7ed5/4: Difference between revisions
Created page with "'''7ED5/4''' is the equal division of the just major third into seven parts of 55.1877 cents each, corresponding to every fourth step of..." |
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'''7ED5/4''' is the [[Equal-step tuning|equal division]] of the [[5/4|just major third]] into seven parts of 55.1877 [[cent|cents]] each, corresponding to | {{Infobox ET}} | ||
'''7ED5/4''' is the [[Equal-step tuning|equal division]] of the [[5/4|just major third]] into seven parts of 55.1877 [[cent|cents]] each, corresponding to 21.7440 [[EDO|edo]] (very nearly [[61ed7]]). It is related to the [[Hemifamity temperaments|alphaquarter temperament]] and the 5-limit temperament which tempers out |234 -7 -96> (0.198463 cents, 5-limit 1783&7980 comma). | |||
== Harmonics == | |||
{{Harmonics in equal | |||
| steps = 7 | |||
| num = 5 | |||
| denom = 4 | |||
}} | |||
{{Harmonics in equal | |||
| steps = 7 | |||
| num = 5 | |||
| denom = 4 | |||
| start = 12 | |||
| collapsed = 1 | |||
}} | |||
==Intervals== | ==Intervals== | ||
| Line 377: | Line 392: | ||
|} | |} | ||
[[Category: | ==7ED5/4 as a generator== | ||
===Alphaquarter=== | |||
7ED5/4 leads the alphaquarter temperament using its three steps for [[11/10]], its nine steps for [[4/3]], and its 61 steps for [[7/1]]. Alphaquarter tempers out 3025/3024, 4000/3993, and 5120/5103 in the 11-limit, supported by [[87edo]], [[152edo]], [[239edo]], and [[391edo]] among others. | |||
===1783&7980 temperament=== | |||
7ED5/4 leads 1783&7980 temperament using its 96 steps for 64/3 (four octaves plus just perefect fourth). | |||
Comma: |234 -7 -96> | |||
POTE generator: 55.188 | |||
Mapping: [<1 6 2|, <0 -96 7|] | |||
EDOs: 1783, 4414, 6197, 7980, 9763, 11546, 14177 | |||
Badness: 0.1157 | |||
[[Category:Major third]] | |||
[[Category:Equal-step tuning]] | [[Category:Equal-step tuning]] | ||