Krikos 3: Prelude & Centrifugue on the Opening

of Schoenberg's Opus 33a

for 2 pianos or Csound

[6:55]

Krikoi Overview

(See also the Algorithms page "Krikos" section.)

Measure 1 [three chords] of Schoenberg's Opus 33a is space proportionally dot-graphed.  The graph is pinned to a fixed grid calibrating its point positions with respect to pitch and time.  The pin prepares the graph for rotation around an axis just below its extreme NE point.  After initial performance of the source measure, the graph is rotated until two or more points come into new horizontal or vertical alignment.  Now shifted against the grid, the points receive correspondingly shifted pitch/time readings, which are in turn performed.  Horizontal alignment sounds as recurrence--pitches momentarily identical in their reversal of height. Vertical alignment sounds as simultaneity--attacks momentarily identical in their reversal of sequence.  Rotation then continues to the next realignment/ rereading/performance in a process usually running half-circle.  At 90 degrees [heard as three repetition levels] notes-at-a-time have become times-at-a-note.  At 180 degrees rotation has conspired with position of its axis to approximate source measure 2.

Sharing the 'Krikos' name, several independent pieces pursue selected constraints on this generative process.

Krikos 3

There are two movements:

Prelude: static.  The succession of coincidences is extracted.   Its rotating halves are mutually overlaid, so that each concidence is heard transparently against its conceptual (perpendicular) opposite.  Section 1, recurrences; section 2, simultaneities.

Centrifugue: dynamic.  The entire alignment-succession is presented.   Its temporal evolution is strictly ordinal, as durations are constrained to a unit value in perpetuo.  Section 1, clockwise; section 2, anticlockwise.

Access: the only score is yellowed paper;

its only audio was on cassette, now lost.