33edt: Difference between revisions
Jump to navigation
Jump to search
Created page with "'''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..." Tags: Mobile edit Mobile web edit |
m Removing from Category:Edonoi using Cat-a-lot |
||
| (6 intermediate revisions by 5 users not shown) | |||
| Line 1: | Line 1: | ||
{{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). | ||
== Intervals == | |||
{{Interval table}} | |||
== Harmonics == | |||
{{Harmonics in equal | |||
| steps = 33 | |||
| num = 3 | |||
| denom = 1 | |||
| intervals = integer | |||
}} | |||
{{Harmonics in equal | |||
| steps = 33 | |||
| num = 3 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
| intervals = integer | |||
}} | |||
{{stub}} | |||
Latest revision as of 19:21, 1 August 2025
| ← 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).
Intervals
| Steps | Cents | Hekts | Approximate ratios |
|---|---|---|---|
| 0 | 0 | 0 | 1/1 |
| 1 | 57.6 | 39.4 | 27/26, 28/27 |
| 2 | 115.3 | 78.8 | 15/14 |
| 3 | 172.9 | 118.2 | 11/10, 21/19 |
| 4 | 230.5 | 157.6 | |
| 5 | 288.2 | 197 | 13/11, 20/17 |
| 6 | 345.8 | 236.4 | 11/9, 27/22, 28/23 |
| 7 | 403.4 | 275.8 | 19/15 |
| 8 | 461.1 | 315.2 | 13/10, 17/13 |
| 9 | 518.7 | 354.5 | 23/17, 27/20 |
| 10 | 576.4 | 393.9 | 7/5 |
| 11 | 634 | 433.3 | 13/9 |
| 12 | 691.6 | 472.7 | |
| 13 | 749.3 | 512.1 | 17/11, 20/13 |
| 14 | 806.9 | 551.5 | 27/17 |
| 15 | 864.5 | 590.9 | 23/14, 28/17 |
| 16 | 922.2 | 630.3 | 17/10 |
| 17 | 979.8 | 669.7 | 23/13 |
| 18 | 1037.4 | 709.1 | 20/11 |
| 19 | 1095.1 | 748.5 | 17/9 |
| 20 | 1152.7 | 787.9 | |
| 21 | 1210.3 | 827.3 | |
| 22 | 1268 | 866.7 | 23/11, 27/13 |
| 23 | 1325.6 | 906.1 | 15/7, 28/13 |
| 24 | 1383.2 | 945.5 | 20/9 |
| 25 | 1440.9 | 984.8 | 23/10 |
| 26 | 1498.5 | 1024.2 | |
| 27 | 1556.1 | 1063.6 | 22/9, 27/11 |
| 28 | 1613.8 | 1103 | 28/11 |
| 29 | 1671.4 | 1142.4 | |
| 30 | 1729.1 | 1181.8 | 19/7 |
| 31 | 1786.7 | 1221.2 | 14/5 |
| 32 | 1844.3 | 1260.6 | 26/9 |
| 33 | 1902 | 1300 | 3/1 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +10.3 | +0.0 | +20.7 | -19.8 | +10.3 | -26.0 | -26.6 | +0.0 | -9.5 | -1.6 | +20.7 |
| Relative (%) | +17.9 | +0.0 | +35.9 | -34.4 | +17.9 | -45.1 | -46.2 | +0.0 | -16.5 | -2.8 | +35.9 | |
| Steps (reduced) |
21 (21) |
33 (0) |
42 (9) |
48 (15) |
54 (21) |
58 (25) |
62 (29) |
66 (0) |
69 (3) |
72 (6) |
75 (9) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.6 | -15.7 | -19.8 | -16.3 | -6.0 | +10.3 | -25.6 | +0.8 | -26.0 | +8.7 | -10.6 |
| Relative (%) | -4.6 | -27.2 | -34.4 | -28.3 | -10.4 | +17.9 | -44.5 | +1.5 | -45.1 | +15.2 | -18.4 | |
| Steps (reduced) |
77 (11) |
79 (13) |
81 (15) |
83 (17) |
85 (19) |
87 (21) |
88 (22) |
90 (24) |
91 (25) |
93 (27) |
94 (28) | |
|
This page is a stub. You can help the Xenharmonic Wiki by expanding it. |