Meantone family: Difference between revisions
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[[de:mitteltönig]]</span> | [[de:mitteltönig]]</span> | ||
The [[ | The [[5-limit]] parent [[Comma|comma]] of the [[Meantone|meantone]] family is the Didymus or [http://en.wikipedia.org/wiki/Syntonic_comma syntonic comma], 81/80. This is the one they all temper out. The [[Monzos_and_Interval_Space|monzo]] for 81/80 goes |-4 4 -1>, and that can be flipped around to the corresponding [[Wedgies_and_Multivals|wedgie]], <<1 4 4||, which tells us that the period is an octave, the generator is a fifth, and four fifths go to make up a 5/1 interval. | ||
=5-limit meantone= | |||
Comma: 81/80 | |||
[[POTE_tuning|POTE generator]]: ~3/2 = 696.239 | [[POTE_tuning|POTE generator]]: ~3/2 = 696.239 | ||
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[[Map|Map]]: [<1 0 -4|, <0 1 4|] | [[Map|Map]]: [<1 0 -4|, <0 1 4|] | ||
EDOs: [[5edo|5]], [[7edo|7]], [[12edo|12]], [[19edo|19 | EDOs: [[5edo|5]], [[7edo|7]], [[12edo|12]], [[19edo|19]], [[26edo|26]], [[31edo|31]], [[43edo|43]], [[45edo|45]], [[50edo|50]], [[55edo|55]], [[67edo|67]], [[69edo|69]], [[74edo|74]], [[81edo|81]], [[88edo|88]], [[98edo|98]], [[105edo|105]], [[117edo|117]], [[205edo|205b]] | ||
[[Badness|Badness]]: 0.00736 | [[Badness|Badness]]: 0.00736 | ||
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[[Comma|Comma]]s: 81/80, 126/125 | [[Comma|Comma]]s: 81/80, 126/125 | ||
7 and [[9-limit|9-limit]] minimax | 7 and [[9-odd-limit|9-limit]] minimax | ||
[|1 0 0 0>, |1 0 1/4 0>, |0 0 1 0>, |-3 0 5/2 0>] | [|1 0 0 0>, |1 0 1/4 0>, |0 0 1 0>, |-3 0 5/2 0>] | ||