Catakleismic: Difference between revisions
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== Chords == | == Chords == | ||
: ''Main article: [[Chords of catakleismic]] and [[Chords of tridecimal catakleismic]]'' | |||
== Scales == | == Scales == | ||
Revision as of 13:56, 7 September 2021
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.
Interval chain
| # | Cents* | Approximate Ratios |
|---|---|---|
| 0 | 0.0 | 1/1 |
| 1 | 316.7 | 6/5 |
| 2 | 633.5 | 13/9 |
| 3 | 950.2 | 26/15 |
| 4 | 67.0 | 25/24, 26/25, 27/26, 28/27 |
| 5 | 383.7 | 5/4 |
| 6 | 700.4 | 3/2 |
| 7 | 1017.2 | 9/5 |
| 8 | 133.9 | 13/12, 14/13, 27/25 |
| 9 | 450.7 | 13/10 |
| 10 | 767.4 | 14/9 |
| 11 | 1084.1 | 15/8, 28/15 |
| 12 | 200.9 | 9/8 |
| 13 | 517.6 | 27/20 |
| 14 | 834.4 | 13/8, 21/13 |
| 15 | 1151.1 | 35/18 |
| 16 | 267.9 | 7/6 |
| 17 | 584.6 | 7/5 |
| 18 | 901.3 | 27/16 |
| 19 | 18.1 | 81/80 |
* in 2.3.5.7.13 POTE tuning
Chords
- Main article: Chords of catakleismic and Chords of tridecimal catakleismic
Scales
Spectrum of catakleismic tunings by eigenmonzos
| Eigenmonzo | Minor Third | Comments |
|---|---|---|
| 6/5 | 315.641 | |
| (5\19) | 315.789 | |
| 14/13 | 316.037 | |
| 15/14 | 316.414 | |
| 9/7 | 316.492 | |
| 11/8 | 316.604 | |
| 7/5 | 316.618 | |
| (19\72) | 316.667 | |
| 7/6 | 316.679 | |
| 14/11 | 316.686 | |
| 12/11 | 316.690 | |
| 11/10 | 316.731 | |
| 11/9 | 316.745 | 11-odd-limit minimax |
| (52\197) | 316.751 | |
| 8/7 | 316.765 | 7-, 9-, 13- and 15-odd-limit minimax |
| 15/11 | 316.780 | |
| 10/9 | 316.799 | |
| (33\125) | 316.800 | |
| 13/11 | 316.835 | |
| (14\53) | 316.981 | |
| 4/3 | 316.993 | 5-odd-limit minimax |
| 16/15 | 317.115 | |
| 13/10 | 317.135 | |
| 16/13 | 317.181 | |
| (23\87) | 317.241 | |
| 5/4 | 317.263 | |
| 13/12 | 317.322 | |
| 15/13 | 317.420 | |
| (9\34) | 317.647 | |
| 18/13 | 318.309 |