Krikos 1: Circular Variations 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 1

Circular Variations.  An anticlockwise survey.  Its inner sections cast in alternating texture their respective half-circle rotations.  Its outer sections distill simultaneities from alternative cycle readings denoting exclusively either time-only or pitch-only exchange.

There are five movements:

      Perpetual        

Static        

         Suspended        

    At libery        

 Flying        

Access: audio per movement ( K1a, K1b, K1c, K1d, K1e)

at IMSLP; or complete ( K1) at SoundCloud.