User:TallKite/Midpoints: Difference between revisions

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The gamuts are P1, m2-M2, m3-M3, P4-A4, d5-P5, m6-M6, m7-M7, P8. (See Kite's Rationales for gamuts below.) The endpoints of these gamuts define both kinds of mids, which collectively Kite calls midpoints. For example, a mid 2nd is the midpoint of m2 and M2, which is (m2 + M2)/2 = m3/2. And a mid plus 2nd is (M2 + m3)/2 = P4/2.

Inner mid and outer mid are qualities like perfect, major and minor. Neutral and interordinal are also qualities, although slightly vague ones. Perfect, major and minor are in theory precise qualities but in practice they are slightly vague. e.g. 5/4. They can diverge from their exact size by adding super- and sub- serve to . Likewise supermid, subneutral and superoutside, but subinterordinal is going too far. -ish serves to

One could label various interordinals as perfect, major, minor, etc. But outsiders aren't major or minor, they're just outside. Analogous to how mids are just mid. IOW mid and outside are themselves qualities. Neutral is also a quality, although a vague one, whereas mid is exact. Major, minor, etc. are in theory exact, but in practice vague. If they were in practice exact, we would describe e.g. 5/4 as "majorish".

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== Occurences ==

While neutrals and interordinals exist in JI, just intervals are never midpoints, because of the unique prime-factorization theorem. Mid intervals only exist in edos of even sharpness and rank-2 or higher temps that have an EI of vvA1 or v⁴A1 or v⁶A1, etc. And mid interordinals only exist in edos of even penta-sharpness and rank-2 or higher temps that have an EI of vvm2 or v⁴m2 or v⁶m2, etc.

While neutrals and interordinals exist in JI, just intervals are never midpoints, because of the unique prime-factorization theorem. Mid intervals only exist in edos of even sharpness and rank-2 or higher temps that have an [[Enharmonic unison|EU]] of vvA1 or v⁴A1 or v⁶A1, etc. And mid interordinals only exist in edos of even penta-sharpness and rank-2 or higher temps that have an EU of vvm2 or v⁴m2 or v⁶m2, etc.

What about (P8/2, P5)? it has vvd2 and a +4.

Any other pergens? ~~ask Praveen~~

(note to self -- Any other pergens?)

But we can still talk about a just mid 3rd. it's half of a just P5. And the just mid +2nd is half a just P4. Thus a just midpoint is simply half a just 3-limit interval, and is really a 3-limit midpoint.

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 The gamuts are P1, m2-M2, m3-M3, P4-A4, d5-P5, m6-M6, m7-M7, P8. (See Kite's Rationales for gamuts below.) The endpoints of these gamuts define both kinds of mids, which collectively Kite calls midpoints. For example, a mid 2nd is the midpoint of m2 and M2, which is (m2 + M2)/2 = m3/2. And a mid plus 2nd is (M2 + m3)/2 = P4/2.
-Inner mid and outer mid are qualities like perfect, major and minor. Neutral and interordinal are also qualities, although slightly vague ones. Perfect, major and minor are in theory precise qualities but in practice they are slightly vague. e.g. 5/4. They can diverge from their exact size by adding super- and sub- serve to . Likewise supermid, subneutral and superoutside, but subinterordinal is going too far. -ish serves to
 One could label various interordinals as perfect, major, minor, etc. But outsiders aren't major or minor, they're just outside. Analogous to how mids are just mid. IOW mid and outside are themselves qualities. Neutral is also a quality, although a vague one, whereas mid is exact. Major, minor, etc. are in theory exact, but in practice vague. If they were in practice exact, we would describe e.g. 5/4 as "majorish".
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 == Occurences ==
-While neutrals and interordinals exist in JI, just intervals are never midpoints, because of the unique prime-factorization theorem. Mid intervals only exist in edos of even sharpness and rank-2 or higher temps that have an EI of vvA1 or v⁴A1 or v⁶A1, etc. And mid interordinals only exist in edos of even penta-sharpness and rank-2 or higher temps that have an EI of vvm2 or v⁴m2 or v⁶m2, etc.
+While neutrals and interordinals exist in JI, just intervals are never midpoints, because of the unique prime-factorization theorem. Mid intervals only exist in edos of even sharpness and rank-2 or higher temps that have an [[Enharmonic unison|EU]] of vvA1 or v⁴A1 or v⁶A1, etc. And mid interordinals only exist in edos of even penta-sharpness and rank-2 or higher temps that have an EU of vvm2 or v⁴m2 or v⁶m2, etc.
 What about (P8/2, P5)? it has vvd2 and a +4.
-Any other pergens? ask Praveen
+(note to self -- Any other pergens?)
 But we can still talk about a just mid 3rd. it's half of a just P5. And the just mid +2nd is half a just P4. Thus a just midpoint is simply half a just 3-limit interval, and is really a 3-limit midpoint.