36edt
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Prime factorization
22 × 32
Step size
52.8321¢
Octave
23\36edt (1215.14¢)
Consistency limit
2
Distinct consistency limit
2
Special properties
| ← 35edt | 36edt | 37edt → |
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
| 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) | |
| 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) | |