75edt: Difference between revisions
Jump to navigation
Jump to search
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 |
m Text replacement - "[[the Riemann zeta function and tuning" to "[[Riemann zeta function" |
||
| (6 intermediate revisions by 5 users not shown) | |||
| Line 1: | Line 1: | ||
'''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 [[Riemann zeta function#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 19:21, 16 July 2026
| ← 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) | |