36edt

← 35edt

36edt

37edt →

Prime factorization	22 × 32
Step size	52.8321¢
Octave	23\36edt (1215.14¢)
Consistency limit	2
Distinct consistency limit	2
Special properties	Highly composite

36EDT is the equal division of the third harmonic into 36 parts of 52.8321 cents each, corresponding to 22.7135 edo.

The patent val has a generally sharp tendency for harmonics up to 18, with the exception for 13. It tempers out 16875/16807 and 413343/390625 in the 7-limit; 891/875, 3087/3025, and 6075/5929 in the 11-limit; 169/165, 351/343, 637/625, and 729/715 in the 13-limit; 189/187, 429/425, 459/455, 833/825, and 845/833 in the 17-limit (no-twos subgroup).

One step of 36edt is close to the TE tuning step of the quartkeenlig temperament.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	52.8
2	105.7	18/17
3	158.5	11/10, 12/11, 23/21
4	211.3	17/15, 26/23
5	264.2	7/6
6	317	6/5
7	369.8	21/17, 26/21
8	422.7	14/11, 23/18
9	475.5
10	528.3	23/17
11	581.2	7/5
12	634	13/9
13	686.8
14	739.6	23/15, 26/17, 29/19
15	792.5
16	845.3	18/11
17	898.1
18	951	26/15
19	1003.8	25/14
20	1056.6	11/6
21	1109.5
22	1162.3
23	1215.1
24	1268	25/12, 27/13
25	1320.8	15/7
26	1373.6
27	1426.5	25/11
28	1479.3
29	1532.1	17/7
30	1585	5/2
31	1637.8	18/7
32	1690.6
33	1743.5	11/4
34	1796.3	17/6
35	1849.1
36	1902	3/1

Harmonics

Approximation of harmonics in 36edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+15.1	+0.0	-22.6	+13.8	+15.1	+12.4	-7.4	+0.0	-23.9	+22.4	-22.6
	Relative (%)	+28.7	+0.0	-42.7	+26.1	+28.7	+23.5	-14.0	+0.0	-45.3	+42.4	-42.7
Steps (reduced)		23 (23)	36 (0)	45 (9)	53 (17)	59 (23)	64 (28)	68 (32)	72 (0)	75 (3)	79 (7)	81 (9)

Approximation of harmonics in 36edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.6	-25.3	+13.8	+7.7	+8.4	+15.1	-25.6	-8.8	+12.4	-15.3	+13.4
	Relative (%)	-5.0	-47.8	+26.1	+14.6	+16.0	+28.7	-48.5	-16.6	+23.5	-28.9	+25.4
Steps (reduced)		84 (12)	86 (14)	89 (17)	91 (19)	93 (21)	95 (23)	96 (24)	98 (26)	100 (28)	101 (29)	103 (31)