Magic: Difference between revisions

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=== Functional harmony ===

~~In terms of generator steps, the just major triad (1-5/4-3/2) and just minor triad (1-6/5-3/2) are 0-1-5 and 0-4-5; this is similar, but~~ also in ~~clear contrast to the 0~~-~~4-1 and 0-(−3)-1 of [[meantone]]. Two approaches to functional harmony thus arise.~~

First, we suggest using the triads above as the basis of harmony, but swapping the roles of 3 and 5 according to their temperamental complexities (number of generator steps). Thus a "dominant" chord is 5/4 over tonic; a "subdominant" chord is 5/4 under tonic. This leads to an approach closely adherent to mos scales. The 7-tone mos contains a tonic and a "dominant" chord. The 10-tone mos is good for encapsulating tonic, "pre-dominant", and "dominant" functions. We also have the augmented triad (~~1-5~~/~~4-14~~/9) as the magic analog of the suspended chord of meantone.

In terms of generator steps, the just major triad (1–5/4–3/2) and just minor triad (1–6/5–3/2) are 0–1–5 and 0–4–5; this is similar, but also in clear contrast to the 0-4-1 and 0-(−3)-1 of [[meantone]]. Two approaches to functional harmony thus arise.

First, we suggest using the triads above as the basis of harmony, but swapping the roles of 3 and 5 according to their temperamental complexities (number of generator steps). Thus a "dominant" chord is 5/4 over tonic; a "subdominant" chord is 5/4 under tonic. This leads to an approach closely adherent to mos scales. The 7-tone mos contains a tonic and a "dominant" chord. The 10-tone mos is good for encapsulating tonic, "pre-dominant", and "dominant" functions. We also have the augmented triad (1–5/4–14/9) as the magic analog of the suspended chord of meantone.

Second, we suggest using the same triads as the basis of harmony, and keeping the roles of 3 and 5 as in meantone. This means dominant is still 3/2 over tonic, for example. A consequence is we must step out of the logic of mos scales, as they are often too restrictive without the many fifths to stack. Try starting unlimited and thinking directly about ratios and comma pumps. You might end up with a diatonic-like scale with comma-level inflections here and there, but it is also possible to slap whatever scale you like, using inflections to reach the ratios.

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 === Functional harmony ===
-In terms of generator steps, the just major triad (1-5/4-3/2) and just minor triad (1-6/5-3/2) are 0-1-5 and 0-4-5; this is similar, but also in clear contrast to the 0-4-1 and 0-(−3)-1 of [[meantone]]. Two approaches to functional harmony thus arise.
+{{See also| Functional harmony in rank-2 temperaments }}
-First, we suggest using the triads above as the basis of harmony, but swapping the roles of 3 and 5 according to their temperamental complexities (number of generator steps). Thus a "dominant" chord is 5/4 over tonic; a "subdominant" chord is 5/4 under tonic. This leads to an approach closely adherent to mos scales. The 7-tone mos contains a tonic and a "dominant" chord. The 10-tone mos is good for encapsulating tonic, "pre-dominant", and "dominant" functions. We also have the augmented triad (1-5/4-14/9) as the magic analog of the suspended chord of meantone.
+In terms of generator steps, the just major triad (1–5/4–3/2) and just minor triad (1–6/5–3/2) are 0–1–5 and 0–4–5; this is similar, but also in clear contrast to the 0-4-1 and 0-(−3)-1 of [[meantone]]. Two approaches to functional harmony thus arise.
+First, we suggest using the triads above as the basis of harmony, but swapping the roles of 3 and 5 according to their temperamental complexities (number of generator steps). Thus a "dominant" chord is 5/4 over tonic; a "subdominant" chord is 5/4 under tonic. This leads to an approach closely adherent to mos scales. The 7-tone mos contains a tonic and a "dominant" chord. The 10-tone mos is good for encapsulating tonic, "pre-dominant", and "dominant" functions. We also have the augmented triad (1–5/4–14/9) as the magic analog of the suspended chord of meantone.
 Second, we suggest using the same triads as the basis of harmony, and keeping the roles of 3 and 5 as in meantone. This means dominant is still 3/2 over tonic, for example. A consequence is we must step out of the logic of mos scales, as they are often too restrictive without the many fifths to stack. Try starting unlimited and thinking directly about ratios and comma pumps. You might end up with a diatonic-like scale with comma-level inflections here and there, but it is also possible to slap whatever scale you like, using inflections to reach the ratios.