29ed5

← 28ed5

29ed5

30ed5 →

Prime factorization	29 (prime)
Step size	96.0798¢
Octave	12\29ed5 (1152.96¢)
Twelfth	20\29ed5 (1921.6¢)
Consistency limit	2
Distinct consistency limit	2

Division of the 5th harmonic into 29 equal parts (29ED5) is compared to every other step of 25EDO, but with the 5/1 rather than the 2/1 being just. The step size is about 96.0798 cents, corresponding to 12.4896 EDO.

Intervals

degree	cents value	corresponding JI intervals	comments
0	0.0000	exact 1/1
1	96.0798	18/17, 19/18
2	192.1596	19/17
3	288.2393	13/11
4	384.3191	5/4
5	480.3989	33/25
6	576.4787	53/38, 60/43	-6.0 cents from 7/5
7	672.5585	28/19
8	768.6383	14/9
9	864.7180	28/17
10	960.7978	54/31
11	1056.8776	46/25	+39.3 cents from 9/5
12	1152.9574	35/18, 37/19, 72/37
13	1249.0372	35/17, 37/18, 72/35
14	1345.1170	50/23
15	1441.1967	23/10
16	1537.2765	17/7
17	1633.3563	18/7	-20.9 cents from 13/5
18	1729.4361	19/7
19	1825.5159
20	1921.5957	88/29	+19.6 cents from 3/1
21	2017.6754
22	2113.7552		-4.9 cents from 17/5
23	2209.8350
24	2305.9148	72/19	-5.3 cents from 19/5
25	2401.9946	4/1
26	2498.0744	72/17	+13.6 cents from 21/5
27	2594.1541		-47.8 cents from 23/5
28	2690.2339	52/11
29	2786.3137	exact 5/1	just major third plus two octaves

Harmonics

Approximation of harmonics in 29ed5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-47.0	+19.6	+2.0	+0.0	-27.4	-6.0	-45.0	+39.3	-47.0	-19.9	+21.6
	Relative (%)	-49.0	+20.4	+2.1	+0.0	-28.5	-6.3	-46.9	+40.9	-49.0	-20.7	+22.5
Steps (reduced)		12 (12)	20 (20)	25 (25)	29 (0)	32 (3)	35 (6)	37 (8)	40 (11)	41 (12)	43 (14)	45 (16)

Approximation of harmonics in 29ed5

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-20.9	+43.0	+19.6	+4.0	-4.9	-7.8	-5.3	+2.0	+13.6	+29.1	-47.8
	Relative (%)	-21.7	+44.8	+20.4	+4.2	-5.1	-8.1	-5.5	+2.1	+14.2	+30.3	-49.8
Steps (reduced)		46 (17)	48 (19)	49 (20)	50 (21)	51 (22)	52 (23)	53 (24)	54 (25)	55 (26)	56 (27)	56 (27)