In ModuloCycles from the Perfect Squared Squarefor solo piano[3:40]SOURCES
A square divided into subsquares is "Squared". Where division has ensured
that the subsquare sizes are unique, this framing square is also "Perfect".
Further, if its subsquares number 21 - proven as the fewest possible - then
their framing square is the "Simplest".I took up this figure originally for a different sort of division, that of Fibonacci's
integer series, commandeering the subsquare dimensions as moduli. The
result, Additudes! for Csound (2005) consisted of 21 movements, one per
modulus, in which the mod-cycle values determined pitch assignment and
their occurrence frequencies set note-durations.COMPOSITION
In Modulo is a reworking of that music for piano solo, translating pitch values
from frequency-cycles-per-second to standard keyboard notation and that of
duration values from decimal seconds to standard notes. New in this process
has been my use of the cycle values' occurrence frequencies to determine
both note durations and voice density. The latter has varied (as occurrence-
frequency series yielded subcycles of their own), suggesting several levels
of voice combination. Finally, I have patterned those levels to determine the
order of movements.The score's line lengths roughly parallel the modulus values themselves, so
as to reflect them horizontally as the pitch ranges do vertically. Please note,
however, that this parallel is not at all reflected in the tempo settings - or in
the audio file performance lengths, varying intuitively from 2 to 22 seconds.
PERFORMANCE
Most problematic in the result, despite many vertical &/or horizontal pattern
reflections (marked "<>" in the score) is a resistance often shown to metrical
organization, especially where tuplets (of 3 or 5) are concerned. Although
measures are defined so as to encompass all of any tuplet's members, the
members themselves are only seldom positioned together! Inevitably, then,
any sense of "beat" is often only fleetingly available, facing imminent upset.
Accordingly, many of the score's time signatures I have hazarded mainly to
suggest a most probably usable beat value.Regarding articulation: all notes within a slur are to be connected, with the
last then curtailed to detach from what follows; the sustain pedal may help
within slurs to connect what the hands cannot, but its use must not "smooth
over" slur-end detachments.SOUND FILE
The audio accompanying this score was produced by the composer via
*Rosegarden* and realized via Pianoteq's "D4 Pointillist" instrument.