251edo

← 250edo

251edo

252edo →

Prime factorization	251 (prime)
Step size	4.78088 ¢
Fifth	147\251 (702.789 ¢)
Semitones (A1:m2)	25:18 (119.5 ¢ : 86.06 ¢)
Consistency limit	9
Distinct consistency limit	9

Theory

251et tempers out 1600000/1594323 (amity comma) and 562949953421312/556182861328125 (maquila comma) in the 5-limit; 4375/4374, 5120/5103, and 40500000/40353607 in the 7-limit.

Using the patent val, it tempers out 1331/1323, 1375/1372, 16896/16807, and 24057/24010 in the 11-limit; 352/351, 676/675, 847/845, and 1573/1568 in the 13-limit.

Using the 251e val, it tempers out 540/539, 5632/5625, 6250/6237, and 12005/11979 in the 11-limit; 364/363, 676/675, 1716/1715, and 3584/3575 in the 13-limit.

Odd harmonics

Approximation of odd harmonics in 251edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+0.83	+0.94	+1.69	+1.67	-1.52	+0.91	+1.77	+0.22	-1.10	-2.26	-1.98
	Relative (%)	+17.4	+19.6	+35.4	+34.9	-31.7	+19.0	+37.0	+4.7	-23.0	-47.2	-41.4
Steps (reduced)		398 (147)	583 (81)	705 (203)	796 (43)	868 (115)	929 (176)	981 (228)	1026 (22)	1066 (62)	1102 (98)	1135 (131)

Subsets and supersets

251edo is the 54th prime EDO.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[398 -251⟩	⟨251 398]	-0.2630	0.2630	5.50
2.3.5	[9 -13 5⟩, [49 -6 -17⟩	⟨251 398 583]	-0.3099	0.2247	4.70
2.3.5.7	4375/4374, 5120/5103, 6144/6125	⟨251 398 583 705]	-0.3830	0.2322	4.86

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator (reduced)	Cents (reduced)	Associated ratio	Temperaments
1	71\251	339.44	243/200	Amity
1	75\251	358.57	315/256	Restles
1	91\251	435.06	9/7	Supermajor
1	96\251	458.96	125/96	Majvam
1	112\251	535.46	512/375	Maquila
1	117\251	559.26	864/625	Tritriple

Music

Francium

• "hope in dark times" from hope in dark times (2024) – Spotify | Bandcamp | YouTube