2023

Bagatelle without Teleology, no. 2

Bagatelle without Teleology, no. 1

The late 70s were probably the golden age of musical "set theory" (better described as "musical combinatorics").  Twelve-tone theory had evolved to great maturity by then, still few yet found the associated music in any way retardataire.  But computers were slow then, difficult to program, and confined to large institutions.  Thus the answers to many simple, musically meaningful questions remained unattainable.  Now (with Moore's Law flattening) should be the golden age!

All-interval rows have been around for more than a century.   Morris and Starr could enumerate them all in 1974 --- starting on pitch class 0, there exist 3856.  

This piece works with a special, and essentially unique pair of such, namely
[0 11 19 25 28 38 39 44 46 53 57 66 ]
[0  4  7 15 22 32 33 35 41 50 61 66 ].
Traditionally, twelve-tone rows order pitch classes in *time*, and that leaves register as either a free and expressive dimension or else a parameter that the composer may control by other means.   In this piece the rows order the register of the tones, thereby determining two twelve note chords (hence my choice above not to reduce mod 12).  

Any chord built up from an all-interval row will span exactly 5 1/2 octaves; and these two all interval rows, taken together, their union divides those 5 1/2 octaves more evenly than will any other pair (save their inversions, of course).  

The result is, paradoxically, maximal harmonic contrast between two full aggregate chords.   With the rows controlling register,  the two chords get broken melodically in myriads of ways.  Structurally they push against each other, blurring any hard distinction between the linear and vertical, or, if you will, the melodic and the harmonic.

(Of course bad puns in the title are a doff of the hat to Milton Babbitt.)

A Tier of Two Series (piano and marimba)

A realization here of a second-order open-form piece.

...it lay on my fevered spirit with a touch of infinite calm, for piano

a local habitation, for e flat clarinet

Morphosis, for oboe

Can Chance Music Be Sentimental?   No. 2

Can Chance Music Be Sentimental?  No. 1

There's also a version with obbligato alto flute (or alto sax).

The Turbulent Surge, for two pianos (Not Your Grandparents' 12-Tone Music VI)

The title is a riddle about how I made the piece.

Pinkfairies, for piano

The process:  generate a potential scale by selecting 7 random frequencies within an octave.  Discard the scale unless
1) [justness] all the 21 intervals coincide, within about a cent, to rational ratios having terms (numerator and denominator) no greater than 40;
2) [nondegeneracy] the approximating ratios do not include 1:1 or 2:1;
3)[ubiquitous commas] given any x,y and z, three frequencies in the scale, if, in 1) above,
 b/a approximates y/x and d/c approximates z/y, the relevant approximation of z/x does *not* equal (b/a)*(d/c), but rather differs from it by a nontrivial comma (approximate unison).

A search through 400,000,000 trial scales produced a mere 17 that meet all three requirements.  The piece presents these 17 in a kind of four-part harmony that contextualizes the relevant intervals.  The base line provides the common (approximate) fundamental, and the soprano interpolates the overtones over that fundamental that sit between the two notes (heard in the tenor and alto).  The 21 intervals got arranged from the most complex to most simple (within the given scale), so roughly from most dissonant to most consonant.  Bits of melody and harmonic progression then emerge from this objective arrangement of the materials.

Search For Extraterrestrial Intonation [electronic]

The punny title alludes to my long interest in making music where pitches arise compositionally rather than precompositionally, so not where the composer commits early to a fixed scale or temperament.    The challenge then lies in achieve some harmonic coherence absent such an over-abiding framework.

I chose the simple "Columbia-Princeton" timbres to let timbre get out of the way and let the pitches and their complex ratios shine.  If that makes the piece a bit of a pastiche, fine.

Without Frets [electronic]

This is the audio part of an audio-visual work of which you can see here just the first frame.

...the last threads of a blown-out sail of a ship after a storm..., for piano and harpsichord

The same generative process underlying the music also generates the images in this video:

https://www.youtube.com/watch?v=QeZaBFeIY4Q&list=PL5XFDmREe2DrLvQoTwiH2kTKzEj6CoIPr&index=2

This is one of a series of pieces all built on the same principle but sounding quite differently one from another.   More to come.

Double Shuffle, for piano

Double Shuffle [18]

The music theory behind the piece:  

The 7-note scale here consists of seven of the eight tones one obtains by dividing the octave into eight parts.  This scale affords seven distinct trichords (i.e. three-tone sonorities) up to transposition.  Turns out that one can select *particular* transpositions of the trichords, so that 
1) any two notes in the scale belong to exactly one of these special trichords, and 
2)also any two of these special trichords have a common tone.    

Of the total 5040 permutations of the seven tones, 168 preserve the set of special trichords just described, and these permutations thus constitute symmetries of the configuration.   

The basic material of the piece is a 7-tone "cyclic row"  which, when played in canon with itself, produces the 7-special trichords (as two consecutive notes from the first voice and one from the second voice).
Some of those 168 symmetries simply spin the cycle, so the symmetries generate only 168/7=24 variations.  

The piece consists of producing these variations in a florid style.

The work can be performed on harp by retuning a mere 9 strings to obtain the necessary quarter tones.   The performance requires no pedaling.

as the moon releases twig by twig the night-entangled trees, for harp

Concerning most musical works, one can reasonably say that they unfold within some preexisting musical language (so "language" at least in the sense of a vocabulary governed by a syntax governed by stylistic norms).  On one hand, many conservatives contend that a common language constitutes a minimum prerequisite for "communication," and that that principle makes any fiat language (e.g. Schoenberg's twelve-tone system) fundamentally problematic; on the other, hand many radicals advocate for language-free music grounded only in visceral sensation, music that explores the lives of individual sounds with no "glue" at all.  Of course myriad intermediate positions exist as well.

This piece indeed projects a fiat language (not Schoenberg's!), but by design allows listeners to internalize the workings that language gradually.  Now the following effect may be lost on certain experts possessed of excellent universal ear training and audacious on-the-fly analytical ability: for many listeners, jumping right to the middle of the piece may make the music there seem quite "random" and difficult to parse, while listening from the beginning renders the whole work quite legible on account of how the piece naturally trains the ear to hear what's coming next.

Apsides, an atonal passacaglia for piano

Up to transposition, there are 250 ways that an interval can transition to another interval without any note repeated (all notes within the chromatic scale).  The basic material here is a cycle of intervals that survey all 250 transitions.   Constant variations within the dimensions of timbre and articulation, though they might at first seem to work distractions away from the harmonic idea, actually mitigate exhaustion of the ear and so keep fresh the perception of all the intervals, and the intervals between intervals.

Every Bridge, for nine instruments

An amalgamation of opposites.  Rhythmically, a kind of regular, slow, breathing pulse gets elaborated with entropic details.  Harmonically, an atonal tone cluster undergoes variations that make every note function as a leading tone.  While the piece feels like it rises and rises, if you listen to the whole and start over, you'll hear that it ends just where it begins, like the pedestrians on Escher's staircase.

A Slow Climb In Difficult Weather, for piano

The opening and closing may seem pointillist, but by a gradual process of substituting notes for rests and then the reverse the texture becomes intensely contrapuntal.

Clearing, for flute and harpsichord

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

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2023

David Victor Feldman