15ed11/5

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15ed11/5

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Prime factorization	3 × 5
Step size	91.0003¢
Octave	13\15ed11/5 (1183¢)
Twelfth	21\15ed11/5 (1911.01¢) (→7\5ed11/5)
Consistency limit	4
Distinct consistency limit	4

15 equal divisions of 11/5 (abbreviated 15ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 15 equal parts of about 91 ¢ each. Each step represents a frequency ratio of (11/5)^1/15, or the 15th root of 11/5.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	91	18/17, 19/18, 20/19, 21/20, 22/21, 23/22
2	182.001	10/9, 11/10, 19/17, 21/19
3	273.001	7/6, 13/11, 20/17, 22/19
4	364.001	11/9, 21/17
5	455.001	9/7, 13/10, 17/13, 22/17
6	546.002	15/11, 18/13, 19/14
7	637.002	10/7, 13/9, 19/13
8	728.002	20/13, 23/15
9	819.003	21/13
10	910.003	17/10, 22/13
11	1001.003	9/5, 23/13
12	1092.003	13/7, 17/9, 19/10
13	1183.004	2/1
14	1274.004	19/9, 21/10, 23/11
15	1365.004	11/5, 20/9

Harmonics

Approximation of harmonics in 15ed11/5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-17.0	+9.1	-34.0	+34.7	-7.9	-1.8	+40.0	+18.1	+17.7	+34.7	-24.9
	Relative (%)	-18.7	+9.9	-37.4	+38.1	-8.7	-2.0	+44.0	+19.9	+19.4	+38.1	-27.4
Steps (reduced)		13 (13)	21 (6)	26 (11)	31 (1)	34 (4)	37 (7)	40 (10)	42 (12)	44 (14)	46 (1)	47 (2)

Approximation of harmonics in 15ed11/5

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+18.5	-18.8	+43.7	+23.0	+9.1	+1.1	-1.5	+0.7	+7.2	+17.7	+31.7
	Relative (%)	+20.3	-20.7	+48.1	+25.3	+10.0	+1.2	-1.6	+0.8	+8.0	+19.4	+34.9
Steps (reduced)		49 (4)	50 (5)	52 (7)	53 (8)	54 (9)	55 (10)	56 (11)	57 (12)	58 (13)	59 (14)	60 (0)