Aleatoric Exercise: Let's Roll!

Karlheinz Stockhausen 
presenting a graphical score

Aleatoric (or "chance") music is any music where some of the performance or composition elements are left up to chance. 20th century classical composers such as Pierre Boulez,  Karlheinz Stockhausen, and John Cage used a variety of techniques to incorporate randomness in their compositions. Boulez would compose a number of musical options that the musician could choose during a performance. This would create what Boulez called a "mobile form". Stockhausen would often use non-standard graphic notation which provides the performer with a general guide to interpret the music in her own manner. Thus the piece would change from performance to performance depending on the interpretation of the graphic. Cage composed his Music for Changes by consulting the I Ching (an ancient Chinese book that is used for divination) to determine duration and pitch as used in the composition.

The I Ching: 64 hexagrams used by 
composer John Cage 
and jazz guitarist Pat Martino

As jazz musicians explored "free" jazz and the avant-garde in the 1960s they would also add chance elements to their playing. In improvisation, musicians like Ornette Coleman, John Coltrane and Sun Ra would make one or more elements of the performance "free". They may abandon a defined meter, tonality, harmonic progressions, or even the beat. These elements would be free to the improvisor and their ensemble to collectively determine during the performance. Jazz guitarist Pat Martino has also used the above mentioned I Ching to explore string combinations available on the guitar.

An important aspect of all of the above examples is to recognize that the artist only uses chance for a part of the project. If the entire creation was left up to chance there would be no human input. It would not be music. However, using varying degrees of chance to lock in certain elements can get the musician to explore those other elements more freely (see the previous post on Limitation Exercises).

Let's explore. Any element of music can be left up to chance. Melody, harmony, chord progression, rhythm, and form are all fair game. It is best to start with just one and explore that thoroughly. You can also explore this as composition or as a spontaneous improvisation.

A set of polyhedral dice 
(d4, d6, d8, d10, d12, d20)

The first thing we need is a random generator. I don't think you need anything as esoteric as the I Ching. A simple set of polyhedral dice that you would would find at a game or hobby shop (or Amazon) would work well. For our purposes the most useful would be the following dice: d4, d6 (which you probably have already), d8, and d12. You can actually create any sided dice by always rerolling certain numbers (a d6 can be a d5 by rerolling any 6s).

I recommend real dice because nothing beats the feel of chance in your hands. But if you must, here is a useful "virtual dice" website.

I hesitate to define this process too much. Part of the fun is the exploration and the freedom. If one of these ideas sounds intriguing go for it. Don't be afraid to change it as you go or to even abandon the chance technique. If you hear something in your ear so strongly, then by all means stop the chance and start creating.

To get you going, I recommend you follow these steps:

1. Choose a main element of composition or improvisation you would like to explore (harmony, melody, rhythm, form). 
2. Define one aspect of that element (intervals, measures, chord tones, sections, chord quality, rhythm, meter, etc.)
3. Match that aspect with the dice (d2/coin, d4, d6, d8, d10, d12, d20) that you feel is most appropriate. This is where you can be creative. Eventually you can combine these elements as well.

Here are some ideas to get you going. Choose one of them that seems interesting. Or let them inspire you to create your own. However, DO NOT do all of them at once. You will be overwhelmed. Choose just one for now! Later on you may combine them. Let's roll!

Melody:

• Roll a dice to determine the interval from one pitch of a melody to the next. You can make the melody ascend/descend as needed to determine an appropriate contour. Use larger dice for a more disjunct melody. You can make the intervals major or minor depending on the key. 
• Example: A roll of : 4, 2, 5 would yield a four-note motive. You can choose if you wish to ascend or descend with each interval.  Keeping it diatonic in the key of C Major and starting on Do could yield: C (up a 4th) F (down a 2nd) E (up a 5th) B.
• Or you can ignore the key and use a coin or dice to determine if the interval is major/minor/augmented/diminished.
• Roll a 12 sided dice to create a pseudo-"tone row". Designate 1 as a pitch with the other 11 forming the chromatic scale. You could ignore repeated notes or embrace them.
• Choose a pitch collection that fits a particular dice. Some examples:
• d4 - tones of a 7th chord; a tetrachord (like Do Re Me Fa or Fa So La Ti)
• d6 - a hexatonic structure (like Do Re Mi So La Ti); a whole tone scale; a pentatonic scale (reroll 6s); a blues scale (1 b3, 4, b5, 5, b7)
• d8 - any 7 note scale (major, harmonic/melodic minor, or their modes (reroll 8s), octatonic (diminished scale)
• d12 - the chromatic scale
• Then with that chosen pitch collection/dice, roll to compose a melody. Assign a value of the dice to each note. Roll until you feel you have a complete melody/phrase. Or you can even predetermine randomly how many rolls you will make. The choice of octave is up to you.
• You can also any of the above to determine root motion (see harmony below).
• You will need to create the rhythm and harmonic accompaniment of the "chance" melodies. This is how you will make this chance process musical and human. So once you have your notes, add rhythm and harmony to make it your own.

Harmony:

• Roll a d4 to determine the quality of the next chord (major, minor, diminished, augmented).
• Roll a d6, d8, or d12 to determine the root of the next chord.
• Roll a d8 to determine the function (roman numeral of the next chord).
• Roll a d12 to determine a single pitch that MUST be present in all of the chords you place in a piece (or a section of a piece). That tone may be in the basic triad or in one of the extensions (7th, 9th, 11th, 13th or altered sounds).

Meter/rhythm:

• Roll any dice to choose a meter.
• Roll a d4 to build an irregular compound meter. (e.g. You roll 3, 2, 2, 3. That could be a 10/8 time signature with the following pulse in bold (1 2 3 4 5 6 7 8 9 10) or in konokol (ta-ki-ta, ta-ka, ta-ka, ta-ki-ta)
• Roll a d6 to determine the rhythmic value of the next note or group of notes. Assign a value to each number (e.g. 1 - whole, 2 - dotted half, 3 - half, 4 - quarter, 5 - eighth, 6 - sixteenth).

Form:

• Roll a d20 to determine a length of a section (# of bars)
• Roll a d4, d6, or d8 to determine the number of sections.

Good luck. In future posts I will pick one of these and demonstrate the process. Keep in mind that these techniques do not have to be used to compose a whole piece. You may use it just to get going, or to get you out of a dead end. You also may not wish to create a whole piece with the technique. You may just wish to use this as an exploration tool. I explore that in future posts as well.