48edo: Difference between revisions
Tag: Reverted |
No need to remind readers of what a regular temperament is everywhere Tag: Undo |
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== Theory == | == Theory == | ||
Since 48 is a multiple of 12, it has attracted a small amount of interest. However, its best major third, of 375 cents, is over 11 cents flat. An alternative third is the familiar 400 cent major third. Using this third, 48 tunes to the same values as 12 in the [[5-limit]], but [[tempering out|tempers out]] [[2401/2400]] in the [[7-limit]], making it a tuning for [[squares]] temperament. In the [[11-limit]] we can add [[99/98]] and [[121/120]] to the list, and in the [[13-limit]], [[66/65]]. While [[31edo]] can also do 13-limit squares, 48 might be preferred for some purposes. | Since 48 is a multiple of 12, it has attracted a small amount of interest. However, its best major third, of 375 cents, is over 11 cents flat. An alternative third is the familiar 400 cent major third. Using this third, 48 tunes to the same values as 12 in the [[5-limit]], but [[tempering out|tempers out]] [[2401/2400]] in the [[7-limit]], making it a tuning for [[squares]] temperament. In the [[11-limit]] we can add [[99/98]] and [[121/120]] to the list, and in the [[13-limit]], [[66/65]]. While [[31edo]] can also do 13-limit squares, 48 might be preferred for some purposes. | ||
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== Regular temperament properties == | == Regular temperament properties == | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||