36edt

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← 35edt36edt37edt →
Prime factorization 22 × 32
Step size 52.8321¢ 
Octave 23\36edt (1215.14¢)
Consistency limit 2
Distinct consistency limit 2
Special properties

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 52.832
2 105.664 18/17
3 158.496 11/10, 12/11, 23/21
4 211.328 17/15, 26/23
5 264.16 7/6
6 316.993 6/5
7 369.825 21/17, 26/21
8 422.657 14/11, 23/18
9 475.489
10 528.321 23/17
11 581.153 7/5
12 633.985 13/9
13 686.817
14 739.649 23/15, 26/17, 29/19
15 792.481
16 845.313 18/11
17 898.145
18 950.978 26/15
19 1003.81 25/14
20 1056.642 11/6
21 1109.474
22 1162.306
23 1215.138
24 1267.97 25/12, 27/13
25 1320.802 15/7
26 1373.634
27 1426.466 25/11
28 1479.298
29 1532.13 17/7
30 1584.963 5/2
31 1637.795 18/7
32 1690.627
33 1743.459 11/4
34 1796.291 17/6
35 1849.123
36 1901.955 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)