29ed7

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29ed7

30ed7 →

Prime factorization	29 (prime)
Step size	116.166 ¢
Octave	10\29ed7 (1161.66 ¢)
Twelfth	16\29ed7 (1858.66 ¢)
Consistency limit	3
Distinct consistency limit	3

29 equal divisions of the 7th harmonic (abbreviated 29ed7) is a nonoctave tuning system that divides the interval of 7/1 into 29 equal parts of about 116 ¢ each. Each step represents a frequency ratio of 7^1/29, or the 29th root of 7. It is similar to every third step of 31edo.

Intervals

Intervals of 29ed7

degree	cents value	corresponding JI intervals	comments
0	0.0000	exact 1/1
1	116.1664	77/72, 15/14
2	232.3328	8/7
3	348.4992	11/9, 49/40
4	464.6656	98/75
5	580.8321	7/5
6	696.9985	112/75, 121/81, 136/91, 187/125
7	813.1649	8/5
8	929.3313	65/38
9	1045.4977	64/35
10	1161.6641	88/45, 96/49, 49/25
11	1277.8305	44/21
12	1393.9969	38/17, 85/38
13	1510.1633
14	1626.3297	64/25
15	1742.4962	52/19
16	1858.6626	38/13
17	1974.8290	25/8
18	2090.9954
19	2207.1618	68/19
20	2323.3282	65/17
21	2439.4946	45/11
22	2555.6610	35/8
23	2671.8274
24	2787.9939	5/1
25	2904.1603	75/14
26	3020.3267	40/7, 63/11
27	3136.4931	49/8
28	3252.6595	98/15, 72/11
29	3368.8259	exact 7/1	harmonic seventh plus two octaves

Harmonics

Approximation of harmonics in 29ed7

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-38.3	-43.3	+39.5	+1.7	+34.5	+0.0	+1.2	+29.6	-36.7	+30.7	-3.8
	Relative (%)	-33.0	-37.3	+34.0	+1.4	+29.7	+0.0	+1.0	+25.5	-31.6	+26.4	-3.3
Steps (reduced)		10 (10)	16 (16)	21 (21)	24 (24)	27 (27)	29 (0)	31 (2)	33 (4)	34 (5)	36 (7)	37 (8)

Approximation of harmonics in 29ed7

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-26.2	-38.3	-41.6	-37.2	-26.0	-8.8	+13.8	+41.2	-43.3	-7.7	+31.5
	Relative (%)	-22.6	-33.0	-35.8	-32.0	-22.4	-7.5	+11.9	+35.4	-37.3	-6.6	+27.2
Steps (reduced)		38 (9)	39 (10)	40 (11)	41 (12)	42 (13)	43 (14)	44 (15)	45 (16)	45 (16)	46 (17)	47 (18)

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