36ed7

← 35ed7

36ed7

37ed7 →

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	93.6	18/17, 19/18
2	187.2	19/17, 29/26
3	280.7
4	374.3	26/21
5	467.9	17/13
6	561.5	18/13, 29/21
7	655	19/13, 22/15
8	748.6	17/11
9	842.2
10	935.8	12/7
11	1029.4
12	1122.9	21/11, 23/12
13	1216.5
14	1310.1
15	1403.7
16	1497.3	26/11
17	1590.8	5/2
18	1684.4	29/11
19	1778	14/5
20	1871.6
21	1965.1	25/8
22	2058.7	23/7
23	2152.3
24	2245.9	11/3
25	2339.5
26	2433
27	2526.6
28	2620.2
29	2713.8	24/5
30	2807.4
31	2900.9
32	2994.5
33	3088.1
34	3181.7
35	3275.2
36	3368.8	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)

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