29ed11/5

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29ed11/5

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Prime factorization	29 (prime)
Step size	47.0691¢
Octave	25\29ed11/5 (1176.73¢)
Twelfth	40\29ed11/5 (1882.76¢)
Consistency limit	3
Distinct consistency limit	3

29 equal divisions of 11/5 (abbreviated 29ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 29 equal parts of about 47.1 ¢ each. Each step represents a frequency ratio of (11/5)^1/29, or the 29th root of 11/5.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	47.069
2	94.138
3	141.207	25/23
4	188.276	10/9, 19/17
5	235.346
6	282.415	13/11
7	329.484	17/14, 23/19
8	376.553
9	423.622	14/11
10	470.691	17/13, 25/19
11	517.76	23/17, 27/20
12	564.829
13	611.898
14	658.968	19/13, 22/15, 25/17
15	706.037	3/2
16	753.106	17/11
17	800.175
18	847.244
19	894.313	5/3
20	941.382	19/11
21	988.451	23/13
22	1035.52
23	1082.59
24	1129.659	21/11, 25/13
25	1176.728
26	1223.797
27	1270.866	23/11
28	1317.935
29	1365.004	11/5

Harmonics

Approximation of harmonics in 29ed11/5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-23.3	-19.2	+0.5	-9.2	+4.6	+20.2	-22.7	+8.7	+14.6	-9.2	-18.7
	Relative (%)	-49.4	-40.8	+1.1	-19.6	+9.8	+42.8	-48.3	+18.5	+30.9	-19.6	-39.7
Steps (reduced)		25 (25)	40 (11)	51 (22)	59 (1)	66 (8)	72 (14)	76 (18)	81 (23)	85 (27)	88 (1)	91 (4)

Approximation of harmonics in 29ed11/5

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-16.0	-3.1	+18.6	+1.0	-9.8	-14.6	-14.0	-8.7	+1.0	+14.6	-15.3
	Relative (%)	-34.1	-6.6	+39.6	+2.2	-20.8	-31.0	-29.8	-18.5	+2.0	+30.9	-32.6
Steps (reduced)		94 (7)	97 (10)	100 (13)	102 (15)	104 (17)	106 (19)	108 (21)	110 (23)	112 (25)	114 (27)	115 (28)