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Created page with "'''75EDT''' is the equal division of the third harmonic into 75 parts of 25.3594 cents each, corresponding to 47.3197 edo. It is related to the 7-limit te..." Tags: Mobile edit Mobile web edit |
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'''75EDT''' is the [[Edt|equal division of the third harmonic]] into 75 parts of 25.3594 [[cent|cents]] each, corresponding to 47.3197 [[edo]]. It is related to the 7-limit temperament which tempers out 2401/2400 and |-130 138 -37 -1 | {{Infobox ET}} | ||
'''75EDT''' is the [[Edt|equal division of the third harmonic]] into 75 parts of 25.3594 [[cent|cents]] each, corresponding to 47.3197 [[edo]]. It is related to the 7-limit temperament which tempers out 2401/2400 and {{vector|-130 138 -37 -1}}, which is supported by [[284edo]], [[1183edo]], [[1467edo]], and [[2650edo]] among others. | |||
75EDT is the 14th [[ | 75EDT is the 14th [[the Riemann zeta function and tuning#Removing primes|no-twos zeta peak EDT]]. | ||
== Intervals == | |||
{{Interval table}} | |||
==Harmonics== | |||
{{Harmonics in equal | |||
| steps = 75 | |||
| num = 3 | |||
| denom = 1 | |||
| intervals = prime | |||
}} | |||
{{Harmonics in equal | |||
| steps = 75 | |||
| num = 3 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
| intervals = prime | |||
}} | |||
Latest revision as of 19:23, 1 August 2025
| ← 74edt | 75edt | 76edt → |
75EDT is the equal division of the third harmonic into 75 parts of 25.3594 cents each, corresponding to 47.3197 edo. It is related to the 7-limit temperament which tempers out 2401/2400 and [-130 138 -37 -1⟩, which is supported by 284edo, 1183edo, 1467edo, and 2650edo among others.
75EDT is the 14th no-twos zeta peak EDT.
Intervals
| Steps | Cents | Hekts | Approximate ratios |
|---|---|---|---|
| 0 | 0 | 0 | 1/1 |
| 1 | 25.4 | 17.3 | |
| 2 | 50.7 | 34.7 | |
| 3 | 76.1 | 52 | 23/22 |
| 4 | 101.4 | 69.3 | 18/17, 35/33 |
| 5 | 126.8 | 86.7 | 14/13, 29/27 |
| 6 | 152.2 | 104 | |
| 7 | 177.5 | 121.3 | 31/28 |
| 8 | 202.9 | 138.7 | |
| 9 | 228.2 | 156 | |
| 10 | 253.6 | 173.3 | 22/19, 29/25 |
| 11 | 279 | 190.7 | 20/17, 27/23 |
| 12 | 304.3 | 208 | 25/21, 31/26 |
| 13 | 329.7 | 225.3 | 23/19 |
| 14 | 355 | 242.7 | 27/22, 38/31 |
| 15 | 380.4 | 260 | |
| 16 | 405.8 | 277.3 | |
| 17 | 431.1 | 294.7 | |
| 18 | 456.5 | 312 | 13/10 |
| 19 | 481.8 | 329.3 | 33/25 |
| 20 | 507.2 | 346.7 | |
| 21 | 532.5 | 364 | |
| 22 | 557.9 | 381.3 | 29/21 |
| 23 | 583.3 | 398.7 | 7/5 |
| 24 | 608.6 | 416 | 27/19 |
| 25 | 634 | 433.3 | 13/9 |
| 26 | 659.3 | 450.7 | 19/13 |
| 27 | 684.7 | 468 | |
| 28 | 710.1 | 485.3 | |
| 29 | 735.4 | 502.7 | 26/17, 29/19 |
| 30 | 760.8 | 520 | 31/20 |
| 31 | 786.1 | 537.3 | |
| 32 | 811.5 | 554.7 | |
| 33 | 836.9 | 572 | |
| 34 | 862.2 | 589.3 | 23/14, 28/17 |
| 35 | 887.6 | 606.7 | 5/3 |
| 36 | 912.9 | 624 | 22/13 |
| 37 | 938.3 | 641.3 | 31/18 |
| 38 | 963.7 | 658.7 | |
| 39 | 989 | 676 | 23/13 |
| 40 | 1014.4 | 693.3 | 9/5 |
| 41 | 1039.7 | 710.7 | 31/17 |
| 42 | 1065.1 | 728 | |
| 43 | 1090.5 | 745.3 | |
| 44 | 1115.8 | 762.7 | |
| 45 | 1141.2 | 780 | 29/15 |
| 46 | 1166.5 | 797.3 | |
| 47 | 1191.9 | 814.7 | |
| 48 | 1217.3 | 832 | |
| 49 | 1242.6 | 849.3 | |
| 50 | 1268 | 866.7 | 27/13 |
| 51 | 1293.3 | 884 | 19/9 |
| 52 | 1318.7 | 901.3 | 15/7 |
| 53 | 1344 | 918.7 | |
| 54 | 1369.4 | 936 | |
| 55 | 1394.8 | 953.3 | 38/17 |
| 56 | 1420.1 | 970.7 | 25/11 |
| 57 | 1445.5 | 988 | 30/13 |
| 58 | 1470.8 | 1005.3 | |
| 59 | 1496.2 | 1022.7 | |
| 60 | 1521.6 | 1040 | |
| 61 | 1546.9 | 1057.3 | 22/9 |
| 62 | 1572.3 | 1074.7 | |
| 63 | 1597.6 | 1092 | |
| 64 | 1623 | 1109.3 | 23/9 |
| 65 | 1648.4 | 1126.7 | |
| 66 | 1673.7 | 1144 | |
| 67 | 1699.1 | 1161.3 | |
| 68 | 1724.4 | 1178.7 | |
| 69 | 1749.8 | 1196 | |
| 70 | 1775.2 | 1213.3 | |
| 71 | 1800.5 | 1230.7 | 17/6 |
| 72 | 1825.9 | 1248 | |
| 73 | 1851.2 | 1265.3 | |
| 74 | 1876.6 | 1282.7 | |
| 75 | 1902 | 1300 | 3/1 |
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -8.1 | +0.0 | +3.2 | +4.0 | +7.6 | -2.6 | -10.6 | -0.3 | -1.4 | +3.1 | -10.9 |
| Relative (%) | -32.0 | +0.0 | +12.7 | +15.7 | +30.1 | -10.4 | -41.8 | -1.1 | -5.4 | +12.2 | -43.1 | |
| Steps (reduced) |
47 (47) |
75 (0) |
110 (35) |
133 (58) |
164 (14) |
175 (25) |
193 (43) |
201 (51) |
214 (64) |
230 (5) |
234 (9) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +12.4 | +12.2 | +5.8 | +4.0 | -1.1 | -9.3 | +9.1 | -1.2 | -0.1 | +2.5 | -7.4 |
| Relative (%) | +49.0 | +48.2 | +23.1 | +15.8 | -4.4 | -36.5 | +35.9 | -4.6 | -0.4 | +9.9 | -29.3 | |
| Steps (reduced) |
247 (22) |
254 (29) |
257 (32) |
263 (38) |
271 (46) |
278 (53) |
281 (56) |
287 (62) |
291 (66) |
293 (68) |
298 (73) | |