Kite's thoughts on pergens: Difference between revisions

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C — C^/=Dbv/ — Db//=D\ — D^=Ebv — Eb/=E\\ — E^/=Fv\ — F

When ups and downs are used to notate edos, a third symbol is used, a '''mid''' , written ~. The mid is only for relative notation (intervals), never for absolute notation (notes). It only applies to imperfect intervals. The mid interval is the interval exactly midway between major and minor. For example, 17edo's 2nds and 3rds run minor-mid-major. This avoids having to constantly choose between the equivalent terms upminor and downmajor. 72edo's 2nds and 3rds run minor, upminor, downmid, mid, upmid, downmajor, major. This makes the terms more concise. Mids can be used in pergen notation too. For single-pair, E must be an A1, with any number of downs except 3. v5A1 creates m ^m v~ ^~ vM M. Using mids with double-pair notation ~~has not yet been fully investigated~~. ~~There may be pergens for which a 2nd mid symbol is useful~~. If one pair appears only in the perchain and the other pair only in the genchain, then the mids appear only in the genchain, ~~and only~~ if ~~the genchain's E is an A1 that isn't triple-downed~~.

When ups and downs are used to notate edos, a third symbol is used, a '''mid''' , written ~. The mid is only for relative notation (intervals), never for absolute notation (notes). It only applies to imperfect intervals. The mid interval is the interval exactly midway between major and minor. For example, 17edo's 2nds and 3rds run minor-mid-major. This avoids having to constantly choose between the equivalent terms upminor and downmajor. 72edo's 2nds and 3rds run minor, upminor, downmid, mid, upmid, downmajor, major. This makes the terms more concise. Mids can be used in pergen notation too. For single-pair, E must be an A1, with any number of downs except 3. v5A1 creates m ^m v~ ^~ vM M. Using mids with double-pair notation is trickier. Mids never appear in the perchain. If one accidental pair appears only in the perchain and the other pair only in the genchain, then the mids appear only in the genchain, if at all.

==Alternate enharmonics==

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Chord progressions can be written out by applying ups and downs to the chord roots as needed, e.g. I.v -- vIII.v -- vVI.^m -- I.v. A porcupine (third-4th) comma pump can be written out like so: C.v -- Av.^m -- Dv.v -- [Bvv=Bb^]^m -- Eb^.v -- G.^m -- G.v -- C.v. Brackets are used to show that Bvv and Bb^ are enharmonically equivalent. The equivalence is shown roughly half-way through the pump. Bvv is written first to show that this root is a vM6 above the previous root, Dv. Bb^ is second to show the P4 relationship to the next root, Eb^. Such an equivalence of course couldn't be used on the staff, where the chord would be written as either Bvv.^m or Bb^.^m, or possibly Bb^.vvM = Bb^ Dv F^.

Lifts and drops, like ups and downs, precede the note head and any sharps or flats. Scores for melody instruments could instead have them above or below the staff. This score uses ups and downs, and has chord names.

Lifts and drops, like ups and downs, precede the note head and any sharps or flats. Scores for melody instruments could instead have them above or below the staff. This score uses ups and downs, and has chord names. It's for the third-4th pergen, with E = v3A1. As noted above, it can be played in EDOs 15, 22 or 29 as is, because ^1 maps to 1 edostep. But to be played in EDOs 30, 37 or 44, ^1 must be interpreted as two edosteps.

Mizarian Porcupine Overture by Herman Miller (P8, P4/3)

Mizarian Porcupine Overture by Herman Miller (P8, P4/3) C^3 = C#

[[File:Mizarian_Porcupine_Overture.png|alt=Mizarian Porcupine Overture.png|800x692px|Mizarian Porcupine Overture.png]]

@@ Line 1,220: / Line 1,220: @@
 <span style="display: block; text-align: center;">C — C^/=Dbv/ — Db//=D\ — D^=Ebv — Eb/=E\\ — E^/=Fv\ — F
-When ups and downs are used to notate edos, a third symbol is used, a '''mid''' , written ~. The mid is only for relative notation (intervals), never for absolute notation (notes). It only applies to imperfect intervals. The mid interval is the interval exactly midway between major and minor. For example, 17edo's 2nds and 3rds run minor-mid-major. This avoids having to constantly choose between the equivalent terms upminor and downmajor. 72edo's 2nds and 3rds run minor, upminor, downmid, mid, upmid, downmajor, major. This makes the terms more concise. Mids can be used in pergen notation too. For single-pair, E must be an A1, with any number of downs except 3. v<sup>5</sup>A1 creates m ^m v~ ^~ vM M. Using mids with double-pair notation has not yet been fully investigated. There may be pergens for which a 2nd mid symbol is useful. If one pair appears only in the perchain and the other pair only in the genchain, then the mids appear only in the genchain, and only if the genchain's E is an A1 that isn't triple-downed.
+When ups and downs are used to notate edos, a third symbol is used, a '''mid''' , written ~. The mid is only for relative notation (intervals), never for absolute notation (notes). It only applies to imperfect intervals. The mid interval is the interval exactly midway between major and minor. For example, 17edo's 2nds and 3rds run minor-mid-major. This avoids having to constantly choose between the equivalent terms upminor and downmajor. 72edo's 2nds and 3rds run minor, upminor, downmid, mid, upmid, downmajor, major. This makes the terms more concise. Mids can be used in pergen notation too. For single-pair, E must be an A1, with any number of downs except 3. v<sup>5</sup>A1 creates m ^m v~ ^~ vM M. Using mids with double-pair notation is trickier. Mids never appear in the perchain. If one accidental pair appears only in the perchain and the other pair only in the genchain, then the mids appear only in the genchain, if at all.
 ==Alternate enharmonics==
@@ Line 1,268: / Line 1,268: @@
 Chord progressions can be written out by applying ups and downs to the chord roots as needed, e.g. I.v -- vIII.v -- vVI.^m -- I.v. A porcupine (third-4th) comma pump can be written out like so: C.v -- Av.^m -- Dv.v -- [Bvv=Bb^]^m -- Eb^.v -- G.^m -- G.v -- C.v. Brackets are used to show that Bvv and Bb^ are enharmonically equivalent. The equivalence is shown roughly half-way through the pump. Bvv is written first to show that this root is a vM6 above the previous root, Dv. Bb^ is second to show the P4 relationship to the next root, Eb^. Such an equivalence of course couldn't be used on the staff, where the chord would be written as either Bvv.^m or Bb^.^m, or possibly Bb^.vvM = Bb^ Dv F^.
-Lifts and drops, like ups and downs, precede the note head and any sharps or flats. Scores for melody instruments could instead have them above or below the staff. This score uses ups and downs, and has chord names.
+Lifts and drops, like ups and downs, precede the note head and any sharps or flats. Scores for melody instruments could instead have them above or below the staff. This score uses ups and downs, and has chord names. It's for the third-4th pergen, with E = v<sup>3</sup>A1. As noted above, it can be played in EDOs 15, 22 or 29 as is, because ^1 maps to 1 edostep. But to be played in EDOs 30, 37 or 44, ^1 must be interpreted as two edosteps.
-<u><span style="font-size: 110%;">Mizarian Porcupine Overture by Herman Miller (P8, P4/3)</span></u>
+<u><span style="font-size: 110%;">Mizarian Porcupine Overture by Herman Miller (P8, P4/3) C^<sup>3</sup> = C#</span></u>
 [[File:Mizarian_Porcupine_Overture.png|alt=Mizarian Porcupine Overture.png|800x692px|Mizarian Porcupine Overture.png]]