Meantone: Difference between revisions

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'''Septimal meantone''' or '''7-limit meantone''' is a natural extension of meantone which also addresses septimal intervals including but not limited to [[7/4]], [[7/5]], and [[7/6]]. By extending the [[circle of fifths]], consonant septimal intervals start to appear. For example, 7/4 is represented by an augmented sixth and is notably present in the augmented sixth chord; it can also be seen as a diesis-flat minor seventh.

'''Septimal meantone''' or '''7-limit meantone''' is a natural extension of meantone which also addresses septimal intervals including but not limited to [[7/4]], [[7/5]], and [[7/6]]. By extending the [[circle of fifths]], consonant septimal intervals start to appear. For example, 7/4 is represented by an augmented sixth (+10 fifths), and is notably present in the augmented sixth chord; it can also be seen as a diesis-flat minor seventh, as the diesis represents [[36/35]]. This mapping is rationalized by the fact that 81/80 factors as ([[126/125]])*([[225/224]]), and septimal meantone tempers out both of these commas. Notably, septimal meantone equates the interval of a diminished fifth between the third and the seventh of a [[dominant seventh chord]] to [[10/7]], making it a [[9-odd-limit]] [[essentially tempered chord]].

See [[huygens vs meanpop]] for a comparison of undecimal (11-limit) extensions.

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 {{Wikipedia| Septimal meantone temperament }}
-'''Septimal meantone''' or '''7-limit meantone''' is a natural extension of meantone which also addresses septimal intervals including but not limited to [[7/4]], [[7/5]], and [[7/6]]. By extending the [[circle of fifths]], consonant septimal intervals start to appear. For example, 7/4 is represented by an augmented sixth and is notably present in the augmented sixth chord; it can also be seen as a diesis-flat minor seventh.
+'''Septimal meantone''' or '''7-limit meantone''' is a natural extension of meantone which also addresses septimal intervals including but not limited to [[7/4]], [[7/5]], and [[7/6]]. By extending the [[circle of fifths]], consonant septimal intervals start to appear. For example, 7/4 is represented by an augmented sixth (+10 fifths), and is notably present in the augmented sixth chord; it can also be seen as a diesis-flat minor seventh, as the diesis represents [[36/35]]. This mapping is rationalized by the fact that 81/80 factors as ([[126/125]])*([[225/224]]), and septimal meantone tempers out both of these commas. Notably, septimal meantone equates the interval of a diminished fifth between the third and the seventh of a [[dominant seventh chord]] to [[10/7]], making it a [[9-odd-limit]] [[essentially tempered chord]].
 See [[huygens vs meanpop]] for a comparison of undecimal (11-limit) extensions.