204edo

← 203edo

204edo

205edo →

Prime factorization	22 × 3 × 17
Step size	5.88235 ¢
Fifth	119\204 (700 ¢) (→ 7\12)
Semitones (A1:m2)	17:17 (100 ¢ : 100 ¢)
Consistency limit	3
Distinct consistency limit	3

204edo is the first merger of 12edo and 17edo. Using the patent val, it tempers out 531441/524288 (Pythagorean comma) and [30 6 -17⟩ in the 5-limit; 1728/1715, 3136/3125 and 14348907/14049280 in the 7-limit; 441/440, 1944/1925, 5632/5625, and 35937/35840 in the 11-limit. It supports the 7-limit semisept temperament, and the alternative 204e val can support the 11-limit semisept. It supports intercom temperament.

Odd harmonics

Approximation of odd harmonics in 204edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-1.96	+1.92	+1.76	+1.97	+1.62	+0.65	-0.03	+0.93	+2.49	-0.19	+1.14
	Relative (%)	-33.2	+32.7	+30.0	+33.5	+27.6	+11.0	-0.6	+15.8	+42.3	-3.3	+19.3
Steps (reduced)		323 (119)	474 (66)	573 (165)	647 (35)	706 (94)	755 (143)	797 (185)	834 (18)	867 (51)	896 (80)	923 (107)

Subsets and supersets

Since 204 factors into 2² × 3 × 17, 204edo has subset edos 2, 3, 4, 6, 12, 17, 34, 51, 68, and 102.