33edt: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
'''33EDT''' is the [[Edt|equal division of the third harmonic]] into 33 parts of 57.6350 [[cent|cents]] each, corresponding to 20.8207 [[edo]]. It has a distinct flat tendency, in the sense that if 3 is pure, 5, 7, 11, 13, 17, 19, and 23 are all flat. It is consistent to the no-twos 23-limit, tempering out 3125/3087 and 588245/531441 in the 7-limit; 125/121, 3087/3025, and 3773/3645 in the 11-limit; 147/143, 175/169, 847/845, and 2197/2187 in the 13-limit; 119/117, 189/187, 225/221, and 1105/1089 in the 17-limit; 171/169, 175/171, 247/243, and 325/323 in the 19-limit; 209/207, 255/253, and 299/297 in the 23-limit (no-twos subgroup). | '''33EDT''' is the [[Edt|equal division of the third harmonic]] into 33 parts of 57.6350 [[cent|cents]] each, corresponding to 20.8207 [[edo]]. It has a distinct flat tendency, in the sense that if 3 is pure, 5, 7, 11, 13, 17, 19, and 23 are all flat. It is consistent to the no-twos 23-limit, tempering out 3125/3087 and 588245/531441 in the 7-limit; 125/121, 3087/3025, and 3773/3645 in the 11-limit; 147/143, 175/169, 847/845, and 2197/2187 in the 13-limit; 119/117, 189/187, 225/221, and 1105/1089 in the 17-limit; 171/169, 175/171, 247/243, and 325/323 in the 19-limit; 209/207, 255/253, and 299/297 in the 23-limit (no-twos subgroup). | ||
== Harmonics == | |||
{{Harmonics in equal|33|3|1|prec=2|columns=16}} | |||
[[Category:Edt]] | [[Category:Edt]] | ||
[[Category:Edonoi]] | [[Category:Edonoi]] | ||
Revision as of 04:52, 6 October 2024
| ← 32edt | 33edt | 34edt → |
33EDT is the equal division of the third harmonic into 33 parts of 57.6350 cents each, corresponding to 20.8207 edo. It has a distinct flat tendency, in the sense that if 3 is pure, 5, 7, 11, 13, 17, 19, and 23 are all flat. It is consistent to the no-twos 23-limit, tempering out 3125/3087 and 588245/531441 in the 7-limit; 125/121, 3087/3025, and 3773/3645 in the 11-limit; 147/143, 175/169, 847/845, and 2197/2187 in the 13-limit; 119/117, 189/187, 225/221, and 1105/1089 in the 17-limit; 171/169, 175/171, 247/243, and 325/323 in the 19-limit; 209/207, 255/253, and 299/297 in the 23-limit (no-twos subgroup).
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +10.34 | +0.00 | +20.67 | -19.83 | +10.34 | -26.00 | -26.63 | +0.00 | -9.50 | -1.60 | +20.67 | -2.63 | -15.66 | -19.83 | -16.29 | -5.98 |
| Relative (%) | +17.9 | +0.0 | +35.9 | -34.4 | +17.9 | -45.1 | -46.2 | +0.0 | -16.5 | -2.8 | +35.9 | -4.6 | -27.2 | -34.4 | -28.3 | -10.4 | |
| Steps (reduced) |
21 (21) |
33 (0) |
42 (9) |
48 (15) |
54 (21) |
58 (25) |
62 (29) |
66 (0) |
69 (3) |
72 (6) |
75 (9) |
77 (11) |
79 (13) |
81 (15) |
83 (17) |
85 (19) | |