Krikos 2: Time^Space Vortex on the Opening

of Schoenberg's Opus 33a

for 2 pianos, 8 instruments, 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 2

Time^Space Vortex.  Here pitch-only or time-only evolution -- i.e., with change to the other parameter disabled -- is applied globally, yielding a study in mutual exclusion.   In this version scored for mixed ensemble, the 8 instruments are unspecified, although plans had assumed a quartette pair "with homogeneity desirable within, though optional between" the members -- presumably strings vs woodwinds.

There are two movements:

  Delta-X, Suspended

   Delta-Y, Whirling      

Access: the only score is yellowed paper;

its only audio was on cassette, now lost.