Huygens vs meanpop: Difference between revisions

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'''Meantone''' and '''meanpop''', both discussed at [[meantone family]], are two different temperaments in the 11-limit. This page compares and contrasts them in detail.

Extending meantone from the 5-limit to the 7-limit, there is one obvious mapping that is not too complex and adds hardly any additional error (so we're not talking about dominant temperament here). This is called "7-limit meantone" or "septimal meantone" and is an amazingly efficient (and beautiful) temperament. But extending it from the 7-limit to the 11-limit is not so simple. There are two mappings that are comparable in complexity and error: 11-limit meantone (12&31) and meanpop (19&31).

Extending meantone from the 5-limit to the 7-limit, there is one obvious mapping which doesn't split the fifth that is not too complex and adds hardly any additional error (so we're not talking about dominant temperament here). This is called "7-limit meantone" or "septimal meantone" and is an amazingly efficient (and beautiful) temperament. But extending it from the 7-limit to the 11-limit is not so simple. There are two mappings that are comparable in complexity and error: 11-limit meantone (12&31) and meanpop (19&31).

In 11-limit meantone, 11/8 is represented by the doubly augmented third, for example C-Ex (where "x" represents the standard double sharp symbol, equivalent in meaning to "##"). This is 18 fifths along the circle of fifths; Ex is 18 fifths up from C.

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 '''Meantone''' and '''meanpop''', both discussed at [[meantone family]], are two different temperaments in the 11-limit. This page compares and contrasts them in detail.
-Extending meantone from the 5-limit to the 7-limit, there is one obvious mapping that is not too complex and adds hardly any additional error (so we're not talking about dominant temperament here). This is called "7-limit meantone" or "septimal meantone" and is an amazingly efficient (and beautiful) temperament. But extending it from the 7-limit to the 11-limit is not so simple. There are two mappings that are comparable in complexity and error: 11-limit meantone (12&amp;31) and meanpop (19&amp;31).
+Extending meantone from the 5-limit to the 7-limit, there is one obvious mapping which doesn't split the fifth that is not too complex and adds hardly any additional error (so we're not talking about dominant temperament here). This is called "7-limit meantone" or "septimal meantone" and is an amazingly efficient (and beautiful) temperament. But extending it from the 7-limit to the 11-limit is not so simple. There are two mappings that are comparable in complexity and error: 11-limit meantone (12&amp;31) and meanpop (19&amp;31).
 In 11-limit meantone, 11/8 is represented by the doubly augmented third, for example C-Ex (where "x" represents the standard double sharp symbol, equivalent in meaning to "##"). This is 18 fifths along the circle of fifths; Ex is 18 fifths up from C.