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Created page with "'''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..." Tags: Mobile edit Mobile web edit |
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'''36EDT''' is the [[Edt|equal division of the third harmonic]] into 36 parts of 52.8321 [[cent|cents]] each, corresponding to 22.7135 [[edo]] | {{Infobox ET}} | ||
'''36EDT''' is the [[Edt|equal division of the third harmonic]] into 36 parts of 52.8321 [[cent|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 == | |||
{{Interval table}} | |||
== Harmonics == | |||
{{Harmonics in equal | |||
| steps = 36 | |||
| num = 3 | |||
| denom = 1 | |||
| intervals = integer | |||
}} | |||
{{Harmonics in equal | |||
| steps = 36 | |||
| num = 3 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
| intervals = integer | |||
}} | |||
{{todo|expand}} | |||
Latest revision as of 19:21, 1 August 2025
| ← 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 | Hekts | Approximate ratios |
|---|---|---|---|
| 0 | 0 | 0 | 1/1 |
| 1 | 52.8 | 36.1 | |
| 2 | 105.7 | 72.2 | 18/17 |
| 3 | 158.5 | 108.3 | 11/10, 12/11, 23/21 |
| 4 | 211.3 | 144.4 | 17/15, 26/23 |
| 5 | 264.2 | 180.6 | 7/6 |
| 6 | 317 | 216.7 | 6/5 |
| 7 | 369.8 | 252.8 | 21/17, 26/21 |
| 8 | 422.7 | 288.9 | 14/11, 23/18 |
| 9 | 475.5 | 325 | |
| 10 | 528.3 | 361.1 | 23/17 |
| 11 | 581.2 | 397.2 | 7/5 |
| 12 | 634 | 433.3 | 13/9 |
| 13 | 686.8 | 469.4 | |
| 14 | 739.6 | 505.6 | 23/15, 26/17, 29/19 |
| 15 | 792.5 | 541.7 | |
| 16 | 845.3 | 577.8 | 18/11 |
| 17 | 898.1 | 613.9 | |
| 18 | 951 | 650 | 26/15 |
| 19 | 1003.8 | 686.1 | 25/14 |
| 20 | 1056.6 | 722.2 | 11/6 |
| 21 | 1109.5 | 758.3 | |
| 22 | 1162.3 | 794.4 | |
| 23 | 1215.1 | 830.6 | |
| 24 | 1268 | 866.7 | 25/12, 27/13 |
| 25 | 1320.8 | 902.8 | 15/7 |
| 26 | 1373.6 | 938.9 | |
| 27 | 1426.5 | 975 | 25/11 |
| 28 | 1479.3 | 1011.1 | |
| 29 | 1532.1 | 1047.2 | 17/7 |
| 30 | 1585 | 1083.3 | 5/2 |
| 31 | 1637.8 | 1119.4 | 18/7 |
| 32 | 1690.6 | 1155.6 | |
| 33 | 1743.5 | 1191.7 | 11/4 |
| 34 | 1796.3 | 1227.8 | 17/6 |
| 35 | 1849.1 | 1263.9 | |
| 36 | 1902 | 1300 | 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) | |