157edo

The 157 equal divisions of the octave (157edo), or the 157(-tone) equal temperament (157tet, 157et) when viewed from a regular temperament perspective, is the equal division of the octave into 157 parts of 7.6433 cents each.

Theory

157et tempers out 78732/78125 (sensipent comma) and 137438953472/134521003125 in the 5-limit; 2401/2400, 5120/5103, and 110592/109375 in the 7-limit (supporting the hemififths and the catafourth). Using the patent val, it tempers out 176/175, 1331/1323, 3773/3750 and 8019/8000 in the 11-limit; 351/350, 352/351, 847/845, 1573/1568, and 2197/2187 in the 13-limit.

157edo is the 37th prime EDO.

Regular temperament properties

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
				Absolute (¢)	Relative (%)
2.3	[249 -157⟩	[⟨157 249]]	-0.388	0.388	5.08
2.3.5	78732/78125, ⟨37 -16 -5]	[⟨157 249 365]]	-0.760	0.614	8.04
2.3.5.7	2401/2400, 5120/5103, 78732/78125	[⟨157 249 365 441]]	-0.737	0.533	6.98
2.3.5.7.11	176/175, 1331/1323, 2401/2400, 5120/5103	[⟨157 249 365 441 543]]	-0.532	0.629	8.24
2.3.5.7.11.13	176/175, 351/350, 847/845, 1331/1323, 2197/2187	[⟨157 249 365 441 543 581]]	-0.454	0.600	7.86
2.3.5.7.11.13.17	176/175, 256/255, 351/350, 442/441, 715/714, 2197/2187	[⟨157 249 365 441 543 581 642]]	-0.461	0.556	7.28
2.3.5.7.11.13.17.19	176/175, 256/255, 286/285, 351/350, 361/360, 442/441, 476/475	[⟨157 249 365 441 543 581 642 667]]	-0.420	0.531	6.95

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per octave	Generator (reduced)	Cents (reduced)	Associated ratio	Temperament
1	46\157	351.59	49/40	Hemififths
1	56\157	428.03	2800/2187	Osiris
1	58\157	443.31	162/125	Sensipent
1	64\157	489.17	250/189	Catafourth