308edo

← 307edo

308edo

309edo →

Prime factorization	22 × 7 × 11
Step size	3.8961¢
Fifth	180\308 (701.299¢) (→45\77)
Semitones (A1:m2)	28:24 (109.1¢ : 93.51¢)
Consistency limit	5
Distinct consistency limit	5

308 equal divisions of the octave (308edo), or 308-tone equal temperament (308tet), 308 equal temperament (308et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 308 equal parts of about 3.9 ¢ each.

Theory

308et only is consistent in the 5-limit. Ignoring the harmonics 7, 11 and 13, 308et is strong in the 2.3.5.17.19.23.29.31 subgroup.

308et tempers out following commas:

7-limit commas: 4096000/4084101, 390625/388962, 26873856/26796875, 19683/19600, 78125000/78121827, 65625/65536, 1640558367/1638400000

11-limit commas: 806736/805255, 1835008/1830125, 14700/14641, 26214400/26198073, 166698/166375, 243/242, 131072/130977, 6250/6237, 107495424/107421875, 9765625/9732096, 137781/137500, 180224/180075, 1375/1372, 17537553/17500000, 47265625/47258883, 9801/9800, 539055/537824, 202397184/201768035

Using the 308d val, it supports unidec and gammic.

Prime harmonics

Approximation of prime harmonics in 308edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	absolute (¢)	+0.00	-0.66	-0.60	+1.30	+1.93	+1.03	+0.24	-1.41	-1.00	-1.01	+0.42
	relative (%)	+0	-17	-15	+33	+50	+26	+6	-36	-26	-26	+11
Steps (reduced)		308 (0)	488 (180)	715 (99)	865 (249)	1066 (142)	1140 (216)	1259 (27)	1308 (76)	1393 (161)	1496 (264)	1526 (294)

Subsets and supersets

308 factors into 2² x 7 x 11, with subset edos 2, 4, 7, 11, 14, 22, 28, 44, 77, and 154.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[-122 77⟩	⟨308 488]	0.2070	0.2071	5.32
2.3.5	[-36 11 8⟩, [-7 22 -12⟩	⟨308 488 715]	0.2241	0.1708	4.38

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator (Reduced)	Cents (Reduced)	Associated Ratio	Temperaments
1	9\308	35.06	128/125	Gammic (308d)
28	128\308 (4\308)	498.70 (15.58)	4/3 (2048/2025)	Oquatonic