8ed9/5

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8ed9/5

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Prime factorization	23
Step size	127.2 ¢
Octave	9\8ed9/5 (1144.8 ¢)
Twelfth	15\8ed9/5 (1907.99 ¢) (convergent)
Consistency limit	3
Distinct consistency limit	3

8 equal divisions of 9/5 (abbreviated 8ed9/5) is a nonoctave tuning system that divides the interval of 9/5 into 8 equal parts of about 127 ¢ each. Each step represents a frequency ratio of (9/5)^1/8, or the 8th root of 9/5.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	127.2	19/18, 21/20
2	254.4	7/6, 13/11, 15/13, 17/15, 22/19
3	381.6	11/9, 19/15
4	508.8	15/11, 17/13
5	636	10/7, 13/9, 19/13, 22/15
6	763.2	17/11
7	890.4	5/3, 12/7, 22/13
8	1017.6	9/5

Harmonics

Approximation of harmonics in 8ed9/5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-55.2	+6.0	+16.8	+12.1	-49.2	-61.6	-38.4	+12.1	-43.1	+46.3	+22.8
	Relative (%)	-43.4	+4.7	+13.2	+9.5	-38.7	-48.5	-30.2	+9.5	-33.9	+36.4	+17.9
Steps (reduced)		9 (1)	15 (7)	19 (3)	22 (6)	24 (0)	26 (2)	28 (4)	30 (6)	31 (7)	33 (1)	34 (2)

Approximation of harmonics in 8ed9/5

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+11.5	+10.4	+18.1	+33.6	+55.8	-43.1	-9.5	+28.9	-55.6	-8.9	+41.3
	Relative (%)	+9.0	+8.1	+14.2	+26.4	+43.9	-33.9	-7.5	+22.7	-43.7	-7.0	+32.5
Steps (reduced)		35 (3)	36 (4)	37 (5)	38 (6)	39 (7)	39 (7)	40 (0)	41 (1)	41 (1)	42 (2)	43 (3)