55edt: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
'''55EDT''' is the [[Edt|equal division of the third harmonic]] into 55 parts of 34.5810 [[cent|cents]] each, corresponding to 34.7011 [[edo]]. It is related to the regular temperament which tempers out 420175/419904 and 205891132094649/204800000000000 in the 7-limit, which is supported by 243, 347, and 590 EDOs among others. | '''55EDT''' is the [[Edt|equal division of the third harmonic]] into 55 parts of 34.5810 [[cent|cents]] each, corresponding to 34.7011 [[edo]]. It is related to the regular temperament which tempers out 420175/419904 and 205891132094649/204800000000000 in the 7-limit, which is supported by [[243edo|243]], [[347edo|347]], and [[590edo|590]] EDOs among others. | ||
=Related regular temperaments= | == Intervals == | ||
==243&347 temperament== | {{Interval table}} | ||
===7-limit=== | |||
== Harmonics == | |||
{{Harmonics in equal | |||
| steps = 55 | |||
| num = 3 | |||
| denom = 1 | |||
| intervals = integer | |||
}} | |||
{{Harmonics in equal | |||
| steps = 55 | |||
| num = 3 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
| intervals = integer | |||
}} | |||
==Related regular temperaments== | |||
===243&347 temperament=== | |||
====7-limit==== | |||
Commas: 420175/419904, |-22 30 -11> | Commas: 420175/419904, |-22 30 -11> | ||
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Map: [<1 0 -2 2|, <0 55 150 28|] | Map: [<1 0 -2 2|, <0 55 150 28|] | ||
EDOs: 243, 347, 590 | EDOs: {{EDOs|243, 347, 590}} | ||
===11-limit=== | ====11-limit==== | ||
Commas: 137781/137500, 352947/352000, 16808715/16777216 | Commas: 137781/137500, 352947/352000, 16808715/16777216 | ||
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Map: [<1 0 -2 2 10|, <0 55 150 28 -227|] | Map: [<1 0 -2 2 10|, <0 55 150 28 -227|] | ||
EDOs: 243, 347, 590 | EDOs: {{EDOs|243, 347, 590}} | ||
===13-limit=== | ====13-limit==== | ||
Commas: 4459/4455, 15379/15360, 67392/67375, 83349/83200 | Commas: 4459/4455, 15379/15360, 67392/67375, 83349/83200 | ||
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Map: [<1 0 -2 2 10 2|, <0 55 150 28 -227 59|] | Map: [<1 0 -2 2 10 2|, <0 55 150 28 -227 59|] | ||
EDOs: 243, 347, 590 | EDOs: {{EDOs|243, 347, 590}} | ||