29ed7/4

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29ed7/4

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Prime factorization	29 (prime)
Step size	33.4078¢
Octave	36\29ed7/4 (1202.68¢)
Twelfth	57\29ed7/4 (1904.24¢)
Consistency limit	4
Distinct consistency limit	3

Division of the septimal subminor seventh into 29 equal parts (29ED7/4) is very nearly identical to 36edo, but with the 7/4 rather than the 2/1 being just. The octave is stretched by about 2.68 cents and the step size is about 33.41 cents.

Theory

This tuning tempers out 50/49 in the 7-limit; 99/98 and 100/99 in the 11-limit; 85/84 in the 17-limit; 77/76 in the 19-limit; and 92/91 in the 23-limit.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	33.4
2	66.8	23/22, 27/26
3	100.2	17/16, 18/17, 19/18
4	133.6	13/12, 14/13
5	167	11/10, 21/19
6	200.4	9/8, 19/17
7	233.9	8/7, 23/20
8	267.3	7/6
9	300.7	19/16
10	334.1	17/14
11	367.5	16/13, 21/17, 26/21
12	400.9	24/19
13	434.3	9/7
14	467.7	17/13, 21/16
15	501.1	4/3
16	534.5	15/11, 19/14, 26/19
17	567.9	18/13
18	601.3	17/12, 24/17, 27/19
19	634.7	13/9
20	668.2	22/15
21	701.6	3/2
22	735	23/15, 26/17
23	768.4	14/9
24	801.8	19/12, 27/17
25	835.2	13/8, 21/13
26	868.6
27	902	22/13, 27/16
28	935.4	12/7
29	968.8	7/4

Harmonics

Approximation of harmonics in 29ed7/4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+2.7	+2.3	+5.4	-13.5	+5.0	+5.4	+8.0	+4.6	-10.8	-8.8	+7.6
	Relative (%)	+8.0	+6.9	+16.0	-40.3	+14.9	+16.0	+24.1	+13.7	-32.3	-26.2	+22.9
Steps (reduced)		36 (7)	57 (28)	72 (14)	83 (25)	93 (6)	101 (14)	108 (21)	114 (27)	119 (3)	124 (8)	129 (13)

Approximation of harmonics in 29ed7/4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+2.7	+8.0	-11.2	+10.7	+6.0	+7.3	+13.9	-8.1	+7.6	-6.1	-16.2
	Relative (%)	+8.1	+24.1	-33.5	+32.1	+17.9	+21.7	+41.5	-24.3	+22.9	-18.2	-48.5
Steps (reduced)		133 (17)	137 (21)	140 (24)	144 (28)	147 (2)	150 (5)	153 (8)	155 (10)	158 (13)	160 (15)	162 (17)