29ed4

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29ed4

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Prime factorization	29 (prime)
Step size	82.7586¢
Octave	15\29ed4 (1241.38¢)
Twelfth	23\29ed4 (1903.45¢) (convergent)
Consistency limit	1
Distinct consistency limit	1

29 equal divisions of the 4th harmonic (abbreviated 29ed4) is a nonoctave tuning system that divides the interval of 4/1 into 29 equal parts of about 82.8 ¢ each. Each step represents a frequency ratio of 4^1/29, or the 29th root of 4.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	82.8	22/21, 23/22
2	165.5	21/19, 23/21
3	248.3	15/13, 22/19
4	331	23/19
5	413.8	19/15
6	496.6
7	579.3	7/5
8	662.1	19/13, 22/15
9	744.8	17/11, 23/15
10	827.6	21/13
11	910.3	22/13
12	993.1	23/13
13	1075.9	13/7
14	1158.6
15	1241.4
16	1324.1	15/7
17	1406.9
18	1489.7
19	1572.4
20	1655.2	13/5
21	1737.9	19/7
22	1820.7
23	1903.4	3/1
24	1986.2	19/6, 22/7
25	2069	23/7
26	2151.7
27	2234.5
28	2317.2	19/5, 23/6
29	2400

Harmonics

Approximation of harmonics in 29ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+41.4	+1.5	+0.0	+27.5	-39.9	+24.3	+41.4	+3.0	-13.9	-13.4	+1.5
	Relative (%)	+50.0	+1.8	+0.0	+33.2	-48.2	+29.3	+50.0	+3.6	-16.8	-16.2	+1.8
Steps (reduced)		15 (15)	23 (23)	29 (0)	34 (5)	37 (8)	41 (12)	44 (15)	46 (17)	48 (19)	50 (21)	52 (23)

Approximation of harmonics in 29ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+28.4	-17.1	+29.0	+0.0	-22.2	-38.4	+33.5	+27.5	+25.8	+28.0	+33.8
	Relative (%)	+34.4	-20.7	+35.0	+0.0	-26.8	-46.4	+40.5	+33.2	+31.1	+33.8	+40.8
Steps (reduced)		54 (25)	55 (26)	57 (28)	58 (0)	59 (1)	60 (2)	62 (4)	63 (5)	64 (6)	65 (7)	66 (8)