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.
- 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