35ed11/5

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35ed11/5

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Prime factorization	5 × 7
Step size	39.0001¢
Octave	31\35ed11/5 (1209¢)
Twelfth	49\35ed11/5 (1911.01¢) (→7\5ed11/5)
Consistency limit	4
Distinct consistency limit	4

35 equal divisions of 11/5 (abbreviated 35ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 35 equal parts of about 39 ¢ each. Each step represents a frequency ratio of (11/5)^1/35, or the 35th root of 11/5.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	39
2	78	21/20, 22/21, 23/22
3	117	15/14
4	156	23/21
5	195.001	19/17
6	234.001	23/20
7	273.001	20/17
8	312.001
9	351.001
10	390.001
11	429.001
12	468.001	17/13
13	507.002
14	546.002	26/19
15	585.002	7/5
16	624.002	10/7
17	663.002	19/13, 22/15, 28/19
18	702.002	3/2
19	741.002	20/13, 23/15, 26/17
20	780.002	11/7
21	819.003
22	858.003	23/14, 28/17
23	897.003
24	936.003
25	975.003
26	1014.003
27	1053.003
28	1092.003
29	1131.004
30	1170.004
31	1209.004
32	1248.004
33	1287.004	19/9, 21/10
34	1326.004	15/7, 28/13
35	1365.004	11/5

Harmonics

Approximation of harmonics in 35ed11/5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+9.0	+9.1	+18.0	-17.3	+18.1	-14.8	-12.0	+18.1	-8.3	-17.3	-11.9
	Relative (%)	+23.1	+23.2	+46.2	-44.4	+46.3	-38.0	-30.7	+46.4	-21.3	-44.4	-30.6
Steps (reduced)		31 (31)	49 (14)	62 (27)	71 (1)	80 (10)	86 (16)	92 (22)	98 (28)	102 (32)	106 (1)	110 (5)

Approximation of harmonics in 35ed11/5

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+5.5	-5.8	-8.3	-3.0	+9.1	-11.9	+11.5	+0.7	-5.8	-8.3	-7.3
	Relative (%)	+14.1	-14.9	-21.2	-7.7	+23.2	-30.5	+29.5	+1.8	-14.8	-21.3	-18.6
Steps (reduced)		114 (9)	117 (12)	120 (15)	123 (18)	126 (21)	128 (23)	131 (26)	133 (28)	135 (30)	137 (32)	139 (34)