Canou temperament

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The canou temperament is a rank-3 regular temperament for the 2.3.5.7.17.19 subgroup (or any immediate restrictions thereof), defined by tempering out 1216/1215, 1225/1224, and 1445/1444. It is generated by a perfect fifth (~3/2) and an ultramajor second (~81/70). It is first found and explored by Flora Canou.

See Canou family #Canou for more technical data.

Overview

The temperament was at first discovered as 7-limit only, where it tempers out the canousma, 4802000/4782969 = [4 -14 3 4. It passes as a microtemperament with the 9-odd-limit minimax error of 0.98¢ (1/7 canousma). Extending it to the 2.3.5.7.17.19 subgroup adds virtually no additional error as the number of minimax error is also characteristic of the tonality diamond of 1.3.5.7.9.15.17.19.21.

Name Ratio Cents Monzo
Password 1216/1215 1.42430 [6 -5 -1 0 0 0 0 1
Noema 1225/1224 1.41383 [-3 -2 2 2 0 0 -1
Aureusma 1445/1444 1.19850 [-2 0 1 0 0 0 2 -2

The password equates 19/15 with 81/64, 20/19 with 256/243, and 81/80 with 76/75. It characterizes the temperament with a counterpyth fifth and enables 19-odd-limit essentially tempered chords. The aureusma splits the 5/4 major third into a stack of two 19/17's and enables 19-odd-limit essentially tempered chords. The noema equates 35/34 with 36/35 and enables 25-odd-limit essentially tempered chords. Finally, canou tempers out 165376/165375, the decimillisma, the difference between 1216/1215 and 1225/1224.

Name Ratio Cents Monzo
Decimillisma 165376/165375 0.01047 [9 -3 -3 -2 0 0 1 1

Recommendable edo tunings include 94, 99, 118, 193, 217, 311, 410 and 721, with 721 giving the OPV for the 2.3.5.7.17.19 subgroup.

Decent amount of harmonic resources are provided by a simple 9-note scale. Flora Canou commented:

— It sounds somewhat like a Phrygian scale but the abundance of small intervals of 28/27 makes it melodically active.

14- and 19-note scales are also highly concise for the temperament. See #scales for more information.

Scales

Main article: Canou scales

Fokker blocks of 9, 14 and 19 tones are among the most useful canou scales.