35ed5/4

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35ed5/4

36ed5/4 →

Prime factorization	5 × 7
Step size	11.0375¢
Octave	109\35ed5/4 (1203.09¢)
Twelfth	172\35ed5/4 (1898.46¢)
Consistency limit	2
Distinct consistency limit	2

35 equal divisions of 5/4 (abbreviated 35ed5/4) is a nonoctave tuning system that divides the interval of 5/4 into 35 equal parts of about 11 ¢ each. Each step represents a frequency ratio of (5/4)^1/35, or the 35th root of 5/4.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	11.038
2	22.075
3	33.113
4	44.15
5	55.188
6	66.225
7	77.263	21/20, 23/22, 24/23
8	88.3	20/19, 22/21
9	99.338	18/17, 19/18
10	110.375
11	121.413
12	132.45	13/12, 14/13, 27/25
13	143.488
14	154.525	12/11
15	165.563	11/10, 21/19, 23/21
16	176.601
17	187.638	10/9
18	198.676	19/17
19	209.713	26/23
20	220.751	17/15
21	231.788
22	242.826	15/13, 23/20
23	253.863	22/19
24	264.901	7/6
25	275.938
26	286.976	13/11, 20/17
27	298.013	25/21
28	309.051
29	320.089	6/5
30	331.126	17/14, 23/19
31	342.164	28/23
32	353.201	11/9
33	364.239	21/17
34	375.276	26/21
35	386.314

Harmonics

Approximation of harmonics in 35ed5/4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+3.09	-3.50	-4.85	-4.85	-0.41	-2.38	-1.76	+4.04	-1.76	-1.20	+2.68
	Relative (%)	+28.0	-31.7	-44.0	-44.0	-3.7	-21.5	-16.0	+36.6	-16.0	-10.9	+24.3
Steps (reduced)		109 (4)	172 (32)	217 (7)	252 (7)	281 (1)	305 (25)	326 (11)	345 (30)	361 (11)	376 (26)	390 (5)

Approximation of harmonics in 35ed5/4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-3.44	+0.71	+2.68	+1.33	-4.29	-3.91	+1.83	+1.33	+5.16	+1.89	+2.19
	Relative (%)	-31.2	+6.5	+24.3	+12.0	-38.9	-35.4	+16.6	+12.0	+46.8	+17.1	+19.9
Steps (reduced)		402 (17)	414 (29)	425 (5)	435 (15)	444 (24)	453 (33)	462 (7)	470 (15)	478 (23)	485 (30)	492 (2)