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Created page with "'''Division of the third harmonic into 87 equal parts''' (87EDT) is related to 55 edo, but with the 3/1 rather than the 2/1 being just. The octave is about 2..." Tags: Mobile edit Mobile web edit |
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{{Infobox ET}} | |||
'''[[Edt|Division of the third harmonic]] into 87 equal parts''' (87EDT) is related to [[55edo|55 edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 2.3853 cents stretched and the step size is about 21.8616 cents. Unlike 55edo, it is only consistent up to the [[3-odd-limit|4-integer-limit]], with discrepancy for the 5th harmonic. | '''[[Edt|Division of the third harmonic]] into 87 equal parts''' (87EDT) is related to [[55edo|55 edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 2.3853 cents stretched and the step size is about 21.8616 cents. Unlike 55edo, it is only consistent up to the [[3-odd-limit|4-integer-limit]], with discrepancy for the 5th harmonic. | ||
Lookalikes: [[55edo]], [[142ed6]], [[154ed7]] | Lookalikes: [[55edo]], [[142ed6]], [[154ed7]] | ||
== Intervals == | |||
{{Interval table}} | |||
== Harmonics == | |||
{{Harmonics in equal | |||
| steps = 87 | |||
| num = 3 | |||
| denom = 1 | |||
| intervals = integer | |||
}} | |||
{{Harmonics in equal | |||
| steps = 87 | |||
| num = 3 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
| intervals = integer | |||
}} | |||
Latest revision as of 19:23, 1 August 2025
| ← 86edt | 87edt | 88edt → |
Division of the third harmonic into 87 equal parts (87EDT) is related to 55 edo, but with the 3/1 rather than the 2/1 being just. The octave is about 2.3853 cents stretched and the step size is about 21.8616 cents. Unlike 55edo, it is only consistent up to the 4-integer-limit, with discrepancy for the 5th harmonic.
Lookalikes: 55edo, 142ed6, 154ed7
Intervals
| Steps | Cents | Hekts | Approximate ratios |
|---|---|---|---|
| 0 | 0 | 0 | 1/1 |
| 1 | 21.9 | 14.9 | |
| 2 | 43.7 | 29.9 | 38/37, 39/38, 40/39, 41/40 |
| 3 | 65.6 | 44.8 | 27/26, 28/27 |
| 4 | 87.4 | 59.8 | 20/19, 41/39 |
| 5 | 109.3 | 74.7 | 33/31 |
| 6 | 131.2 | 89.7 | 14/13, 41/38 |
| 7 | 153 | 104.6 | 12/11 |
| 8 | 174.9 | 119.5 | 21/19, 31/28, 41/37 |
| 9 | 196.8 | 134.5 | 37/33 |
| 10 | 218.6 | 149.4 | 17/15 |
| 11 | 240.5 | 164.4 | 23/20, 31/27 |
| 12 | 262.3 | 179.3 | |
| 13 | 284.2 | 194.3 | 20/17, 33/28 |
| 14 | 306.1 | 209.2 | 31/26, 37/31 |
| 15 | 327.9 | 224.1 | 23/19, 29/24 |
| 16 | 349.8 | 239.1 | 11/9, 38/31 |
| 17 | 371.6 | 254 | 26/21, 36/29 |
| 18 | 393.5 | 269 | |
| 19 | 415.4 | 283.9 | 14/11, 33/26 |
| 20 | 437.2 | 298.9 | 9/7 |
| 21 | 459.1 | 313.8 | 30/23 |
| 22 | 481 | 328.7 | 29/22, 37/28 |
| 23 | 502.8 | 343.7 | |
| 24 | 524.7 | 358.6 | 23/17 |
| 25 | 546.5 | 373.6 | 37/27 |
| 26 | 568.4 | 388.5 | |
| 27 | 590.3 | 403.4 | 38/27 |
| 28 | 612.1 | 418.4 | 37/26 |
| 29 | 634 | 433.3 | 13/9 |
| 30 | 655.8 | 448.3 | 19/13 |
| 31 | 677.7 | 463.2 | 34/23, 40/27 |
| 32 | 699.6 | 478.2 | 3/2 |
| 33 | 721.4 | 493.1 | 41/27 |
| 34 | 743.3 | 508 | 20/13 |
| 35 | 765.2 | 523 | 14/9 |
| 36 | 787 | 537.9 | 41/26 |
| 37 | 808.9 | 552.9 | |
| 38 | 830.7 | 567.8 | 21/13 |
| 39 | 852.6 | 582.8 | 18/11 |
| 40 | 874.5 | 597.7 | |
| 41 | 896.3 | 612.6 | |
| 42 | 918.2 | 627.6 | 17/10 |
| 43 | 940 | 642.5 | 31/18 |
| 44 | 961.9 | 657.5 | |
| 45 | 983.8 | 672.4 | 30/17 |
| 46 | 1005.6 | 687.4 | 34/19 |
| 47 | 1027.5 | 702.3 | 29/16, 38/21 |
| 48 | 1049.4 | 717.2 | 11/6 |
| 49 | 1071.2 | 732.2 | 13/7 |
| 50 | 1093.1 | 747.1 | |
| 51 | 1114.9 | 762.1 | 40/21 |
| 52 | 1136.8 | 777 | 27/14 |
| 53 | 1158.7 | 792 | 39/20, 41/21 |
| 54 | 1180.5 | 806.9 | |
| 55 | 1202.4 | 821.8 | 2/1 |
| 56 | 1224.2 | 836.8 | |
| 57 | 1246.1 | 851.7 | 37/18, 39/19 |
| 58 | 1268 | 866.7 | 27/13 |
| 59 | 1289.8 | 881.6 | 40/19 |
| 60 | 1311.7 | 896.6 | |
| 61 | 1333.6 | 911.5 | 41/19 |
| 62 | 1355.4 | 926.4 | |
| 63 | 1377.3 | 941.4 | 31/14 |
| 64 | 1399.1 | 956.3 | |
| 65 | 1421 | 971.3 | |
| 66 | 1442.9 | 986.2 | 23/10 |
| 67 | 1464.7 | 1001.1 | 7/3 |
| 68 | 1486.6 | 1016.1 | 26/11, 33/14 |
| 69 | 1508.4 | 1031 | |
| 70 | 1530.3 | 1046 | 29/12 |
| 71 | 1552.2 | 1060.9 | 27/11 |
| 72 | 1574 | 1075.9 | |
| 73 | 1595.9 | 1090.8 | |
| 74 | 1617.8 | 1105.7 | 28/11 |
| 75 | 1639.6 | 1120.7 | |
| 76 | 1661.5 | 1135.6 | |
| 77 | 1683.3 | 1150.6 | 37/14 |
| 78 | 1705.2 | 1165.5 | |
| 79 | 1727.1 | 1180.5 | 19/7 |
| 80 | 1748.9 | 1195.4 | 11/4 |
| 81 | 1770.8 | 1210.3 | 39/14 |
| 82 | 1792.6 | 1225.3 | 31/11 |
| 83 | 1814.5 | 1240.2 | |
| 84 | 1836.4 | 1255.2 | 26/9 |
| 85 | 1858.2 | 1270.1 | 38/13, 41/14 |
| 86 | 1880.1 | 1285.1 | |
| 87 | 1902 | 1300 | 3/1 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.39 | +0.00 | +4.77 | -9.90 | +2.39 | -2.15 | +7.16 | +0.00 | -7.51 | +2.38 | +4.77 |
| Relative (%) | +10.9 | +0.0 | +21.8 | -45.3 | +10.9 | -9.8 | +32.7 | +0.0 | -34.4 | +10.9 | +21.8 | |
| Steps (reduced) |
55 (55) |
87 (0) |
110 (23) |
127 (40) |
142 (55) |
154 (67) |
165 (78) |
174 (0) |
182 (8) |
190 (16) |
197 (23) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.63 | +0.24 | -9.90 | +9.54 | -7.97 | +2.39 | -3.77 | -5.13 | -2.15 | +4.76 | -6.61 |
| Relative (%) | -12.0 | +1.1 | -45.3 | +43.6 | -36.4 | +10.9 | -17.3 | -23.4 | -9.8 | +21.8 | -30.2 | |
| Steps (reduced) |
203 (29) |
209 (35) |
214 (40) |
220 (46) |
224 (50) |
229 (55) |
233 (59) |
237 (63) |
241 (67) |
245 (71) |
248 (74) | |