Tritikleismic

Tritikleismic

Subgroups	2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.13.17
Comma basis	1029/1024, 15625/15552 (7-limit);
Reduced mapping	⟨3; 6 5 -2 3 14 18]
ET join	72 & 87
Generators (CWE)	~6/5 = 316.938 ¢
MOS scales	3L 6s, 9L 3s, 12L 3s, 15L 12s, ...
Ploidacot	triploid gamma-hexacot
Pergen	(P8/3, cP5/6)
Minimax error	11-odd-limit: 2.41 ¢; 17-limit 21-odd-limit: 3.34 ¢
Target scale size	11-odd-limit: 57 notes; 17-limit 21-odd-limit: 72 notes

Tritikleismic is the rank-2 temperament that extends 5-limit kleismic to the 7-limit by tempering out 1029/1024, thus splitting the octave into three. In the 11-limit, it splits the perfect fourth into three 11/10s (tempering out 4000/3993). The mapping for 13 comes from 2.3.5.13 kleismic (sometimes known as cata), which equates 25/24, 26/25, and 27/26. Finally, the mapping for 17 is reached by equating two generators of slendric to 17/13.

For technical data, see Kleismic family #Tritikleismic.

Intervals

Todo: complete section

Tunings

Todo: complete section