SUMMARY

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

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.

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.