Meantone: Difference between revisions

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|MOS scales=[[2L 3s]], [[5L 2s]], [[7L 5s]]

|Title=Meantone}}

'''Meantone''' is a familiar historical [[temperament]] based on a chain of fifths (or fourths). The more ~~technical part~~ is discussed in [[~~meantone~~ family]] in the context of the associated family of temperaments. {{Wikipedia|Meantone temperament}}

'''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 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.

Technical temperament data is discussed at [[Meantone family #Meantone]] in the context of the associated family of temperaments. {{Wikipedia|Meantone temperament}}

== History ==

Meantone with fifths flatter than 700{{cent}} were the dominant tuning used in Europe from around late 15th century to around early 18th century, after which various [[well temperament]]s and eventually [[12edo|12-tone equal temperament]] won in popularity. However, even today, the vast majority of common-practice Western music theory is based exclusively on meantone, as 12-tone equal temperament is itself a meantone tuning.

== ~~Theory and classification~~ ==

== Extensions ==

Meantone temperaments are based on two generating intervals; the octave and the fifth, from which all pitches are composed. This qualifies it as a [[Regular Temperaments|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]]. This 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 just.

[[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.

=== Septimal meantone ===

{{Infobox regtemp

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Dominant is an alternative extension of meantone, which represents 7/4 as a minor seventh rather than an augmented sixth. This equates 6/5 with 7/6 and 5/4 with 9/7, tempering out [[36/35]] (septimal quarter tone) and [[64/63]] (Archytas' comma).

~~==== Sharptone ====~~

~~{{See also| Meantone family #Sharptone }}~~

~~Sharptone is a low-accuracy temperament ([[exotemperament]]) which represents 7/4 as a major sixth. This equates 7/6 with 9/8 and 4/3 with 7/5, tempering out [[21/20]] and [[28/27]].~~

== Chords ==

@@ Line 13: / Line 13: @@
 |MOS scales=[[2L 3s]], [[5L 2s]], [[7L 5s]]
 |Title=Meantone}}
-'''Meantone''' is a familiar historical [[temperament]] based on a chain of fifths (or fourths). The more technical part is discussed in [[meantone family]] in the context of the associated family of temperaments. {{Wikipedia|Meantone temperament}}
+'''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 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.
+Technical temperament data is discussed at [[Meantone family #Meantone]] in the context of the associated family of temperaments. {{Wikipedia|Meantone temperament}}
 == History ==
 Meantone with fifths flatter than 700{{cent}} were the dominant tuning used in Europe from around late 15th century to around early 18th century, after which various [[well temperament]]s and eventually [[12edo|12-tone equal temperament]] won in popularity. However, even today, the vast majority of common-practice Western music theory is based exclusively on meantone, as 12-tone equal temperament is itself a meantone tuning.
-== Theory and classification ==
+== Extensions ==
-Meantone temperaments are based on two generating intervals; the octave and the fifth, from which all pitches are composed. This qualifies it as a [[Regular Temperaments|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]]. This 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 just.
-[[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.
 === Septimal meantone ===
 {{Infobox regtemp
@@ Line 50: / Line 51: @@
 Dominant is an alternative extension of meantone, which represents 7/4 as a minor seventh rather than an augmented sixth. This equates 6/5 with 7/6 and 5/4 with 9/7, tempering out [[36/35]] (septimal quarter tone) and [[64/63]] (Archytas' comma).
-==== Sharptone ====
-{{See also| Meantone family #Sharptone }}
-Sharptone is a low-accuracy temperament ([[exotemperament]]) which represents 7/4 as a major sixth. This equates 7/6 with 9/8 and 4/3 with 7/5, tempering out [[21/20]] and [[28/27]].
 == Chords ==