Continuing with my polytempo inventions, I deviated from prime numbers for this 3-part Invention. Why? Because I had set out to base this on the prime numbers 569:359:137 and, after my preliminary math realized that I was essentially working with 570:360:138, which ultimately led me to 95:60:23, which better facilitates the primitive technology I am working with. I am currently working with a calculator, paper and pencil, and Finale-MIDI, which responds well to tempos in whole numbers. I am also intentionally working in short musical statements in small musical forms. Not to shy away from 569:359:137, but the interest in its “primeness,” or complexity of tempo relationship, would best be heard at a fairly slow tempo, in a lengthy composition, and using technology that will render it precisely.
The three tempos used here are: 190, 120, and 46 beats per minute. There are six cycles, each cycle lasting about 30 seconds. The entire invention is 3 minutes long. The form is passacaglia, and the 6 cycles proceed like this:
I – passacaglia theme alone (46 bpm)
II – entry of the middle voice (120 bpm)
III – entry of the top voice (190 bpm)
IV – thickening of texture, especially quickening of the top voice
V – reduction and fragmenting of the texture, including simplification of the passacaglia theme
VI – further reduction of texture, essentially leaving only long-value chords in the top two voices; passacaglia theme whole