Catakleismic: Difference between revisions
+interval chain |
Reinterpret as a 2.3.5.7.13 subgroup temperament |
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The '''catakleismic temperament''' is one of the best extensions of hanson, the 5-limit temperament tempering out the [[kleisma]]. | |||
Catakleismic is naturally viewed as a 2.3.5.7.13 temperament, first extending hanson to include the harmonic 13 (called '''cata'''), and then to include 7. Various reasonable extensions exist for harmonic 11. These are ''undecimal catakleismic'', mapping 11 to -21 generator steps, ''cataclysmic'', to +32 steps, ''catalytic'', to +51 steps, and cataleptic, to -2 steps. | |||
See [[Kleismic family #Catakleismic]] for technical data. | See [[Kleismic family #Catakleismic]] for technical data. | ||
| Line 44: | Line 48: | ||
|- | |- | ||
| 9 | | 9 | ||
| 450. | | 450.7 | ||
| 13/10 | | 13/10 | ||
|- | |- | ||
| Line 64: | Line 68: | ||
|- | |- | ||
| 14 | | 14 | ||
| 834. | | 834.4 | ||
| '''13/8''', 21/13 | | '''13/8''', 21/13 | ||
|- | |- | ||
| 15 | | 15 | ||
| 1151.1 | | 1151.1 | ||
| 35/18 | | 35/18 | ||
|- | |- | ||
| 16 | | 16 | ||
| 267. | | 267.9 | ||
| 7/6 | | 7/6 | ||
|- | |- | ||
| 17 | | 17 | ||
| 584. | | 584.6 | ||
| 7/5 | | 7/5 | ||
|- | |- | ||
| Line 84: | Line 88: | ||
|- | |- | ||
| 19 | | 19 | ||
| 18. | | 18.1 | ||
| 81/80 | | 81/80 | ||
|} | |} | ||
<nowiki>*</nowiki> in 13 | <nowiki>*</nowiki> in 2.3.5.7.13 POTE tuning | ||
== Chords == | == Chords == | ||