29ed7/3

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29ed7/3

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Prime factorization	29 (prime)
Step size	50.5818¢
Octave	24\29ed7/3 (1213.96¢)
Twelfth	38\29ed7/3 (1922.11¢)
Consistency limit	3
Distinct consistency limit	3

29 equal divisions of 7/3 (abbreviated 29ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 29 equal parts of about 50.6 ¢ each. Each step represents a frequency ratio of (7/3)^1/29, or the 29th root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	50.582
2	101.164
3	151.745	25/23
4	202.327	9/8, 19/17
5	252.909	15/13, 22/19
6	303.491
7	354.072
8	404.654	19/15
9	455.236	13/10, 17/13, 22/17
10	505.818	4/3
11	556.399
12	606.981
13	657.563	19/13, 22/15, 25/17
14	708.145	3/2
15	758.726	14/9, 17/11
16	809.308
17	859.89
18	910.472	17/10, 22/13, 27/16
19	961.053	7/4, 26/15
20	1011.635
21	1062.217	13/7
22	1112.799	19/10
23	1163.38
24	1213.962
25	1264.544
26	1315.126	15/7
27	1365.707	11/5
28	1416.289	25/11
29	1466.871	7/3

Harmonics

Approximation of harmonics in 29ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+14.0	+20.2	-22.7	-4.3	-16.5	+20.2	-8.7	-10.3	+9.6	-3.6	-2.5
	Relative (%)	+27.6	+39.8	-44.8	-8.5	-32.6	+39.8	-17.2	-20.3	+19.1	-7.1	-5.0
Steps (reduced)		24 (24)	38 (9)	47 (18)	55 (26)	61 (3)	67 (9)	71 (13)	75 (17)	79 (21)	82 (24)	85 (27)

Approximation of harmonics in 29ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+10.7	-16.5	+15.8	+5.3	+1.5	+3.7	+11.2	+23.6	-10.3	+10.3	-16.0
	Relative (%)	+21.1	-32.6	+31.3	+10.4	+2.9	+7.3	+22.2	+46.7	-20.3	+20.5	-31.7
Steps (reduced)		88 (1)	90 (3)	93 (6)	95 (8)	97 (10)	99 (12)	101 (14)	103 (16)	104 (17)	106 (19)	107 (20)