Meantone: Difference between revisions

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== Theory and classification ==

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 C-G-D-A-E) results in a major third (C-E) that is close to just.

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 C-G-D-A-E) 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.

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=== Formula to calculate ''n''-comma meantone ===

A [[perfect fifth]] is 701.955001 cents, while a [[syntonic comma]] is 21.506290 cents.

The generator ''g'' of ''n''-comma meantone, where ''n'' is a fraction (like 1/5, 2/9, etc.), can be found using the following formula:

''g'' = 701.955001-(''n'')*21.50629

== Music ==

@@ Line 11: / Line 11: @@
 == Theory and classification ==
-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 C-G-D-A-E) results in a major third (C-E) that is close to just.
+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 C-G-D-A-E) 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.
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 |}
+=== Formula to calculate ''n''-comma meantone ===
+A [[perfect fifth]] is 701.955001 cents, while a [[syntonic comma]] is 21.506290 cents.
+The generator ''g'' of ''n''-comma meantone, where ''n'' is a fraction (like 1/5, 2/9, etc.), can be found using the following formula:
+''g'' = 701.955001-(''n'')*21.50629
 == Music ==