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Created page with "'''37EDT''' is the equal division of the third harmonic into 37 parts of 21.6131 cents each, corresponding to 51.4042 edo (similar to every third step of..." Tags: Mobile edit Mobile web edit |
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'''37EDT''' is the [[Edt|equal division of the third harmonic]] into 37 parts of | {{Infobox ET}} | ||
'''37EDT''' is the [[Edt|equal division of the third harmonic]] into 37 parts of 51.4042 [[cent|cents]] each, corresponding to 23.4355 [[edo]]. The tunings supplied by [[111edt|111EDT]] (or 70edo) cannot be used for all low-limit just intervals, but they can be used on the 17-limit 8.3.100.70.22.52.68 just intonation subgroup, tempering out 289/288, 325/324, 352/351, 385/384, 561/560, 595/594, 625/624, 676/675, 1089/1088, 1156/1155, 1225/1224, and 1331/1326. | |||
==Harmonics== | |||
{{Harmonics in equal | |||
| steps = 37 | |||
| num = 3 | |||
| denom = 1 | |||
| intervals = prime | |||
}} | |||
{{Harmonics in equal | |||
| steps = 37 | |||
| num = 3 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
| intervals = prime | |||
}} | |||
==Intervals== | |||
{{Interval table}} | |||
{{todo|expand}} | |||
Latest revision as of 19:21, 1 August 2025
| ← 36edt | 37edt | 38edt → |
37EDT is the equal division of the third harmonic into 37 parts of 51.4042 cents each, corresponding to 23.4355 edo. The tunings supplied by 111EDT (or 70edo) cannot be used for all low-limit just intervals, but they can be used on the 17-limit 8.3.100.70.22.52.68 just intonation subgroup, tempering out 289/288, 325/324, 352/351, 385/384, 561/560, 595/594, 625/624, 676/675, 1089/1088, 1156/1155, 1225/1224, and 1331/1326.
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -17.7 | +0.0 | -10.5 | +23.9 | +12.4 | -19.8 | -21.6 | -8.5 | +20.6 | -20.9 | +17.9 |
| Relative (%) | -34.4 | +0.0 | -20.4 | +46.4 | +24.2 | -38.5 | -41.9 | -16.5 | +40.0 | -40.7 | +34.7 | |
| Steps (reduced) |
23 (23) |
37 (0) |
54 (17) |
66 (29) |
81 (7) |
86 (12) |
95 (21) |
99 (25) |
106 (32) |
113 (2) |
116 (5) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +20.0 | -3.5 | +16.8 | +17.0 | +14.7 | -16.8 | -23.1 | +20.1 | +22.5 | -25.6 | -8.1 |
| Relative (%) | +38.8 | -6.9 | +32.7 | +33.1 | +28.5 | -32.7 | -45.0 | +39.1 | +43.8 | -49.8 | -15.8 | |
| Steps (reduced) |
122 (11) |
125 (14) |
127 (16) |
130 (19) |
134 (23) |
137 (26) |
138 (27) |
142 (31) |
144 (33) |
144 (33) |
147 (36) | |
Intervals
| Steps | Cents | Hekts | Approximate ratios |
|---|---|---|---|
| 0 | 0 | 0 | 1/1 |
| 1 | 51.4 | 35.1 | |
| 2 | 102.8 | 70.3 | 18/17 |
| 3 | 154.2 | 105.4 | 23/21 |
| 4 | 205.6 | 140.5 | |
| 5 | 257 | 175.7 | 22/19, 29/25 |
| 6 | 308.4 | 210.8 | 6/5 |
| 7 | 359.8 | 245.9 | 27/22 |
| 8 | 411.2 | 281.1 | 14/11, 19/15 |
| 9 | 462.6 | 316.2 | 17/13 |
| 10 | 514 | 351.4 | |
| 11 | 565.4 | 386.5 | 18/13, 25/18 |
| 12 | 616.9 | 421.6 | |
| 13 | 668.3 | 456.8 | 22/15, 25/17, 28/19 |
| 14 | 719.7 | 491.9 | |
| 15 | 771.1 | 527 | 14/9 |
| 16 | 822.5 | 562.2 | 29/18 |
| 17 | 873.9 | 597.3 | |
| 18 | 925.3 | 632.4 | 17/10, 29/17 |
| 19 | 976.7 | 667.6 | |
| 20 | 1028.1 | 702.7 | |
| 21 | 1079.5 | 737.8 | 28/15 |
| 22 | 1130.9 | 773 | 25/13, 27/14 |
| 23 | 1182.3 | 808.1 | |
| 24 | 1233.7 | 843.2 | |
| 25 | 1285.1 | 878.4 | |
| 26 | 1336.5 | 913.5 | 13/6 |
| 27 | 1387.9 | 948.6 | 29/13 |
| 28 | 1439.3 | 983.8 | |
| 29 | 1490.7 | 1018.9 | |
| 30 | 1542.1 | 1054.1 | 22/9 |
| 31 | 1593.5 | 1089.2 | 5/2 |
| 32 | 1644.9 | 1124.3 | |
| 33 | 1696.3 | 1159.5 | |
| 34 | 1747.7 | 1194.6 | |
| 35 | 1799.1 | 1229.7 | 17/6 |
| 36 | 1850.6 | 1264.9 | 29/10 |
| 37 | 1902 | 1300 | 3/1 |