9ed5/3

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9ed5/3

10ed5/3 →

Prime factorization	32
Step size	98.2621 ¢
Octave	12\9ed5/3 (1179.14 ¢) (→ 4\3ed5/3)
Twelfth	19\9ed5/3 (1866.98 ¢)
Consistency limit	5
Distinct consistency limit	5

9ed5/3 is the equal division of the just major sixth into nine parts of 98.2621 cents each, corresponding to 12.2122edo. It is very closely related to the passion temperament.

Intervals

Degrees	Cents	5/3.4/3.7/3 interpretation
1	98.2621	16/15, 21/20
2	196.5242	28/25
3	294.7862	25/21
4	393.0483	5/4
5	491.3104	4/3
6	589.5725	7/5
7	687.8346	112/75
8	786.0966	25/16, 80/63
9	884.3587	5/3 (just)
10	982.6208	7/4, 16/9
11	1080.8829	28/15
12	1179.1450	49/25
13	1277.4070	25/12
14	1375.6691	20/9
15	1473.9312	7/3

The interval interpretations listed belong to the generator chain of septimal passion without octaves.

Harmonics

Approximation of harmonics in 9ed5/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-20.9	-35.0	-41.7	-35.0	+42.4	-27.9	+35.7	+28.3	+42.4	-24.3	+21.6
	Relative (%)	-21.2	-35.6	-42.4	-35.6	+43.2	-28.4	+36.3	+28.8	+43.2	-24.7	+22.0
Steps (reduced)		12 (3)	19 (1)	24 (6)	28 (1)	32 (5)	34 (7)	37 (1)	39 (3)	41 (5)	42 (6)	44 (8)

Approximation of harmonics in 9ed5/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-18.7	-48.8	+28.3	+14.8	+8.1	+7.5	+12.1	+21.6	+35.4	-45.2	-23.9
	Relative (%)	-19.1	-49.6	+28.8	+15.1	+8.3	+7.6	+12.3	+22.0	+36.0	-46.0	-24.3
Steps (reduced)		45 (0)	46 (1)	48 (3)	49 (4)	50 (5)	51 (6)	52 (7)	53 (8)	54 (0)	54 (0)	55 (1)

See also

• Alpha, beta, and gamma family of equal divisions