59edt: Difference between revisions
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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 335, 1489, 1824, 2159, 2494, 2829, and 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. | ||
=Related regular temperaments= | =Related regular temperaments= | ||
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Map: [<1 0 2|, <0 59 12|] | Map: [<1 0 2|, <0 59 12|] | ||
EDOs: 37, 149, 186, 335, 484, 521 | EDOs: {{EDOs|37, 149, 186, 335, 484, 521}} | ||
===7-limit 149&186=== | ===7-limit 149&186=== | ||
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Map: [<1 0 2 2|, <0 59 12 30|] | Map: [<1 0 2 2|, <0 59 12 30|] | ||
EDOs: 37, 149, 186, 335 | EDOs: {{EDOs|37, 149, 186, 335}} | ||
===7-limit 149d&186=== | ===7-limit 149d&186=== | ||
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Map: [<1 0 2 7|, <0 59 12 -156|] | Map: [<1 0 2 7|, <0 59 12 -156|] | ||
EDOs: 149d, 186, 335d, 521, 707 | EDOs: {{EDOs|149d, 186, 335d, 521, 707}} | ||
===7-limit 149&186d=== | ===7-limit 149&186d=== | ||
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Map: [<1 0 2 -2|, <0 59 12 179|] | Map: [<1 0 2 -2|, <0 59 12 179|] | ||
EDOs: 149, 186d, 335d, 484, 633 | EDOs: {{EDOs|149, 186d, 335d, 484, 633}} | ||
==335&2159 temperament== | ==335&2159 temperament== | ||
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Map: [<1 0 -7|, <0 59 347|] | Map: [<1 0 -7|, <0 59 347|] | ||
EDOs: 335, 1489, 1824, 2159, 2494, 2829, 3164 | EDOs: {{EDOs|335, 1489, 1824, 2159, 2494, 2829, 3164}} | ||
[[Category:Edt]] | [[Category:Edt]] | ||
[[Category:Edonoi]] | [[Category:Edonoi]] | ||
Revision as of 22:27, 6 May 2023
| ← 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.
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|]