37edf: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
'''37EDF''' is the [[EDF|equal division of the just perfect fifth]] into 37 parts of 18.9718 [[cent|cents]] each, corresponding to 63.2519 [[edo]] (similar to every fourth step of [[253edo]]). It is related to the regular temperament which tempers out 385/384, 12005/11979, and 820125/819896 in the 11-limit, which is supported by [[63edo]], [[190edo]], and [[253edo]] among others. | '''37EDF''' is the [[EDF|equal division of the just perfect fifth]] into 37 parts of 18.9718 [[cent|cents]] each, corresponding to 63.2519 [[edo]] (similar to every fourth step of [[253edo]]). | ||
It is related to the [[regular temperament]] which [[tempers out]] 385/384, 12005/11979, and 820125/819896 in the [[11-limit]], which is supported by [[63edo]], [[190edo]], and [[253edo]] among others. | |||
==Harmonics== | |||
{{Harmonics in equal|37|3|2}} | |||
{{Harmonics in equal|37|3|2|start=12|collapsed=1}} | |||
==Intervals== | ==Intervals== | ||
{| class="wikitable" | {| class="wikitable mw-collapsible" | ||
|+ Intervals of 37edf | |||
|- | |- | ||
! | degree | ! | degree | ||
| Line 413: | Line 420: | ||
EDOs: 63, 190, 253 | EDOs: 63, 190, 253 | ||
{{todo|expand}} | |||
[[Category:Edf]] | [[Category:Edf]] | ||
[[Category:Edonoi]] | [[Category:Edonoi]] | ||
Revision as of 05:48, 18 December 2024
| ← 36edf | 37edf | 38edf → |
37EDF is the equal division of the just perfect fifth into 37 parts of 18.9718 cents each, corresponding to 63.2519 edo (similar to every fourth step of 253edo).
It is related to the regular temperament which tempers out 385/384, 12005/11979, and 820125/819896 in the 11-limit, which is supported by 63edo, 190edo, and 253edo among others.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -4.78 | -4.78 | +9.41 | +2.53 | +9.41 | +8.15 | +4.63 | +9.41 | -2.24 | +3.50 | +4.63 |
| Relative (%) | -25.2 | -25.2 | +49.6 | +13.4 | +49.6 | +42.9 | +24.4 | +49.6 | -11.8 | +18.4 | +24.4 | |
| Steps (reduced) |
63 (26) |
100 (26) |
127 (16) |
147 (36) |
164 (16) |
178 (30) |
190 (5) |
201 (16) |
210 (25) |
219 (34) |
227 (5) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.14 | +3.37 | -2.24 | -0.15 | +8.73 | +4.63 | +5.89 | -7.02 | +3.37 | -1.28 | -2.35 |
| Relative (%) | -6.0 | +17.7 | -11.8 | -0.8 | +46.0 | +24.4 | +31.0 | -37.0 | +17.7 | -6.8 | -12.4 | |
| Steps (reduced) |
234 (12) |
241 (19) |
247 (25) |
253 (31) |
259 (0) |
264 (5) |
269 (10) |
273 (14) |
278 (19) |
282 (23) |
286 (27) | |
Intervals
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | exact 1/1 | ||
| 1 | 18.9718 | ||
| 2 | 37.9435 | 45/44 | |
| 3 | 56.9153 | ||
| 4 | 75.887 | 25/24 | |
| 5 | 94.8588 | ||
| 6 | 113.8305 | 16/15 | |
| 7 | 132.8023 | ||
| 8 | 151.7741 | 12/11 | |
| 9 | 170.7458 | ||
| 10 | 189.7176 | 10/9 | |
| 11 | 208.6893 | 9/8 | |
| 12 | 227.6611 | 8/7 | |
| 13 | 246.6328 | 15/13 | |
| 14 | 265.6046 | 7/6 | |
| 15 | 284.5764 | 33/28 | |
| 16 | 303.5481 | 25/21 | |
| 17 | 322.5199 | 6/5 | |
| 18 | 341.4916 | 11/9 | |
| 19 | 360.4634 | 27/22 | |
| 20 | 379.4351 | 5/4 | |
| 21 | 398.4069 | 34/27 | |
| 22 | 417.3786 | 14/11 | |
| 23 | 436.3504 | 9/7 | |
| 24 | 455.3222 | 13/10 | |
| 25 | 474.2939 | ||
| 26 | 493.2657 | 4/3 | |
| 27 | 512.2374 | ||
| 28 | 531.2092 | 15/11 | |
| 29 | 550.1809 | 11/8 | pseudo-25/18 |
| 30 | 569.1527 | real 25/18 | |
| 31 | 588.1245 | 45/32, 7/5 | |
| 32 | 607.0962 | 64/45, 10/7 | |
| 33 | 626.068 | real 36/25 | |
| 34 | 645.0397 | 16/11 | pseudo-36/25 |
| 35 | 664.0115 | 22/15 | |
| 36 | 682.9832 | 40/27 | |
| 37 | 701.955 | exact 3/2 | just perfect fifth |
| 38 | 720.9268 | ||
| 39 | 739.8985 | 135/88 | |
| 40 | 758.8703 | ||
| 41 | 777.842 | 25/16 | |
| 42 | 796.8138 | ||
| 43 | 815.7855 | 8/5 | |
| 44 | 834.7573 | ||
| 45 | 853.7291 | 18/11 | |
| 46 | 872.7008 | ||
| 47 | 891.6726 | 5/3 | |
| 48 | 910.6443 | 27/16 | |
| 49 | 929.6161 | 12/7 | |
| 50 | 948.5978 | 45/26 | |
| 51 | 967.5596 | 7/4 | |
| 52 | 986.5314 | 99/56 | |
| 53 | 1005.5031 | 25/14 | |
| 54 | 1024.4749 | 9/5 | |
| 55 | 1043.4466 | ||
| 56 | 1062.4184 | ||
| 57 | 1081.3901 | 15/8 | |
| 58 | 1100.3619 | 17/9 | |
| 59 | 1119.3336 | 21/11 | |
| 60 | 1138.3054 | 27/14 | |
| 61 | 1157.2772 | 39/20 | |
| 62 | 1176.2489 | ||
| 63 | 1195.2007 | 2/1 | |
| 64 | 1214.1924 | ||
| 65 | 1233.1642 | 45/22 | |
| 66 | 1252.1359 | 33/16 | pseudo-25/12 |
| 67 | 1271.1077 | real 25/12 | |
| 68 | 1290.0795 | 135/64, 21/10 | |
| 69 | 1309.0512 | 32/15, 15/7 | |
| 70 | 1328.023 | real 54/25 | |
| 71 | 1347.9947 | 24/11 | pseudo-54/25 |
| 72 | 1365.9668 | 11/5 | |
| 73 | 1385.9382 | 20/9 | |
| 74 | 1403.91 | exact 9/4 | |
Related regular temperaments
7-limit 63&190
Commas: 2460375/2458624, 514714375/509607936
POTE generator: ~1728/1715 = 18.957
Mapping: [<1 1 3 2|, <0 37 -43 51|]
EDOs: 63, 190, 253
11-limit 63&190
Commas: 385/384, 12005/11979, 820125/819896
POTE generator: ~99/98 = 18.957
Mapping: [<1 1 3 2 3|, <0 37 -43 51 29|]
EDOs: 63, 190, 253
13-limit 63&190
Commas: 385/384, 1575/1573, 2200/2197, 4459/4455
POTE generator: ~99/98 = 18.959
Mapping: [<1 1 3 2 3 4|, <0 37 -43 51 29 -19|]
EDOs: 63, 190, 253