User:VectorGraphics/Monzo notation: Difference between revisions
Created page with "This page serves as an introduction to '''monzos''', a way of notating musical intervals. In tuning theory, intervals within tuning systems (whether just intonation, EDOs, or regular temperaments) are often thought of as being composed by stacking different types of basic intervals, called "generators" or "basis elements" (which for reference make up the "basis"), and it is useful to be able to write an interval directly in terms of the number of generators of each type..." |
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</math> | </math> | ||
In this case, the val | In this case, the val [12 19 28] is the [[patent val]] for [[12-equal]], and [-4 4 1] is 81/80, or the [[syntonic comma]]. [12 19 28][-4 4 -1] tells us that 81/80 is mapped to 0 steps in 12-TET—in other words, it is tempered out—which tells us that 12-TET is a [[meantone]] temperament. It is noteworthy that almost the entirety of Western music composed in the [[Historical temperaments|Renaissance]] and from the sixteenth century onwards, particularly Western music composed for 12-tone circulating temperaments ([[12edo|12 equal]] and unequal [[Well temperament|well temperaments]]), 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: | In general: | ||
<math> | <math> | ||
[ \begin{matrix} a_1 & a_2 & \ldots & a_n \end{matrix} ][ \begin{matrix} b_1 & b_2 & \ldots & b_n \end{matrix} ] \\ | |||
= a_1 b_1 + a_2 b_2 + \ldots + a_n b_n | = a_1 b_1 + a_2 b_2 + \ldots + a_n b_n | ||
</math><!--== Monzos in JI subgroups == | </math><!--== Monzos in JI subgroups == | ||