29ed5/4

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29ed5/4

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Prime factorization	29 (prime)
Step size	13.3212¢
Octave	90\29ed5/4 (1198.9¢)
Twelfth	143\29ed5/4 (1904.93¢)
Consistency limit	8
Distinct consistency limit	6

29 equal divisions of 5/4 (abbreviated 29ed5/4) is a nonoctave tuning system that divides the interval of 5/4 into 29 equal parts of about 13.3 ¢ each. Each step represents a frequency ratio of (5/4)^1/29, or the 29th root of 5/4.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	13.321
2	26.642
3	39.963
4	53.285
5	66.606	23/22, 25/24, 26/25
6	79.927	20/19, 22/21, 24/23
7	93.248	19/18, 21/20
8	106.569	16/15, 17/16, 18/17
9	119.89	15/14
10	133.212	13/12, 14/13
11	146.533	12/11, 25/23
12	159.854
13	173.175	10/9, 11/10, 21/19
14	186.496
15	199.817	19/17
16	213.139	9/8, 17/15, 25/22, 26/23
17	226.46	8/7
18	239.781	23/20
19	253.102	15/13, 22/19
20	266.423	7/6
21	279.744	13/11, 20/17
22	293.066	25/21
23	306.387	19/16
24	319.708	6/5
25	333.029	17/14
26	346.35	11/9
27	359.671	16/13, 26/21, 27/22
28	372.993	21/17
29	386.314	5/4

Harmonics

Approximation of harmonics in 29ed5/4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-1.10	+2.97	-2.19	-2.19	+1.88	+1.43	-3.29	+5.94	-3.29	+4.88	+0.78
	Relative (%)	-8.2	+22.3	-16.4	-16.4	+14.1	+10.7	-24.7	+44.6	-24.7	+36.7	+5.9
Steps (reduced)		90 (3)	143 (27)	180 (6)	209 (6)	233 (1)	253 (21)	270 (9)	286 (25)	299 (9)	312 (22)	323 (4)

Approximation of harmonics in 29ed5/4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-4.58	+0.33	+0.78	-4.38	-2.77	+4.85	+4.49	-4.38	+4.40	+3.79	-6.56
	Relative (%)	-34.4	+2.5	+5.9	-32.9	-20.8	+36.4	+33.7	-32.9	+33.0	+28.4	-49.3
Steps (reduced)		333 (14)	343 (24)	352 (4)	360 (12)	368 (20)	376 (28)	383 (6)	389 (12)	396 (19)	402 (25)	407 (1)