User:MisterShafXen/9ed88

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9ed88

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Prime factorization	32
Step size	861.258 ¢
Octave	1\9ed88 (861.258 ¢)
Twelfth	2\9ed88 (1722.52 ¢) (semiconvergent)
Consistency limit	3
Distinct consistency limit	2

9 equal divisions of the 88th harmonic (abbreviated 9ed88) is a nonoctave tuning system that divides the interval of 88/1 into 9 equal parts of about 861 ¢ each. Each step represents a frequency ratio of 88^1/9, or the 9th root of 88.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	861.3	5/3, 21/13
2	1722.5	19/7
3	2583.8	9/2, 22/5
4	3445	22/3
5	4306.3
6	5167.5
7	6028.8
8	6890.1
9	7751.3

Harmonics

Approximation of prime harmonics in 9ed88

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-339	-179	-203	+76	+155	-134	+263	+70	-261	+199	+84
	Relative (%)	-39.3	-20.8	-23.5	+8.8	+18.0	-15.6	+30.5	+8.1	-30.3	+23.1	+9.7
Steps (reduced)		1 (1)	2 (2)	3 (3)	4 (4)	5 (5)	5 (5)	6 (6)	6 (6)	6 (6)	7 (7)	7 (7)