Fun With A Pair of Dice

Note: The Music Journal is a feature I launched to give myself casual opportunities to explore musical ideas or concepts that don’t regularly turn up in my projects or just interest me in some way.  I think of it as my “musical sandbox.”  The format will be quite loose, the frequency similarly liberal, and I invite you to leave me your own thoughts about my brain doodles in the comments.  Thanks for coming by!

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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:

form

 

 

Length of formal sections is determined by the composer.

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

character

 

 

 

Rate of dynamic change:

dynchange

 

 

 

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

Tempo:

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:

roots

 

 

 

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

qualities

 

 

 

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

change

 

 

 

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:

iterations

 

 

 

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:

articulation

 

 

 

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):

dynamics

 

 

 

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):

span

 

 

 

Specific texture to be used:

texture

 

 

 

Timbral Grouping (length determined by composer taste):

timbralgrouping

 

 

 

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 ( _ )

sample

 

 

 

 

 

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:

plan

 

 

 

 

 

 

Fun stuff!  What can YOU come up with?

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7 comments

  1. Such an interesting way to compose Brandon. I like the way you are searching for intuitive concepts. Cheers Gordon

    Yours Sincerely

    Gordon Gunn Classroom / Instrumental Music Teacher

  2. Nice! I once wrote a piece in college called “The Babbitt’s Cage,” in which all musical parameters were serialized in a similar fashion (merely having an order to map a die value to a musical parameter presupposes some kind of nominal serialism) and the values were determined by dice role. As a class, we came to the consensus that the aesthetic experience of a piece in which everything is tightly controlled (e.g., integral serialism a la Babbitt) and a piece in which everything is left entirely to chance (e.g., aleatory procedures a la Cage) is quite similar.

    Good post, Brandon!

      1. I agree, Brandon. The extremes of compositional technique — total control and total chaos — do seem to curve in toward each other in terms of the listeners’ experience. Back in the early days of PCs I asked a friend if he could generate a randomized listing of the numbers 1 to 88. He could and did. I would then write a piece for the piano in which each key is used only once, whether linearly or in chordally. It took me only a few measures to realize this was going nowhere, and might well be unplayable.

        As for your system with the dice, It strikes me that some of the decisions I make while composing amount to mental dice-rolling or coin flipping, so why not organize it and make use of it as a tool? In setting up the choices for each parameter, it might help to utilize a characteristic of dice that casinos and craps shooters know well: some numbers come up more easily than others. There are six combinations that produce 7, five for 6 and 8, four for 5 and 9, three for 4 and 10, two for 3 and 11, and one each for 2 and 12.

        This also reminds me of an artist, Walt Whippo, who was a frequent guest on a TV talk show on the arts I co-hosted many wears ago. Walt was a great conversationalist, and could fill in at a moment’s notice in the case of a no-show guest. One time we invited him to bring along a painting in progress and let us see him working on it. He refused, saying that would create the erroneous impression that knowing his choice of process would contribute to the understanding of the finished product. This wasn’t, after all, a cooking show.

        So if I tried your dice device (and I just might), I wouldn’t tell anybody, lest they use that as an excuse for liking or disliking the piece. I did one use a certain numerical sequence that had nothing to do with music to generate a shot theme that worked very well in a piece. In the spirit of Walt Whippo, I won’t reveal the numbers or the piece.

  3. Good way to trigger the creative juices. For me I have been acting as a musical engineer following my stream of consciousness under the influence of “Euterpe.” Although I have used 12-sided music dice (notes) for my atonal pieces.

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