208edo

← 207edo

208edo

209edo →

Prime factorization	24 × 13
Step size	5.76923 ¢
Fifth	122\208 (703.846 ¢) (→ 61\104)
Semitones (A1:m2)	22:14 (126.9 ¢ : 80.77 ¢)
Consistency limit	7
Distinct consistency limit	7

Theory

204edo tempers out 15625/15552, the kleisma, and is the optimal patent val for the kleismic temperament metakleismic, and 7, 11 and 13 limit rank three tolerant temperament. It is also the optimal patent val for the rank four 11-limit temperament tempering out 896/891, the pentacircle temperament. Other commas it tempers out include 2200/2187 in the 11-limit and 325/324, 352/351, 364/363 and 625/624 in the 13-limit.

Odd harmonics

Approximation of odd harmonics in 208edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+1.89	+0.22	+0.40	-1.99	+2.53	+1.78	+2.12	-1.11	+2.49	+2.30	+0.57
	Relative (%)	+32.8	+3.9	+7.0	-34.4	+43.8	+30.9	+36.7	-19.2	+43.1	+39.8	+9.9
Steps (reduced)		330 (122)	483 (67)	584 (168)	659 (35)	720 (96)	770 (146)	813 (189)	850 (18)	884 (52)	914 (82)	941 (109)

Subsets and supersets

208 factors into 2⁴ × 13, with subset edos 2, 4, 8, 16, 13, 26, 52, and 104.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[165 -104⟩	⟨208 330]	-0.5966	0.5963	10.34
2.3.5	15625/15552, [57 -33 -2⟩	⟨208 330 483]	-0.4301	0.5409	9.38
2.3.5.7	2401/2400, 15625/15552, 179200/177147	⟨208 330 483 584]	-0.3586	0.4845	8.40
2.3.5.7.11	896/891, 2200/2187, 2401/2400, 3025/3024	⟨208 330 483 584 720]	-0.4330	0.4582	7.94
2.3.5.7.11.13	325/324, 352/351, 364/363, 676/675, 2401/2400	⟨208 330 483 584 720 770]	-0.4410	0.4187	7.26

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator (reduced)	Cents (reduced)	Associated ratio	Temperaments
1	47\208	251.15	1024/875	Quasiorwell
1	55\208	317.31	6/5	Hanson / metakleismic
4	55\208 (3\208)	317.31 (17.31)	6/5 (81/80)	Quadritikleismic