Catakleismic: Difference between revisions
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See [[Kleismic family #Catakleismic]] for technical data. | See [[Kleismic family #Catakleismic]] for technical data. | ||
== Interval chain == | |||
{| class="wikitable center-1 right-2" | |||
! # | |||
! 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 | |||
| 450.6 | |||
| 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 | |||
| 834.3 | |||
| '''13/8''', 21/13 | |||
|- | |||
| 15 | |||
| 1151.1 | |||
| 35/18, 64/33 | |||
|- | |||
| 16 | |||
| 267.8 | |||
| 7/6 | |||
|- | |||
| 17 | |||
| 584.5 | |||
| 7/5 | |||
|- | |||
| 18 | |||
| 901.3 | |||
| 27/16 | |||
|- | |||
| 19 | |||
| 18.0 | |||
| 81/80 | |||
|} | |||
<nowiki>*</nowiki> in 13-limit POTE tuning | |||
== Chords == | == Chords == |
Revision as of 10:01, 14 May 2021
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 | 450.6 | 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 | 834.3 | 13/8, 21/13 |
15 | 1151.1 | 35/18, 64/33 |
16 | 267.8 | 7/6 |
17 | 584.5 | 7/5 |
18 | 901.3 | 27/16 |
19 | 18.0 | 81/80 |
* in 13-limit POTE tuning
Chords
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 |