For any number of players on any instruments
A rhythmic scheme in which up to three pulses are played simultaneously in the following ratios of beats: 3:4:5, 4:5:6, 5:6:7, 6:7:8 and 7:8:9. Each set is called a pulse field.
All the fields resolve to a simultaneity at the lowest common denominators of their component values, respectively 60, 60, 210, 168 and 504 beats, as in 60 = 20 x 3 = 15 x 4 = 12 x 5.
Each field is notated three ways, i.e. in the units of each constituent pulse. For example, the 3:4:5 field is notated in 3/16, 4/16 and 5/16. This is done to help the players(s) express any two pulses in terms of a third. It is not meant to suggest that a given field be played three or any other number of times before resolving to another.
The notated pitches in each field correspond (roughly in some cases) to the frequency ratios of their component intervals. For example, since 3:4 is a perfect fourth, and 4:5 is a major third (in just intonation), the 3:4:5 field can be thought of as a first inversion minor triad in macrocosm. This is not meant to suggest that any field be expressed using only the notated pitches. It may (or may not) suggest harmonic relationships.
The pulses are arrayed in order of duration (i.e. the highest pitch is the shortest pulse) but do not have to played so; e.g., 3:4:5 may be played 5:4:3, 3:5:4 etc. In other words, octave transpositions are allowed.
Constituent pulses in a field may switch voices at simultaneities. In the 3:4:5 field, for example, there are 10 simultaneities, since 3:4 resolves every 12 beats or 4 times , 3:5 every 15 beats or 3 times, 4:5 every 20 beats or 2 times, and 3:4:5 every 60 beats or 1 time per cycle.
The piece is free in all other parameters. It may be played by any number of players on any instruments.
The pulse fields may be played in any order.
Full or partial statements of a given field may be interspersed with rhythmically improvised playing. Improvised passages may occur either between or within fields starting at simultaneities. Fields interrupted by improvisations may (or may not) resume where they leave off.
Pulses from different notated fields may be combined to create new ones (e.g. 6:7:9).
In addition to being kept, pulses may be expressed through meter and/or rhythm. If one pulse in a field is expressed in a particular way, so may the others; e.g. one meter or rhythm may be played in more than one pulse (e.g. 3:4:5/(2+1).
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