Catakleismic

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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.

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

Tuning spectrum

ET
generator
eigenmonzo
(unchanged interval
)
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