123edo

← 122edo

123edo

124edo →

Prime factorization	3 × 41
Step size	9.7561 ¢
Fifth	72\123 (702.439 ¢) (→ 24\41)
Semitones (A1:m2)	12:9 (117.1 ¢ : 87.8 ¢)
Consistency limit	5
Distinct consistency limit	5

123 = 3 × 41, and 123edo shares its fifth with 41edo. The equal temperament tempers out 1990656/1953125 (valentine comma), 67108864/66430125 (misty comma), and [-13 17 -6⟩ (graviton) in the 5-limit; 126/125, 1029/1024 and 537824/531441 in the 7-limit; 243/242, 896/891, 2401/2376, and 3388/3375 in the 11-limit; 196/195, 351/350, 832/825, 1575/1573, and 2197/2178 in the 13-limit. It provides the optimal patent val for the gravid temperament.

Given its inconsistency to the 7-odd-limit and higher odd limits, the mapping ⟨123 195 286 346] (123d) is also possible for the 7-limit. Using the 123d val, it tempers out 2430/2401, 3136/3125, and 5120/5103 in the 7-limit; 176/175, 243/242, 1375/1372, and 2560/2541 in the 11-limit; 169/168, 364/363, 640/637, 729/728, and 832/825 in the 13-limit. Using the 123df val, it tempers out 144/143, 351/350, 352/351, and 847/845 in the 13-limit.

Using the 123ce val, it tempers out 1331/1323 in the 11-limit, as well as 225/224, 245/243, and 1029/1024; 275/273, 352/351, 847/845, 1573/1568, and 3185/3168 in the 13-limit. Using the 123e val, it tempers out 121/120, 176/175, and 441/440 in the 11-limit; 196/195, 351/350, 352/351, 1287/1280, and 2197/2187 in the 13-limit.

5 steps of the 123ce val is related to Triple BP.

Prime harmonics

Approximation of prime harmonics in 123edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	+0.48	+3.93	-2.97	+4.78	-1.50	+2.36	-4.83	-3.88	+4.57	-3.57
	Relative (%)	+0.0	+5.0	+40.3	-30.5	+49.0	-15.4	+24.2	-49.5	-39.8	+46.8	-36.6
Steps (reduced)		123 (0)	195 (72)	286 (40)	345 (99)	426 (57)	455 (86)	503 (11)	522 (30)	556 (64)	598 (106)	609 (117)

Subsets and supersets

Since 123 factors into 3 × 41, 123edo contains 3edo and 41edo as its subsets.