Meantone family: Difference between revisions
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The [[5-limit]] parent [[comma]] of the '''meantone family''' is the Didymus or [[Wikipedia: syntonic comma|syntonic comma]], [[81/80]]. This is the one they all temper out. 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]] of the '''meantone family''' is the Didymus or [[Wikipedia: syntonic comma|syntonic comma]], [[81/80]]. This is the one they all temper out. The period is an octave, the generator is a fifth, and four fifths go to make up a 5/1 interval. | ||
== Meantone == | == Meantone == | ||
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Scales: [[meantone5]], [[meantone7]], [[meantone12]] | Scales: [[meantone5]], [[meantone7]], [[meantone12]] | ||
=== Seven-limit extensions === | |||
The second comma of the normal comma list defines which [[7-limit]] family member we are looking at. | |||
* Septimal meantone adds [[Harrison's comma|{{Monzo| -13 10 0 -1 }}]], | |||
* Flattone adds {{Monzo| -17 9 0 1 }}, | |||
* Dominant adds [[64/63|{{Monzo| 6 -2 0 -1 }}]], | |||
* Sharptone adds [[28/27|{{Monzo| 2 -3 0 1 }}]], | |||
Those all have a fifth as generator. | |||
* Injera adds {{Monzo| -7 8 0 -2 }} with a half-octave period. | |||
* Mohajira adds {{Monzo| -23 11 0 2 }} and splits the fifth in two. | |||
* Godzilla adds [[49/48|{{Monzo| -4 -1 0 2 }}]] with an 8/7 generator, two of which give the fourth (4/3, an octave minus a fifth). | |||
* Mothra adds [[1029/1024|{{Monzo| -10 1 0 3 }}]] with an 8/7 generator, three of which give the fifth. | |||
* Liese adds {{Monzo| -9 11 0 -3 }} with a 10/7 generator, three of which give the twelfth (3/1, an octave plus a fifth). | |||
* Squares adds {{Monzo| -3 9 0 -4 }} with a 9/7 generator, four of which give the eleventh (8/3, two octaves minus a fifth). | |||
* Jerome adds {{Monzo| 3 7 0 -5 }} and slices the fifth in five. | |||
Temperaments discussed elsewhere include [[Very low accuracy temperaments #Plutus|plutus]]. | |||
=== Mohaha === | === Mohaha === | ||
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Badness: 0.025167 | Badness: 0.025167 | ||
== Supermean == | == Supermean == | ||