Brandon Nelson

I’m sure by now we’re all pretty familiar with the idea of using dice (and other such devices) to make chance-based choices in composition.  I decided to see how far I could take this concept and I came up with the:

FLEXIBLE INTEGRAL-ALEATORIC PRECOMPOSITIONAL ALGORITHM
Within a Consonant Neotonal Framework (Optional)

Whole-Piece Governors

Note that any/all of these variables may be altered to suit your individual preferences.  What follows is just one way to “fill in the blanks.”

After the medium has been determined by the composer (e.g., chamber orchestra, band, woodwind quintet, percussion ensemble, etc.) the following procedures are undertaken:

The essential formal outlines of the piece are determined first. Using a standard pair of dice, roll to find the fundamental description:

Length of formal sections is determined by the composer.

The general expressive character of the piece is next determined (this step is optional):

Rate of dynamic change:

Determine now a discrete set of rhythmic data to be used throughout the piece (using the below-described process).

Tempo:

Transitional tempo effects (e.g., ritard, accelerando, etc.) may be decided by the composer’s particular tastes.

Unit Governors

The underlying harmony is next. The root of the chord:

The quality and voice composition (triad, etc.) of the chord:

Rate of harmonic change (the meter will be determined by the melodic data):

Harmonic data are deployed for all voices through the determined duration.

The melodic data is gathered next. Whether chord members only are to be used or if the harmonic data is to be interpreted as scalar is determined by rolling the dice: even for the former and odd for the latter.

Harmonic data is applied to melodic data through rhythmic predetermination:

The rhythmic unit having been determined, next to be determined is the number of iterations of said unit. Roll the pair of dice; the resultant number is the number of iterations.

After the first bar rhythmic iterations have been determined, the hence-derived meter governs the following rhythmic iterations value for as long as the timbral grouping allows (i.e., the subsequent iterations value cannot violate the number of bars previously assigned to the timbral grouping). The subsequent bar(s), then, must be in the same meter to allow for the timbral grouping assignment. Thus, rhythmic iterations of the determined rhythmic unit have already been determined.
For each iteration of the rhythmic unit, an articulation for it is assigned:

In the same way as rhythmic iteration, dynamics are assigned (this is optional and is largely dependent upon the level of difficulty intended by the composer):

Transitional dynamic effects (e.g., crescendo, decrescendo, etc.) may be decided by the composer’s particular tastes.

Texture (for the formal section, entire piece, or harmonic span):

Specific texture to be used:

Timbral Grouping (length determined by composer taste):

Instruments involved in the timbral grouping (solo, small group) are determined by composer taste.

SAMPLE COMPOSITION ILLUSTRATING THE PROCESS

Whole-Piece Governors

Medium: Violin duet

Formal Outline: rolled a 10 (minuet-and-trio)

It was determined by the composer that the minuet section would comprise 32 bars and the trio would compose 24 bars. Each section may be repeated at the performer’s discretion.

General Expressive Character: rolled a 10 (idyllic/pastoral)

Dynamic Rate of Change: rolled an 8 (freely determined)

Since dynamics are to be freely determined, the Dynamic Assignment process is not needed for this piece.

Tempo: rolled an 8 (allegro)

Unit Governors

Underlying Harmony: rolled a 10 (Gb)

Quality and Voice Composition of the Chord: rolled a 12 (+M 7th)

Chordal Manifestation: Gb-Bb-D-F
Scalar Manifestation: Gb-Ab-Bb-C-D-Eb-F

Rate of Harmonic Change: rolled a two (2/bar)

Thus, a new underlying harmony will be determined halfway through this bar.

Use of Harmonic Data: rolled an 8 (chordal manifestation only)

Rhyhtmic Unit: rolled a 7 (dotted-eighth, 16th)

Iterations of the Unit: rolled a 4 (four iterations)

Four “dotted-eight, 16th” patterns will be used. The meter most obviously suggested by this would be 4/4.

Therefore, the Gb+M7 harmonic unit will be used for the first two beats, and another harmonic unit will complete the measure.

Underlying Harmony: rolled a 6 (D)

Quality and Voice Composition of the Chord: rolled an 8 (mm7)

Rate of Harmonic Change already determined (the latter half of the present measure)

Use of Harmonic Data: rolled a 12 (chordal manifestation only)

D-F-A-C

Rhythmic Unit and Iterations of the Unit already determined.

Assignment of Articulation:

Eight rhythmic subunits must be determined, thus the dice must be rolled eight times (one articulation for each unit).

Unit 1: rolled a 5(^)
Unit 2: rolled a 9—must roll again; rolled a 6 (normal)
Unit 3: rolled a 10—must roll again; rolled a 2( _ )
Unit 4: rolled an 8—must roll again; rolled a 6 (normal)
Unit 5: rolled a 7—must roll again; rolled a 6 (normal)
Unit 6: rolled a 6 (normal)
Unit 7: rolled a 3 (.)
Unit 8: rolled a 2 ( _ )

Textural Duration: rolled a 5 (entire piece)

Textural Assignment: rolled a 2 (homophonic – chordal)

Timbral Grouping: rolled a 7 (solo)

In a medium as small as this, small group and tutti are regarded as the same.

It was decided that this timbral grouping should last for two bars, after which a roll of the dice would be required to decide the next texture.
Overall Plan of the Piece:

Fun stuff!  What can YOU come up with?