7ed9/5

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7ed9/5

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Prime factorization	7 (prime)
Step size	145.371¢
Octave	8\7ed9/5 (1162.97¢)
Twelfth	13\7ed9/5 (1889.82¢) (convergent)
Consistency limit	3
Distinct consistency limit	2

7 equal divisions of 9/5 (abbreviated 7ed9/5) is a nonoctave tuning system that divides the interval of 9/5 into 7 equal parts of about 145⁠ ⁠¢ each. Each step represents a frequency ratio of (9/5)^1/7, or the 7th root of 9/5.

Intervals

Step	Interval (¢)	JI approximated	Simplified ratios
1	145.37	37/34, 48/44, 52/48	12/11, 13/12
2	290.74	19/16, 52/44	13/11
3	436.11	40/31, 44/34, 52/40	22/17, 13/10
4	581.48	56/40	7/5
5	726.85	29/19, 52/34	26/17
6	872.23	56/34	28/17
7	1017.60	9/5, 29/16
8	1162.97	31/16, 37/19
9	1308.34	34/16	17/8
10	1453.71	37/16, 44/19
11	1599.08	40/16, 48/19	5/2
12	1744.45	44/16, 52/19	11/4
13	1889.82	3/1, 56/19
14	2035.19	29/9, 52/16	13/4

The subgroup interpretation used is 9/5.3.16.19.29.31.34.37.40.44.48.52.56. Other interpretations are possible. Don't forget that fractions can multiply.

Harmonics

Approximation of harmonics in 7ed9/5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-37.0	-12.1	+71.3	-24.3	-49.2	-25.3	+34.3	-24.3	-61.3	+64.4	+59.2
	Relative (%)	-25.5	-8.3	+49.1	-16.7	-33.8	-17.4	+23.6	-16.7	-42.2	+44.3	+40.7
Steps (reduced)		8 (1)	13 (6)	17 (3)	19 (5)	21 (0)	23 (2)	25 (4)	26 (5)	27 (6)	29 (1)	30 (2)

Approximation of harmonics in 7ed9/5

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+66.0	-62.3	-36.4	-2.8	+37.7	-61.3	-9.5	+47.0	-37.4	+27.4	-49.6
	Relative (%)	+45.4	-42.9	-25.0	-1.9	+25.9	-42.2	-6.6	+32.4	-25.7	+18.9	-34.1
Steps (reduced)		31 (3)	31 (3)	32 (4)	33 (5)	34 (6)	34 (6)	35 (0)	36 (1)	36 (1)	37 (2)	37 (2)

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