Monzo: Difference between revisions

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In this case, the val {{val| 12 19 28 }} is the [[patent val]] for 12-equal, and {{monzo| -4 4 -1 }} is 81/80, or the syntonic comma. The fact that ⟨ 12 19 28 | -4 4 -1 ⟩ tells us that 81/80 is mapped to 0 steps in 12-equal – aka it is tempered out – which tells us that 12-equal is a meantone temperament. It is noteworthy that almost the entirety of Western music composed in the Renaissance and from the sixteenth century onwards, particularly Western music composed for 12-tone circulating temperaments ([[12edo|12 equal]] and unequal [[well temperament]]s), is made possible by the tempering out of 81/80, and common practice Western music theory ~~is heavily~~ based on meantone.

In this case, the val {{val| 12 19 28 }} is the [[patent val]] for 12-equal, and {{monzo| -4 4 -1 }} is 81/80, or the syntonic comma. The fact that ⟨ 12 19 28 | -4 4 -1 ⟩ tells us that 81/80 is mapped to 0 steps in 12-equal – aka it is tempered out – which tells us that 12-equal is a meantone temperament. It is noteworthy that almost the entirety of Western music composed in the Renaissance and from the sixteenth century onwards, particularly Western music composed for 12-tone circulating temperaments ([[12edo|12 equal]] and unequal [[well temperament]]s), is made possible by the tempering out of 81/80, and that almost all aspects of modern common practice Western music theory (chords and scales) in both classical and non-classical music genres are based exclusively on meantone.

In general:

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 </math>
-In this case, the val {{val| 12 19 28 }} is the [[patent val]] for 12-equal, and {{monzo| -4 4 -1 }} is 81/80, or the syntonic comma. The fact that ⟨ 12 19 28 | -4 4 -1 ⟩ tells us that 81/80 is mapped to 0 steps in 12-equal – aka it is tempered out – which tells us that 12-equal is a meantone temperament. It is noteworthy that almost the entirety of Western music composed in the Renaissance and from the sixteenth century onwards, particularly Western music composed for 12-tone circulating temperaments ([[12edo|12 equal]] and unequal [[well temperament]]s), is made possible by the tempering out of 81/80, and common practice Western music theory is heavily based on meantone.
+In this case, the val {{val| 12 19 28 }} is the [[patent val]] for 12-equal, and {{monzo| -4 4 -1 }} is 81/80, or the syntonic comma. The fact that ⟨ 12 19 28 | -4 4 -1 ⟩ tells us that 81/80 is mapped to 0 steps in 12-equal – aka it is tempered out – which tells us that 12-equal is a meantone temperament. It is noteworthy that almost the entirety of Western music composed in the Renaissance and from the sixteenth century onwards, particularly Western music composed for 12-tone circulating temperaments ([[12edo|12 equal]] and unequal [[well temperament]]s), is made possible by the tempering out of 81/80, and that almost all aspects of modern common practice Western music theory (chords and scales) in both classical and non-classical music genres are based exclusively on meantone.
 In general: