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{{Infobox ET}} | {{Infobox ET}} | ||
'''59EDT''' is the [[Edt|equal division of the third harmonic]] into 59 parts of 32.2365 [[cent|cents]] each, corresponding to 37.2249 [[edo]]. It is related to the regular temperament which tempers out |413 -347 59> in the 5-limit, which is supported by [[335edo|335]], [[1489edo|1489]], [[1824edo|1824]], [[2159edo|2159]], [[2494edo|2494]], [[2829edo|2829]], and [[3164edo|3164]] EDOs. | '''59EDT''' is the [[Edt|equal division of the third harmonic]] into 59 parts of 32.2365 [[cent|cents]] each, corresponding to 37.2249 [[edo]]. It is related to the regular temperament which tempers out |413 -347 59> in the 5-limit, which is supported by [[335edo|335]], [[1489edo|1489]], [[1824edo|1824]], [[2159edo|2159]], [[2494edo|2494]], [[2829edo|2829]], and [[3164edo|3164]] EDOs. | ||
== Prime harmonics == | |||
{{Harmonics in equal|59|3|1|intervals=prime}} | |||
=Related regular temperaments= | =Related regular temperaments= | ||
Revision as of 05:18, 6 October 2024
| ← 58edt | 59edt | 60edt → |
59EDT is the equal division of the third harmonic into 59 parts of 32.2365 cents each, corresponding to 37.2249 edo. It is related to the regular temperament which tempers out |413 -347 59> in the 5-limit, which is supported by 335, 1489, 1824, 2159, 2494, 2829, and 3164 EDOs.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -7.2 | +0.0 | -14.0 | +16.0 | +7.2 | +8.1 | -5.0 | -4.1 | -12.5 | +5.2 | -13.5 |
| Relative (%) | -22.5 | +0.0 | -43.3 | +49.7 | +22.3 | +25.2 | -15.5 | -12.8 | -38.9 | +16.2 | -41.9 | |
| Steps (reduced) |
37 (37) |
59 (0) |
86 (27) |
105 (46) |
129 (11) |
138 (20) |
152 (34) |
158 (40) |
168 (50) |
181 (4) |
184 (7) | |
Related regular temperaments
149&186 temperament
5-limit
Comma: |118 12 -59>
POTE generator: ~3125/3072 = 32.2390
Map: [<1 0 2|, <0 59 12|]
EDOs: 37, 149, 186, 335, 484, 521
7-limit 149&186
Commas: 3136/3125, 49433168575/48922361856
POTE generator: ~49/48 = 32.2368
Map: [<1 0 2 2|, <0 59 12 30|]
7-limit 149d&186
Commas: 1280000000/1275989841, 8589934592/8544921875
POTE generator: ~3125/3072 = 32.2456
Map: [<1 0 2 7|, <0 59 12 -156|]
EDOs: 149d, 186, 335d, 521, 707
7-limit 149&186d
Commas: 29360128/29296875, 1937102445/1927561216
POTE generator: ~3125/3072 = 32.2308
Map: [<1 0 2 -2|, <0 59 12 179|]
EDOs: 149, 186d, 335d, 484, 633
335&2159 temperament
5-limit
Comma: |413 -347 59>
POTE generator: ~|-119 100 -17> = 32.2373
Map: [<1 0 -7|, <0 59 347|]