Meantone: Difference between revisions
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| en = Meantone | | en = Meantone | ||
| de = Mitteltönig | | de = Mitteltönig | ||
}}{{Infobox regtemp | }} | ||
| | {{Infobox regtemp | ||
|Comma basis=81/80 | | Title = Meantone | ||
|Mapping=1; 1 4 | | Subgroups = 2.3.5, 2.3.5.7 | ||
|Edo join 1= | | Comma basis = 81/80 (2.3.5); <br>81/80, 126/125 (2.3.5.7) | ||
|Edo join 2= | | Generator = 3/2 | ||
|Optimization method=CWE | | Mapping = 1; 1 4 10 | ||
|Generator tuning=696.7 | | Edo join 1 = 12 | Edo join 2 = 19 | ||
| Optimization method = CWE | |||
|MOS scales=[[2L 3s]], [[5L 2s]], [[7L 5s]] | | Generator tuning = 696.7 | ||
| MOS scales = [[2L 3s]], [[5L 2s]], [[7L 5s]] | |||
}} | |||
'''Meantone''' is a familiar historical [[temperament]] based on a [[chain of fifths]] (or fourths), possessing two [[generator|generating intervals]]: the [[octave]] and the [[3/2|fifth]], from which all pitches are composed. This qualifies it as a [[rank-2 temperament]]. The octave is typically pure or close to pure, and the fifth is a few [[cents]] narrower than pure. The rationale for narrowing the fifth is to temper out the [[syntonic comma]], 81/80, which means that stacking four fifths (such as {{dash|C, G, D, A, E|hair|med}}) results in a major third (C–E) that is close to the just interval [[5/4]] (rather than the more complex Pythagorean interval [[81/64]]). | '''Meantone''' is a familiar historical [[temperament]] based on a [[chain of fifths]] (or fourths), possessing two [[generator|generating intervals]]: the [[octave]] and the [[3/2|fifth]], from which all pitches are composed. This qualifies it as a [[rank-2 temperament]]. The octave is typically pure or close to pure, and the fifth is a few [[cents]] narrower than pure. The rationale for narrowing the fifth is to temper out the [[syntonic comma]], 81/80, which means that stacking four fifths (such as {{dash|C, G, D, A, E|hair|med}}) results in a major third (C–E) that is close to the just interval [[5/4]] (rather than the more complex Pythagorean interval [[81/64]]). | ||
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== Extensions == | == Extensions == | ||
=== Septimal meantone === | === Septimal meantone === | ||
{{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 and is notably present in the augmented sixth chord; it can also be seen as a diesis-flat minor seventh. | ||