29ed5/2

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29ed5/2

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Prime factorization	29 (prime)
Step size	54.7005¢
Octave	22\29ed5/2 (1203.41¢) (semiconvergent)
Twelfth	35\29ed5/2 (1914.52¢)
Consistency limit	12
Distinct consistency limit	6

29 equal divisions of 5/2 (abbreviated 29ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 29 equal parts of about 54.7 ¢ each. Each step represents a frequency ratio of (5/2)^1/29, or the 29th root of 5/2.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	54.7
2	109.401	15/14, 16/15, 17/16, 18/17
3	164.101	11/10
4	218.802	17/15, 25/22, 26/23
5	273.502	7/6, 20/17
6	328.203	17/14, 23/19
7	382.903	5/4
8	437.604	9/7, 22/17
9	492.304	4/3
10	547.005	11/8, 15/11, 26/19
11	601.705	17/12, 24/17
12	656.406	16/11, 19/13, 22/15
13	711.106	3/2
14	765.807	14/9, 25/16
15	820.507	8/5
16	875.208	5/3
17	929.908	12/7
18	984.609	23/13
19	1039.309	11/6, 20/11
20	1094.009	15/8, 17/9
21	1148.71
22	1203.41	2/1
23	1258.111
24	1312.811	15/7, 17/8
25	1367.512	11/5
26	1422.212	16/7, 25/11
27	1476.913	7/3
28	1531.613	17/7
29	1586.314	5/2

Harmonics

Approximation of harmonics in 29ed5/2

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+3.4	+12.6	+6.8	+3.4	+16.0	+22.6	+10.2	+25.1	+6.8	+5.9	+19.4
	Relative (%)	+6.2	+23.0	+12.5	+6.2	+29.2	+41.3	+18.7	+45.9	+12.5	+10.8	+35.4
Steps (reduced)		22 (22)	35 (6)	44 (15)	51 (22)	57 (28)	62 (4)	66 (8)	70 (12)	73 (15)	76 (18)	79 (21)

Approximation of harmonics in 29ed5/2

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-9.8	+26.0	+16.0	+13.6	+18.1	-26.2	-10.4	+10.2	-19.5	+9.3	-12.9
	Relative (%)	-17.9	+47.6	+29.2	+24.9	+33.1	-47.8	-19.0	+18.7	-35.7	+17.1	-23.6
Steps (reduced)		81 (23)	84 (26)	86 (28)	88 (1)	90 (3)	91 (4)	93 (6)	95 (8)	96 (9)	98 (11)	99 (12)