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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]]. | |||
[[Category: | 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 = {{monzo| 4 -14 3 4 }}. It passes as a [[microtemperament]] with the [[9-odd-limit]] [[Minimax tuning|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. | |||
{| class="wikitable" | |||
! Name | |||
! Ratio | |||
! Cents | |||
! Monzo | |||
|- | |||
| Password | |||
| 1216/1215 | |||
| 1.42430 | |||
| {{monzo| 6 -5 -1 0 0 0 0 1 }} | |||
|- | |||
| Noema | |||
| 1225/1224 | |||
| 1.41383 | |||
| {{monzo| -3 -2 2 2 0 0 -1 }} | |||
|- | |||
| Aureusma | |||
| 1445/1444 | |||
| 1.19850 | |||
| {{monzo| -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. | |||
{| class="wikitable" | |||
! Name | |||
! Ratio | |||
! Cents | |||
! Monzo | |||
|- | |||
| Decimillisma | |||
| 165376/165375 | |||
| 0.01047 | |||
| {{monzo| 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| Canou scales }} | |||
Fokker blocks of 9, 14 and 19 tones are among the most useful canou scales. | |||
[[Category:Regular temperament theory]] | |||
[[Category:Canou| ]] <!-- main article --> | |||
[[Category:Canou family]] | |||
{{IoT}} | |||