Catakleismic

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

• Cata7
• Cata11
• Cata15
• Cata19
• Catakleismic34

Tuning spectrum

EDO generator	eigenmonzo (unchanged-interval)	generator (¢)	comments
	6/5	315.641
5\19		315.789	Lower bound of 9-odd-limit diamond monotone
	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	Upper bound of 9-odd-limit diamond monotone
	18/13	318.309