WhirlyOstinato on a Subprime Fibfor solo piano[1:05]COMPOSITION
J. H. Conway's Subprime Fibonacci Sequence (to quote passim from several OEIS
articles) is "similar to Fibonacci recursion, but with each new nonprime term replaced
via division by its least prime factor. Recursion enters a loop after a finite number of
steps. Assuming all seed values (to [10^5, 10^5]), there are seven possible unique
loops, each of unique length."
Conway's original (1, 1, ...) upon producing pair (48, 13) enters an 18-member loop
of values ranging from 13 to 97 - as such directly mappable to an integer pitch range
of 7 octaves. I have built Whirly on its second rotation:
[: 61 37 49 43 46 89 45 67 56 41 97 69 83 76 53 43 48 13 :]
The work is a short study in octave incremented range expansion and contraction -
the former via increasing pitch modulus, the latter (inverted) via interval compression.
This pairing occurs in each of two 7+7 bar sections -- first outwards/inwards from
keyboard center, then both progressions upwards from the bottom.
In the source series only 3 values occur as strict Fibonacci sums, i.e., escaping
subprime division. I have set their corresponding durations to double that of their
neighbors, yielding an overall meter of 7 dotted 8ths.
For visual clarity in the score, staff assignment was set per note simply according to
pitch register. Note distribution between the hands is left to performers' discretion.
PERFORMANCE
As this work may be unplayable at needed speed, some inaccuracy may be expected.
Please do ensure, however, that each pedal release occurs at (not after) its 3rd 16th,
so as to detach from the beat following. I suggest that volume increase as range
expands and decrease as it contracts, with extremes exaggerated in the second half.
SOUND FILE
The audio accompanying this score was developed by the composer via LilyPond
output edits in Rosegarden, then realized via Pianoteq's "D4 Vintage Bösendorfer"
instrument.