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== Harmonics == | == Harmonics == | ||
79edt's representation of most primes is rather mediocre, however it has the property that many prime harmonics lie close to a quarter of the way or halfway between its steps, which is important in that [[316edt]], which quadruples it, is one of the strongest systems less than 1000 notes in the no-twos 19-limit, and among them has the best representation of primes beyond 19. | |||
{{Harmonics in equal|79|3|1|intervals = prime|columns = 9}} | {{Harmonics in equal|79|3|1|intervals = prime|columns = 9}} | ||
{{Harmonics in equal|79|3|1|start = 12|collapsed = 1|intervals = odd}} | {{Harmonics in equal|79|3|1|start = 12|collapsed = 1|intervals = odd}} | ||
Latest revision as of 19:23, 1 August 2025
| ← 78edt | 79edt | 80edt → |
Division of the third harmonic into 79 equal parts (79EDT) is related to 50 edo, but with the 3/1 rather than the 2/1 being just. The octave is about 3.7690 cents stretched and the step size is about 24.0754 cents. It is consistent to the 10-integer-limit.
Additionally, it is an 18-strong consistent circle of the interval 17/15.
Lookalikes: 50edo, 116ed5, 129ed6, 140ed7, 29edf
Intervals
| Steps | Cents | Hekts | Approximate ratios |
|---|---|---|---|
| 0 | 0 | 0 | 1/1 |
| 1 | 24.1 | 16.5 | |
| 2 | 48.2 | 32.9 | 35/34, 36/35, 37/36, 38/37 |
| 3 | 72.2 | 49.4 | 25/24 |
| 4 | 96.3 | 65.8 | 18/17, 19/18, 37/35 |
| 5 | 120.4 | 82.3 | 15/14 |
| 6 | 144.5 | 98.7 | 37/34, 38/35 |
| 7 | 168.5 | 115.2 | |
| 8 | 192.6 | 131.6 | 19/17 |
| 9 | 216.7 | 148.1 | 17/15 |
| 10 | 240.8 | 164.6 | 31/27 |
| 11 | 264.8 | 181 | 7/6 |
| 12 | 288.9 | 197.5 | 13/11 |
| 13 | 313 | 213.9 | 6/5 |
| 14 | 337.1 | 230.4 | 17/14 |
| 15 | 361.1 | 246.8 | 37/30 |
| 16 | 385.2 | 263.3 | 5/4 |
| 17 | 409.3 | 279.7 | 19/15 |
| 18 | 433.4 | 296.2 | 9/7 |
| 19 | 457.4 | 312.7 | |
| 20 | 481.5 | 329.1 | 29/22, 37/28 |
| 21 | 505.6 | 345.6 | |
| 22 | 529.7 | 362 | 19/14, 34/25 |
| 23 | 553.7 | 378.5 | |
| 24 | 577.8 | 394.9 | |
| 25 | 601.9 | 411.4 | 17/12 |
| 26 | 626 | 427.8 | 33/23 |
| 27 | 650 | 444.3 | 35/24 |
| 28 | 674.1 | 460.8 | 28/19, 31/21 |
| 29 | 698.2 | 477.2 | |
| 30 | 722.3 | 493.7 | 38/25 |
| 31 | 746.3 | 510.1 | 37/24 |
| 32 | 770.4 | 526.6 | 25/16 |
| 33 | 794.5 | 543 | 19/12 |
| 34 | 818.6 | 559.5 | |
| 35 | 842.6 | 575.9 | |
| 36 | 866.7 | 592.4 | 28/17 |
| 37 | 890.8 | 608.9 | |
| 38 | 914.9 | 625.3 | 39/23 |
| 39 | 938.9 | 641.8 | 31/18 |
| 40 | 963 | 658.2 | |
| 41 | 987.1 | 674.7 | 23/13 |
| 42 | 1011.2 | 691.1 | |
| 43 | 1035.2 | 707.6 | |
| 44 | 1059.3 | 724.1 | 35/19 |
| 45 | 1083.4 | 740.5 | 28/15 |
| 46 | 1107.5 | 757 | 36/19 |
| 47 | 1131.5 | 773.4 | |
| 48 | 1155.6 | 789.9 | 37/19 |
| 49 | 1179.7 | 806.3 | |
| 50 | 1203.8 | 822.8 | |
| 51 | 1227.8 | 839.2 | |
| 52 | 1251.9 | 855.7 | 35/17 |
| 53 | 1276 | 872.2 | 23/11 |
| 54 | 1300.1 | 888.6 | 36/17 |
| 55 | 1324.1 | 905.1 | |
| 56 | 1348.2 | 921.5 | 37/17 |
| 57 | 1372.3 | 938 | |
| 58 | 1396.4 | 954.4 | |
| 59 | 1420.4 | 970.9 | |
| 60 | 1444.5 | 987.3 | |
| 61 | 1468.6 | 1003.8 | 7/3 |
| 62 | 1492.7 | 1020.3 | |
| 63 | 1516.7 | 1036.7 | 12/5 |
| 64 | 1540.8 | 1053.2 | |
| 65 | 1564.9 | 1069.6 | 37/15 |
| 66 | 1589 | 1086.1 | 5/2 |
| 67 | 1613.1 | 1102.5 | 33/13 |
| 68 | 1637.1 | 1119 | 18/7 |
| 69 | 1661.2 | 1135.4 | |
| 70 | 1685.3 | 1151.9 | 37/14 |
| 71 | 1709.4 | 1168.4 | |
| 72 | 1733.4 | 1184.8 | |
| 73 | 1757.5 | 1201.3 | |
| 74 | 1781.6 | 1217.7 | 14/5 |
| 75 | 1805.7 | 1234.2 | 17/6 |
| 76 | 1829.7 | 1250.6 | |
| 77 | 1853.8 | 1267.1 | 35/12 |
| 78 | 1877.9 | 1283.5 | |
| 79 | 1902 | 1300 | 3/1 |
Harmonics
79edt's representation of most primes is rather mediocre, however it has the property that many prime harmonics lie close to a quarter of the way or halfway between its steps, which is important in that 316edt, which quadruples it, is one of the strongest systems less than 1000 notes in the no-twos 19-limit, and among them has the best representation of primes beyond 19.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +3.8 | +0.0 | +6.4 | +1.7 | -10.4 | -10.7 | +6.4 | +6.5 | -11.3 |
| Relative (%) | +15.7 | +0.0 | +26.7 | +7.2 | -43.0 | -44.3 | +26.7 | +26.9 | -47.0 | |
| Steps (reduced) |
50 (50) |
79 (0) |
116 (37) |
140 (61) |
172 (14) |
184 (26) |
204 (46) |
212 (54) |
225 (67) | |
| Harmonic | 25 | 27 | 29 | 31 | 33 | 35 | 37 | 39 | 41 | 43 | 45 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -11.2 | +0.0 | -3.3 | +1.6 | -10.4 | +8.2 | +8.3 | -10.7 | -0.9 | -11.2 | +6.4 |
| Relative (%) | -46.6 | +0.0 | -13.9 | +6.6 | -43.0 | +33.9 | +34.3 | -44.3 | -3.9 | -46.4 | +26.7 | |
| Steps (reduced) |
231 (73) |
237 (0) |
242 (5) |
247 (10) |
251 (14) |
256 (19) |
260 (23) |
263 (26) |
267 (30) |
270 (33) |
274 (37) | |