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	82.759	22/21, 23/22
2	165.517	21/19, 23/21
3	248.276	15/13, 22/19
4	331.034	23/19
5	413.793	19/15
6	496.552
7	579.31	7/5
8	662.069	19/13, 22/15
9	744.828	17/11, 23/15
10	827.586	21/13
11	910.345	22/13
12	993.103	23/13
13	1075.862	13/7
14	1158.621
15	1241.379
16	1324.138	15/7
17	1406.897
18	1489.655
19	1572.414
20	1655.172	13/5
21	1737.931	19/7
22	1820.69
23	1903.448	3/1
24	1986.207	19/6, 22/7
25	2068.966	23/7
26	2151.724
27	2234.483
28	2317.241	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)