Meantone: Difference between revisions

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| Odd limit 2 = 9 | Mistuning 2 = 10.8 | Complexity 2 = 31

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'''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. ~~In the common tunings of meantone (such~~ as ~~[[quarter-comma meantone]] and [[12edo]]), all the fifths are tuned the same, qualifying meantone as a [[regular temperament]] and more specifically~~ 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]]; good tunings of meantone also lead to soft [[diatonic]] and [[Chromatic scale|chromatic]] scales, which are desirable for interval categorization.

'''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]]; good tunings of meantone also lead to soft [[diatonic]] and [[Chromatic scale|chromatic]] scales, which are desirable for interval categorization.

[[Meantone intervals|Intervals in meantone]] have standard names based on the number of steps of the diatonic scale they span (this corresponds to the [[val]] {{val| 7 11 16 }}), with a modifier {…"double diminished", "diminished", "minor", "major", "augmented", "double augmented"…} that tells you the specific interval in increments of a chromatic semitone. Note that in a general meantone system, all of these intervals are distinct. For example, a diminished fourth is a different interval from a major third.

@@ Line 18: / Line 18: @@
 | Odd limit 2 = 9 | Mistuning 2 = 10.8 | Complexity 2 = 31
 }}
-'''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. In the common tunings of meantone (such as [[quarter-comma meantone]] and [[12edo]]), all the fifths are tuned the same, qualifying meantone as a [[regular temperament]] and more specifically 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]]; good tunings of meantone also lead to soft [[diatonic]] and [[Chromatic scale|chromatic]] scales, which are desirable for interval categorization.
+'''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]]; good tunings of meantone also lead to soft [[diatonic]] and [[Chromatic scale|chromatic]] scales, which are desirable for interval categorization.
 [[Meantone intervals|Intervals in meantone]] have standard names based on the number of steps of the diatonic scale they span (this corresponds to the [[val]] {{val| 7 11 16 }}), with a modifier {…"double diminished", "diminished", "minor", "major", "augmented", "double augmented"…} that tells you the specific interval in increments of a chromatic semitone. Note that in a general meantone system, all of these intervals are distinct. For example, a diminished fourth is a different interval from a major third.