Meantone family: Difference between revisions

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[[de:mitteltönig]]</span>

The [[~~5-limit|~~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.

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

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[[Map|Map]]: [<1 0 -4|, <0 1 4|]

EDOs: [[5edo|5]], [[7edo|7]], [[12edo|12]], [[19edo|19~~]], [[24edo|24~~]], [[26edo|26]], [[31edo|31~~]], [[36edo|36]], [[38edo|38~~]], [[43edo|43]], [[45edo|45]], [[50edo|50]], [[55edo|55~~]], [[57edo|57]], [[62edo|62~~]], [[67edo|67]], [[69edo|69]], [[74edo|74~~]], [[76edo|76~~]], [[81edo|81~~]], [[86edo|86~~]], [[88edo|88~~]], [[93edo|93~~]], [[98edo|98~~]], [[100edo|100~~]], [[105edo|105]], [[117edo|117]], [[~~129edo|129]], [[212edo~~|~~212b~~]]

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

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[[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>]

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 [[de:mitteltönig]]</span>
-The [[5-limit|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&gt;, and that can be flipped around to the corresponding [[Wedgies_and_Multivals|wedgie]], &lt;&lt;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.
+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&gt;, and that can be flipped around to the corresponding [[Wedgies_and_Multivals|wedgie]], &lt;&lt;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
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 [[Map|Map]]: [&lt;1 0 -4|, &lt;0 1 4|]
-EDOs: [[5edo|5]], [[7edo|7]], [[12edo|12]], [[19edo|19]], [[24edo|24]], [[26edo|26]], [[31edo|31]], [[36edo|36]], [[38edo|38]], [[43edo|43]], [[45edo|45]], [[50edo|50]], [[55edo|55]], [[57edo|57]], [[62edo|62]], [[67edo|67]], [[69edo|69]], [[74edo|74]], [[76edo|76]], [[81edo|81]], [[86edo|86]], [[88edo|88]], [[93edo|93]], [[98edo|98]], [[100edo|100]], [[105edo|105]], [[117edo|117]], [[129edo|129]], [[212edo|212b]]
+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
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 [[Comma|Comma]]s: 81/80, 126/125
-and [[9-limit|9-limit]] minimax
+and [[9-odd-limit|9-limit]] minimax
 [|1 0 0 0&gt;, |1 0 1/4 0&gt;, |0 0 1 0&gt;, |-3 0 5/2 0&gt;]