59edt: Difference between revisions
Created page with "'''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 te..." Tags: Mobile edit Mobile web edit |
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'''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. | {{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. | |||
=Related regular temperaments= | == Intervals == | ||
==335&2159 temperament== | {{Interval table}} | ||
===5-limit=== | |||
== Prime harmonics == | |||
{{Harmonics in equal | |||
| steps = 59 | |||
| num = 3 | |||
| denom = 1 | |||
| intervals = prime | |||
}} | |||
{{Harmonics in equal | |||
| steps = 59 | |||
| num = 3 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
| intervals = prime | |||
}} | |||
==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: {{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|] | |||
EDOs: {{EDOs|37, 149, 186, 335}} | |||
====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: {{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: {{EDOs|149, 186d, 335d, 484, 633}} | |||
===335&2159 temperament=== | |||
====5-limit==== | |||
Comma: |413 -347 59> | Comma: |413 -347 59> | ||
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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}} | ||