My piano 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

The conventional wisdom holds that chance operations abolish "glue" (Henry Cowell's term, but often invoked by Cage).  That idea rests on presuming that statistical independence governs how  the operations place musical events within the music framework.  Well, not here.

As x and y coordinatize the Euclidean plane, time and pitch coordinatize musical space as constructed say on a piano roll.  But there's a difference: the plane enjoys rotational symmetry, but its far from clear how one would even compare the magnitude of a time duration with musical interval.

Take a circle and randomly choose 41 chords (meaning, sorry, line segments that connect two points on the circumference).  That makes 820 pairs of chords, but only above one third of the pairs will intersect (meaning, inside the circle).  Those roughly 270 points of intersection, plotted on a virtual piano roll, become the notes of a variation.  The piece consists of 10 variations.  Each note/point sits on two lines, so each line will contain an average of about 13 notes.  This is the emergent clue.  Depending on the slope of the line segment, it will sound as a chord, a broken chord, an arpeggio, a line slowly ascending or descending, or even a pedal tone.  Of course the points/notes on a line don't sit evenly spaced - their position gets determined by the random dispositions of the other chords.  But every note is overdetermined -- by design it sits on two lines and thus helps describe two different musical figures.

Empirically, the 88 note space of the piano (so 352 distinct pitches by the use of eighth-tones) feels like one minute.  Too much faster and the emergent shapes get compressed into illegibility, too much slower and the notes get unglued by the strain on short-term memory.

The accompanying graphic explores a similar construction, but in the visual realm.

Time-Space-Circle-Line-Point #7, for four pianos tuned in eighth tones

Multiple hands keep all registers of the piano engaged nearly constantly with contrast made in other ways.  A type of "moment form" makes disjunct, atonal material surprising legible even on a first hearing.  The music seems to tell a story propulsively, but a story with no beginning, middle or end. 

When the Clouds in Autumn Crack (2016) for piano four hands

From a set that includes
https://soundcloud.com/david-victor-feldman/our-ringlets-to-the-whistling-wind-2016-for-piano-four-hands 
and
https://soundcloud.com/david-victor-feldman/when-the-clouds-in-autumn-crack-2016-for-piano-4-hands



there's no clock in the forest (2016) for piano four hands

You will hear one structure filtered through another.   Leaving aside here any description of the complex underlying structure, the filter simply quantizes (or patterns or metricizes) the otherwise very free rhythms, but on and off every few seconds.  This makes an audible yet subtle contrast, but does not jar the larger musical flow.   

Having finalized the composition,  I abruptly realized its conceptual similarity with a beautiful series of drawings by my friend Jessica Rosner.   In this series she conceives symmetric geometrical structures and then executes half the design freehand, half with straightedge.   The contrast in techniques makes a structure that coexists with a structure leaving the viewer freedom where to direct her mind.

Jessica has generously lent me her running title and permission to feature a very recent addition to this body of work as the cover image for this track.
Find more of her work at http://jessicadeanerosner.com .

Ruled Unruled for piano four hands

The algorithm is simple:  note  n  appears on beats f_n + f_m where
the sequence f_n runs over Fibonacci numbers (positive and negative): ...-377 -233 -144  -89 -55  -34 -21 -13  -8  -5  -3  -2  -1  0  1 2  3  5  8  13 21 34  55 89 144 233 377...  The notes themselves come from a scale that repeats, not at the octave, but at the fifth: 
(b$-3) (c-2) (e$-2) (f-2) (g-2) (b$-2) (c-1) (d-1) (f-1) (g-1) (a-1) (c1) (d1) (e1) (g1) (a1) (b1) (d2) (e2) (f#2) (a2) (b2) (c#3), so the emergent structure is naturally polytonal and  seems to modulate from flat to sharp keys.

Music For Piano Four Hands (The Sums Of Two Fibonacci Numbers) (1978)

We live in strange, sad times.

Recently, for an utterly practical purpose, someone asked me the following question:  

12 people who need to meet by Zoom (due to the pandemic) would all like to get to know each other, one-on-one.  But to save time, they'd like to break out repeatedly into 4 groups of 3 (rather than into groups of 2).  How many times will they have to do so for every pair of people to meet at least once in some small group?

Turns out they will have to break out 7 times, but this means 18 pairs of people will meet twice, so, while best possible, not a very tight solution.  

I sent them such a plan.

Then it occurred to me that if they'd allowed one break out into 3 groups of 4, things can work out perfectly tightly with just 5(=4+1) break outs total..

And then I thought, what if I treated pitch (classes) as the people?  

That makes the groups of 3 into trichords, 4 each from the 4 breakouts into 4 groups of 3.  So then it would seem nice to have all  16 trichords harmonically distinct (even up to transposition, which makes trichords come in 19 possible flavors total).

It turns out that there exist only 20 basic ways (of assigning pitches to people) that accomplish this. 

One of those forms the floor plan of this piece.

But also on my mind: a friend recently lost a close family member. I felt very sad to learn that the pandemic will prevent his relatives from actually gathering, so they have planned a Zoom memorial.   

And so, as I worked on this piece, I began to conceive it as a strange kind of funeral march, albeit without meter or tonality.  Thus  I dedicate it to the memory of all we have lost and will lose in this worldwide catastrophe.

Zoom Memorial, for piano

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

Please don't spam this account!

Time-Space-Circle-Line-Point #7, for four pianos tuned in eighth tones

David Victor Feldman