the chord sits within three octaves, it can feature at most 7 different intervals (because 1+2+3+4+5+6+7+8 =36).  There are just 46 ways to partition the 36 pitches in a three-octave span into three such chords.  

Each "variation" projects one of the 46 possibilities.  You hear each of the rows three times, but with the notes transposed into the three different chords.  

As with much of my music, there is no literal repetition, but also no attempt at "high profile contrast."  Rather the music invites the listener to attend to small differences, and in this case, exactly the small differences imposed by the universe or by the mathematics or however you prefer to think about it.  

It's hard to come up with "questions" like this, questions that indeed turn out to have a manageable but non-zero number of solutions. But having fixed such a question, the set of solution lies beyond human control.  The universe provides what the universe provides.  
This accepting of what I get interests me aesthetically, as does the privilege of having sufficient computer power now in the 21st century actually to discover all the solutions. 

Score on request.

The 46 Possibilities (Not Your Grandparents' 12-Tone Music VII), for bass clarinet

In twelve-tone theory, an all-interval row means an ordering of 12 distinct pitches so that neighboring pairs exhibit 11 distinct intervals.  Most rows have 48 distinct forms (twelve each: prime, inverted, retrograde and retrograde inverted). 

Now think of the musical transformation from one row form to another as a sort of "generalized interval."   

This piece is built on a "row" of the 48 forms (of one particular all-interval row) arranged so that neighboring pairs exhibit all 47 nontrivial generalized intervals.  This not only exhibits a rare and remarkable mathematical structure, but because the musical treatment here avoids the usual (perhaps) gratuitous complexities of twelve-tone music, this structure should emerge clearly, surely for any trained ear, and indeed convey coherence even to the casual listener.

The 48 Forms  ...for solo violin (MIDI realization) (alternate version)

In twelve-tone theory, an all-interval row means an ordering of 12 distinct pitches so that neighboring pairs exhibit 11 distinct intervals. Most rows have 48 distinct forms (twelve each prime, inverted, retrograde and retrograde inverted). Now think of the musical transformation from one form to another as sort of "generalized interval." This piece is built on a "row" of the 48 forms (of one particular all-interval row) arranged so that neighboring pairs exhibit all 47 nontrivial generalized intervals. This not only exhibits a rare and remarkable mathematical structure, but because the musical treatment avoids the usual gratuitous complexities of twelve-tone music the structure should emerge clearly for any trained ear and seem coherent even to the casual listener.

Written for and dedicated to my daughter Linnea Feldman Emison.

A score is currently available from the composer on request.

The 48 Forms  ...for solo violin (MIDI realization)

The structure of this music might remind the listener of Mandelbrot zoom videos, albeit the videos usually zoom in, and this music virtually speaking zooms out.  

The fundamental tone row, like nearly every twelve-tone row, has 48 distinct forms.  The zooming out process causes one form gradually to morph into the next (each morphing takes almost a minute), suggesting a sort of fractal structure.    The relationship between a form and the one to which it morphs determines the micro details of rhythm and phrasing.  Variety arises because of a special ordering of the 48 versions that exhibits all 47 possible relationships between the before-and-after occur exactly one (so for example the final form only equals the retrograde of the preceding one).

This MIDI version stands to any potential human performance as a photograph does to an oil painting derived from it.  The human performer will add nuance, but will necessarily have to artfully and approximately suggest some of the delicate, inhumanly fast passage work. 

Leaving, for violin

This piece is from about 1978.   Solo string music doesn't lend itself to MIDI realization, but this is the best I have as yet.

Like much of my work, the score is in a spatial notation, not because I have vague rhythmic notions, but because my precise ideas would look hideous in standard metric notation.  Thus I prefer players to read a simplified score, really an for aide-memoire, but get the gist of the rhythmic structure from a sound file, thereby doing some important learning by ear.   Learning by ear is a crucial component of folk traditions, and I've hoped to bring folk fluency to into synthetic and experimental musical situations.

Certainly at the time I perceived new classical music as generally held back by alienated performances symptomatic of over-dependence on merely  decoding complicated scores but without a vivid aural conception informing the interpretation.   

7-tet abbreviates seven tone equal temperament.   So the listener will hear a diatonic scale with neutral thirds and no leading tone(s).    One probably doesn't associate "atonality" with music that moves in steps, but the symmetry of the scale does avoid the development of traditional tonal centers.

Arboreal Arabesques in 7-tet for violin (MIDI realization)

An old friend remembered this piece to me that I wrote for her back in high school about 45 years ago.  So I sequenced it so we could hear it (again).   Sadly, can't get sul tasto, sul ponticello, artificial harmonic effects.

Edit:
Some many months ago I posted here a very short viola piece.  Though I'd  originally conceived  it as a final movement, just as it stands here now, at the time of its completion I decided to deem it an independent work.  That reflected my feeling that my style had  undergone a significant shift since I'd written the first movements more than a year before.  Well, at a distance of more than four decades, the style shift seems negligible and multi-movement work seems to have a distinctive shape.

Sonata For Viola Alone

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

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A Friendly Accord between Aggregates and Triads, for guitar

David Victor Feldman