Involution (and Hexany Permutations)

Cover design by Scott Unrein

CD available at

Liner notes: Dean Rosenthal essay, credits, etc.


Technical details for the piece Involution (Disc 1)

Scales

Wilson-Grady Meta-Slendro tuning (Involution 1)

  • 5-note MOS scale: 65/64, 151/128, 43/32, 49/32, 57/32
  • 7-note MOS scale: 1/1, 9/8, 37/32. 5/4, 21/16, 3/2, 7/4

Grady Centaur tuning (Involution 2)

  • Prometheus scale, a just version: 1/1, 9/8, 5/4, 7/5, 5/3, 7/4
  • Marwa scale, a just version: 1/1, 21/20, 5/4, 7/5, 5/3, 15/8

Dual Hexany tuning (Involution 3)

  • Double hexany scale: a 1-3-5-7 hexany (1/1, 7/6, 5/4, 32/24, 5/3, 7/4) , duplicated and transposed up by a major 5-limit half-step (16/15). Combined, they form a 12-note scale where the two hexanies alternate, analogous to whole-tone scales in a conventional tuning.

Hardware

  • 2HP: ADSR (x2), Clock, Switch
  • Bastl: LOL
  • Instruo: øchd
  • Expert Sleepers: Disting Mk 4
  • Make Noise: DPO, Maths, Mimeophon, ModDemix, Optomix, QPAS, René, Tempi, Wogglebug, X-Pan
  • Noise Engineering: Loquelic Iteritas
  • Tubbutec: µTune
  • Raspberry Pi 4
  • Eventide H9

Code

The computer portion of Involution is built on the The Implication Organ, Csound code: https://github.com/DaveSeidel/music-src/tree/master/implication-organ


Modular Synthesizer Layout and Patch Diagram

Involution hardware layout
This is a simulacrum, not a photo. See https://www.modulargrid.net/e/racks/view/1032567

Involution patch diagram (SVG)
Involution patch diagram (SVG), Click to open full size

Notes on Hexany Permutations (Disc 2)

Source Code

Hexany Permutations was written in Csound, with the score generated by Python. The source code is available here.

Score

Hexany Permutations was created as a piece of electronic music, but could theoretically be performed by an ensemble of low-ish strings (eg, cellos, violas, or violas da gamba) as long as each player can commit to playing one oddly-tuned pitch (each player has their own pitch). With that possibility in mind I created a score and parts. If you are interested in performing this piece, get in touch.


Graphics

Spectrogram of Involution 1
Spectrogram of Involution 1, left /top and right/bottom channels, made in Audacity.

Hexany Permutations, graphed
Hexany Permutations, graphed. Six horizontal rows: each row is a section of the piece numbered as shown.

An old mathematical symbol for involution
An old mathematical symbol for involution.