SUMMARY

The Methods

This is a summary of those methods which are recurring in the composing of my music.

• RANGE
• For some compositions, I have used the following methods to keep numbers within a specifiable range. Here n is a natural number and r is the range (the number of discrete elements).

• Conversion Convert n to base r.
• Congruence Arithmetic Replace n by n mod r, i.e. the remainder when n is divided by r.
• Digit Sums Replace n by its digit sum, repeatedly if necessary, until it is less than r.
• Digit Products Replace n by its digit product, repeatedly if necessary, until it is less than r.
• Periodic Functions Replace n by r / 2 cos n - 1 or r / 2 sin n - 1 rounded off to the nearest integer.

• MAPPING OF NUMBERS TO TONES
• The following methods have been used in various ways to map numbers to tones.

• Duration
• All digits/numbers maps to a specified note value.
• Digits or groups of digits maps to specified note values.
• The number n of consecutive equal digits/numbers maps to a tied n multiple of a specified note value.
• The number of digits m of a number maps to the note value 1/m.
• Pitch
• Digits or groups of digits maps to specified pitches, including a pause and change of octave.
• The number n maps to the pitch n scale steps relative to the pitch of the previously determined tone.
• Structure
• Digits of numbers of different powers maps to separate parts.
• Parts are initiated later in a piece by numbers satisfying specified conditions.

INDEX