36ed7

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36ed7

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Prime factorization	22 × 32
Step size	93.5785¢
Octave	13\36ed7 (1216.52¢)
Twelfth	20\36ed7 (1871.57¢) (→5\9ed7)
Consistency limit	2
Distinct consistency limit	2
Special properties	Highly composite

36 equal divisions of the 7th harmonic (abbreviated 36ed7) is a nonoctave tuning system that divides the interval of 7/1 into 36 equal parts of about 93.6 ¢ each. Each step represents a frequency ratio of 7^1/36, or the 36th root of 7.

One step of 36ed7 is very close to Boethius' semitone, 19/18, 93.6030 cents. Making 36ed7 close to the equal multiplication of 19/18 (1ed19/18).

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	93.578	18/17, 19/18
2	187.157	19/17, 29/26
3	280.735
4	374.314	26/21
5	467.892	17/13
6	561.471	18/13, 29/21
7	655.049	19/13, 22/15
8	748.628	17/11
9	842.206
10	935.785	12/7
11	1029.363
12	1122.942	21/11, 23/12
13	1216.52
14	1310.099
15	1403.677
16	1497.256	26/11
17	1590.834	5/2
18	1684.413	29/11
19	1777.991	14/5
20	1871.57
21	1965.148	25/8
22	2058.727	23/7
23	2152.305
24	2245.884	11/3
25	2339.462
26	2433.041
27	2526.619
28	2620.198
29	2713.776	24/5
30	2807.355
31	2900.933
32	2994.512
33	3088.09
34	3181.669
35	3275.247
36	3368.826	7/1

Harmonics

Approximation of harmonics in 36ed7

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+16.5	-30.4	+33.0	+21.0	-13.9	+0.0	-44.0	+32.8	+37.6	-33.9	+2.7
	Relative (%)	+17.7	-32.5	+35.3	+22.5	-14.8	+0.0	-47.0	+35.1	+40.1	-36.2	+2.8
Steps (reduced)		13 (13)	20 (20)	26 (26)	30 (30)	33 (33)	36 (0)	38 (2)	41 (5)	43 (7)	44 (8)	46 (10)

Approximation of harmonics in 36ed7

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-42.3	+16.5	-9.3	-27.5	-38.9	-44.2	-44.3	-39.5	-30.4	-17.3	-0.7
	Relative (%)	-45.2	+17.7	-10.0	-29.4	-41.5	-47.3	-47.3	-42.2	-32.5	-18.5	-0.8
Steps (reduced)		47 (11)	49 (13)	50 (14)	51 (15)	52 (16)	53 (17)	54 (18)	55 (19)	56 (20)	57 (21)	58 (22)