301edo

The 301 equal divisions of the octave (301edo), or the 301(-tone) equal temperament (301tet, 301et) when viewed from a regular temperament perspective, is the equal division of the octave into 301 parts of about 3.99 cents each.

← 300edo

301edo

302edo →

Prime factorization	7 × 43
Step size	3.98671 ¢
Fifth	176\301 (701.661 ¢)
Semitones (A1:m2)	28:23 (111.6 ¢ : 91.69 ¢)
Consistency limit	17
Distinct consistency limit	17

Theory

301edo is a strong 7-limit system, and distinctly consistent through the 17-odd-limit. It tempers out 32805/32768 in the 5-limit, 2401/2400 in the 7-limit, 3025/3024, 5632/5625, 8019/8000 in the 11-limit, 729/728, 847/845, 1001/1000, 1716/1715, 2200/2197 in the 13-limit, and 561/560, 833/832, 1089/1088, 1156/1155, 1275/1274 and 1701/1700 in the 17-limit. Because it tempers out both 32805/32768 and 2401/2400, it supports the sesquiquartififths temperament.

301 is a composite number, since 301 = 7 × 43. This is related to the proposal of the deaf French mathematician and acoustician Joseph Sauveur to divide the octave in 43 parts called merides, and those into seven more parts called heptamerides. Back in the days of slide rules and log tables, this made sense since by multiplying the log base ten of the interval in question by 1000, one came close to how many heptamerides it constituted.

301edo also tempers out [168 -43 -43⟩ and 5250987/5242880, so it supports the meridic temperament.

Regular temperament properties

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
				Absolute (¢)	Relative (%)
2.3	[-477 301⟩	[⟨301 477]]	+0.0927	0.0927	2.33
2.3.5	32805/32768, [3 45 -32⟩	[⟨301 477 699]]	+0.0048	0.1456	3.65
2.3.5.7	2401/2400, 32805/32768, 1959552/1953125	[⟨301 477 699 845]]	+0.0085	0.1262	3.17
2.3.5.7.11	2401/2400, 3025/3024, 5632/5625, 8019/8000	[⟨301 477 699 845 1041]]	+0.0734	0.1720	4.31
2.3.5.7.11.13	729/728, 847/845, 1001/1000, 1716/1715, 3025/3024	[⟨301 477 699 845 1041 1114]]	+0.0310	0.1834	4.60
2.3.5.7.11.13.17	561/560, 729/728, 833/832, 847/845, 1001/1000, 1089/1088	[⟨301 477 699 845 1041 1114 1230]]	+0.0721	0.1973	4.95

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per octave	Generator (reduced)	Cents (reduced)	Associated ratio	Temperaments
1	25\301	99.67	200/189	Quintaschis
1	44\301	175.42	448/405	Sesquiquartififths / sesquart (301e)
1	68\301	271.10	90/77	Quasiorwell
1	76\301	302.99	25/21	Quinmite
1	125\301	498.34	4/3	Helmholtz
7	125\301 (4\301)	498.34 (15.95)	4/3 (245/243)	Septant
43	125\301 (1\301)	498.34 (3.99)	4/3 (540/539)	Meridic