MDPE.Application:4.1 - Generate the small seed and choose its phase

An ensemble wants three audible attacks in a repeating eight-pulse span. Its pulse 0 is fixed by the accompaniment. Another instrument has a cue at pulse 6, where this new part should remain audibly silent. The percussionist has a low-sounding instrument for the right hand and a contrasting high-sounding instrument for the left. The first musical question is whether a two-cycle timbral exchange works with the accompaniment.

Use x for an audible onset and . for a silent pulse. For this specific seed, begin with three onset columns and five silent pulses. Give each onset one silent pulse, leaving two; append the remaining two to the first two columns. Read each column downwards and concatenate:

initial groups:       [x]   [x]   [x]     remaining: . . . . .
after first sharing:  [x .] [x .] [x .]   remaining: . .
after second sharing: [x . .] [x . .] [x .]
concatenated:         x . . x . . x .
positions:            0 1 2 3 4 5 6 7

The onsets are 0, 3 and 6. Their cyclic gaps are 3, 3 and 2, including the return from 6 to the next cycle’s 0. There are three onsets, eight positions and gaps differing by at most one pulse. These facts establish the selected construction, not its musical value. For a different number of onsets or pulses, use the chapter-21 repeated-distribution algorithm or an already qualified seed; the particular two-sharing calculation above is not a general formula for every pair of counts.

The seed places an attack on the other instrument’s cue at 6. Rotate every onset forward by two positions, wrapping at 8: 0 becomes 2, 3 becomes 5, and 6 becomes 0. The ordered result is 0, 2, 5, with gaps 2, 3, 3. It preserves the cyclic spacing family and attack count, includes the fixed pulse 0 and leaves pulse 6 silent. This rotation changes the relation to the accompaniment even though a comparison of unanchored cyclic shapes treats the two patterns as equivalent. Merely rotating the diagram’s labels would not change the performed phase.