Canou temperament
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⟩ |
| Noellisma | 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.
Interval lattice
Scales
Fokker blocks of 9, 14 and 19 tones are among the most useful canou scales.