24edt: Difference between revisions
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{{Infobox ET}} | |||
'''24EDT''' is the [[Edt|equal division of the third harmonic]] into 24 parts of 79.2481 [[cent|cents]] each, corresponding to 15.1423 [[edo]] (similar to every seventh step of [[106edo]]). It is related to the rank-three temperament which tempers out 325/324, 625/624, and 468512/468195 in the 13-limit, which is supported by [[15edo|15]], [[106edo|106]], [[121edo|121]], [[212edo|212]], and [[227edo|227]] EDOs. | '''24EDT''' is the [[Edt|equal division of the third harmonic]] into 24 parts of 79.2481 [[cent|cents]] each, corresponding to 15.1423 [[edo]] (similar to every seventh step of [[106edo]]). It is related to the rank-three temperament which tempers out 325/324, 625/624, and 468512/468195 in the 13-limit, which is supported by [[15edo|15]], [[106edo|106]], [[121edo|121]], [[212edo|212]], and [[227edo|227]] EDOs. | ||
== Theory == | |||
{{Harmonics in equal|24|3|1|prec=2|columns=15}} | |||
== Interval table == | |||
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==Related | ==Related regular temperaments== | ||
===11-limit 15&106&212=== | ===11-limit 15&106&212=== | ||
Commas: 15625/15552, 585640/583443 | Commas: 15625/15552, 585640/583443 | ||
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POTE generators: ~7/4 = 968.8778, ~22/21 = 79.2597 | POTE generators: ~7/4 = 968.8778, ~22/21 = 79.2597 | ||
Mapping: [<1 0 1 0 -1|, <0 24 20 0 25|, <0 0 0 1 1|] | |||
EDOs: 15, 106, 121, 212, 227 | EDOs: 15, 106, 121, 212, 227 | ||
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POTE generators: ~7/4 = 968.8187, ~22/21 = 79.2727 | POTE generators: ~7/4 = 968.8187, ~22/21 = 79.2727 | ||
Mapping: [<1 0 1 0 -1 0|, <0 24 20 0 25 56|, <0 0 0 1 1 0|] | |||
EDOs: 15, 106, 121, 212, 227 | EDOs: 15, 106, 121, 212, 227 | ||
{{todo|expand}} | |||