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 (abbreviated 308edo or 308ed2), also called 308-tone equal temperament (308tet) or 308 equal temperament (308et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 308 equal parts of about 3.896 ¢ each. Each step represents a frequency ratio of 2^1/308, or the 308th root of 2.

Theory

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

Using the patent val nonetheless, the equal temperament tempers out 19683/19600, 65625/65536, and 390625/388962 in the 7-limit, and 243/242, 1375/1372, 6250/6237, 9801/9800, and 14700/14641 in the 11-limit.

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

Since 308 factors into 2² × 7 × 11, 308edo has 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*	Cents*	Associated Ratio*	Temperaments
1	9\308	35.06	128/125	Gammic (308d)
28	128\308 (4\308)	498.70 (15.58)	4/3 (126/125)	Oquatonic (308)

* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct