Meantone: Difference between revisions

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| en = Meantone
| en = Meantone
| de = Mitteltönig
| de = Mitteltönig
}}{{Infobox regtemp
}}
|Generator=3/2
{{Infobox regtemp
|Comma basis=81/80
| Title = Meantone
|Mapping=1; 1 4
| Subgroups = 2.3.5, 2.3.5.7
|Edo join 1=7
| Comma basis = 81/80 (2.3.5); <br>81/80, 126/125 (2.3.5.7)
|Edo join 2=12
| Generator = 3/2
|Optimization method=CWE
| Mapping = 1; 1 4 10
|Generator tuning=696.7
| Edo join 1 = 12 | Edo join 2 = 19
|Subgroups=2.3.5
| Optimization method = CWE
|MOS scales=[[2L 3s]], [[5L 2s]], [[7L 5s]]
| Generator tuning = 696.7
|Title=Meantone}}
| 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&ndash;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&ndash;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 ===
{{Infobox regtemp
{{Wikipedia| Septimal meantone temperament }}
|Generator=3/2
 
|Comma basis=81/80, 225/224
|Mapping=1; 1 4 10
|Edo join 1=12
|Edo join 2=19
|Optimization method=CWE
|Generator tuning=696.7
|Subgroups=2.3.5.7
|MOS scales=[[2L 3s]], [[5L 2s]], [[7L 5s]], [[12L 7s]]
|Title=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.