Gordon Monro - "Study in Dimension 1.245"

"Study in Dimension 1.245"

Tape piece, duration 5 mins 15 secs (1992)

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 2.5 Australia Licence.

Program note

Study in Dimension 1.245 is a MIDI sequence piece; it is based on a fractal curve with dimension approximately 1.245. The procedure for constructing the curve is an iterative one; each successive iteration gives a better approximation, and the actual fractal is the limit curve of all the approximations.

Iterations 1 to 4 of the construction were used to give four increasingly elaborate versions of the same basic melody, ranging from a few sparse notes to long runs of very rapid sounds. (All pitches were quantised to the nearest tempered semitone.) These melodies were then further modified; the piece is constructed in 24 overlapping sections, and each section has a "scale" (set of pitch classes) associated with it. In any particular section, only the notes belonging to the corresponding scale are heard, i.e. the melody was "filtered" through the scale; notes outside the scale were deleted. This meant that sometimes a sparse version of the melody collapsed to a single note.

The scales themselves form a mathematical object called a Hadamard code. If we take any two scales of the 24 used in the piece and mark all the semitones that are in one of the scales but not the other, we find that either 6 or 12 semitones have been so marked. (If all 12 are marked, one scale consists exactly of all the notes not in the other scale.) The fact that the scales form a Hadamard code means that the scales are well spread out in the space of all possible sets of pitch classes.

The overall shape of the piece was controlled by the basic fractal curve; at a place where the curve is high the corresponding section of the piece has more occurrences of the melody. However details beyond this were left to the composer's intuition.

The synthesisers used are a Kawai K1, a Kawai K5 and a Yamaha TX81Z. The sounds are partly factory sounds and partly sounds created by the composer.

Performances, etc