149edo

149edo is the equal division of the octave into 149 equal parts of 8.054 cents each.

Theory

149edo is the smallest division which is uniquely consistent through the 17-odd-limit. It provides the optimal patent val for 7-, 11-, 13-, and 17-limit heinz temperament and the rank-3 temperament ominous in the 13- and 17-limits. It has a general flat tendency, with the fifth 1.28 cents flat, but the major third is a quarter of a cent sharp. In the 5-limit it tempers out the sensipent comma, 78732/78125; in the 7-limit, 1029/1024, 3136/3125 and 19683/19600; in the 11-limit 385/384 and 441/440; in the 13-limit 351/350 and 676/675; in the 17-limit 273/272 and 561/560; in the 19-limit 286/285 and 343/342.

149edo is the 35th prime EDO.

Regular temperament properties

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
				Absolute (¢)	Relative (%)
2.3	[-236 149⟩	[⟨149 236]]	+0.405	0.405	5.03
2.3.5	78732/78125, [-34 20 1⟩	[⟨149 236 346]]	+0.232	0.411	5.11
2.3.5.7	1029/1024, 3136/3125, 19683/19600	[⟨149 236 346 418]]	+0.386	0.445	5.53
2.3.5.7.11	385/384, 441/440, 3136/3125, 19683/19600	[⟨149 236 346 418 515]]	+0.521	0.481	5.97
2.3.5.7.11.13	351/350, 385/384, 441/440, 676/675, 847/845	[⟨149 236 346 418 515 551]]	+0.567	0.451	5.60
2.3.5.7.11.13.17	273/272, 351/350, 385/384, 441/440, 676/675, 847/845	[⟨149 236 346 418 515 551 609]]	+0.495	0.453	5.62

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per octave	Generator (reduced)	Cents (reduced)	Associated ratio	Temperaments
1	3\149	24.16	686/675	Sengagen
1	16\149	128.86	14/13	Tertiathirds
1	18\149	144.97	49/45	Swetneus
1	24\149	193.29	28/25	Luna / hemithirds
1	29\149	233.56	8/7	Slendric
1	47\149	378.52	56/45	Subpental
1	55\149	442.95	162/125	Sensipent
1	57\149	459.06	125/96	Majvam
1	60\149	483.22	45/34	Hemiseven
1	61\149	491.28	3645/2744	Fifthplus
1	68\149	547.65	11/8	Heinz