Porcupine notation: Difference between revisions

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=Kite Giedraitis's approach =

Porcupine divides the perfect 4th into 3 equal steps, thus its [[pergen|pergen]] is (P8, P4/3). [[Ups_and_Downs_Notation|Ups and downs ]][[Ups_and_Downs_Notation|notation]] can be used. The generator is vM2. The enharmonic is v3A1, thus C^3 equals C#. The alternate generator is ~~G - E =~~ ^^m2. The genchain is

Porcupine divides the perfect 4th into 3 equal steps, thus its [[pergen|pergen]] is (P8, P4/3). [[Ups_and_Downs_Notation|Ups and downs]] [[Ups_and_Downs_Notation|notation]] can be used. The generator is vM2. The enharmonic is v3A1, thus ^3C equals C#. The enharmonically equivalent alternate generator is ^^m2. The genchain is

...^1 - M2 - vM3 - ^4 - P5 - vM6 - ^m7 - '''P1''' - vM2 - ^m3 - P4 - v5 - ^m6 - m7 - v8...

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In C, this would be

...C^ - D - Ev - F^ - G - Av - Bb^ - '''C''' - Dv - Eb^ - F - Gv - Ab^ - Bb - Cv...

...^C - D - vE - ^F - G - vA - ^Bb - '''C''' - vD - ^Eb - F - vG - ^Ab - Bb - vC...

Unlike the other proposals ~~here~~, the notes without ups and downs still form the familiar chain of 5ths ...Eb Bb F C G D A E B F# C#..., and interval arithmetic remains unchanged. Staff notation is as usual, with the addition of up and down accidentals before certain notes.

Unlike the other proposals on this page, the notes without ups and downs still form the familiar chain of 5ths ...Eb Bb F C G D A E B F# C#..., and interval arithmetic remains unchanged. Staff notation is as usual, with the addition of up and down accidentals before certain notes.

Porcupine[8] in A is A Bv C^ ~~D Ev~~ F^ G Av A. Porcupine[7] would omit Av.

Porcupine[8] in A is A vB ^C D vE ^F G vA A. Porcupine[7] would omit vA.

Example comma pump, with brackets indicating an enharmonic equivalence:

~~C.v~~ -- ~~Av.~~^m -- ~~Dv.v~~ -- [~~Bvv~~=Bb^].^m -- Eb^.v -- Ab^.v -- ~~C.v~~

Cv -- vA^m -- vDv -- [vvB=^Bb]^m -- ^Ebv -- ^Abv -- Cv

See the ups and downs page for an explanation of the chord names.

This is the rank-2 notation, for a generator of indeterminate cents. The edo notation uses ups and downs to represent one EDOstep. If an edo tempers out porcupine, it must be sharp-3, sharp-6, sharp-9, etc. (See the scale tree on the ~~ups and downs~~ page.) The notation is identical for sharp-3 edos (15, 22, 29, etc.). For sharp-6 edos (e.g. 30 or 72), simply double all ups and downs. The generator is vvM2. The genchain is P1 - vvM2 - ^^m3 - P4 - vv5... or C - ~~Dvv~~ - Eb^^ - F - ~~Gvv~~... Sharp-9 edos are rarely used, but the generator would be v3M2.

This is the rank-2 notation, for a generator of indeterminate cents. The edo notation uses ups and downs to represent one EDOstep. If an edo tempers out porcupine, it must be sharp-3, sharp-6, sharp-9, etc. (See the scale tree on the [[EDO|EDOs]] page.) The notation is identical for sharp-3 edos (15, 22, 29, etc.). For sharp-6 edos (e.g. 30 or 72), simply double all ups and downs. The generator is vvM2. The genchain is P1 - vvM2 - ^^m3 - P4 - vv5... or C - vvD - ^^Eb - F - vvG... Sharp-9 edos are rarely used, but the generator would be v3M2.

@@ Line 136: / Line 136: @@
 =<span style="">Kite Giedraitis's approach </span>=
-<span style=""> Porcupine divides the perfect 4th into 3 equal steps, thus its [[pergen|pergen]] is (P8, P4/3). </span>[[Ups_and_Downs_Notation|Ups and downs ]][[Ups_and_Downs_Notation|notation]]<span style=""> can be used. The generator is vM2. The enharmonic is v</span><span style="vertical-align: super;">3</span><span style="">A1, thus C^</span><span style="vertical-align: super;">3</span> equals C#. The alternate generator is G - E = ^^m2. The genchain is
+<span style=""> Porcupine divides the perfect 4th into 3 equal steps, thus its [[pergen|pergen]] is (P8, P4/3). </span>[[Ups_and_Downs_Notation|Ups and downs]] [[Ups_and_Downs_Notation|notation]]<span style=""> can be used. The generator is vM2. The enharmonic is v</span><span style="vertical-align: super;">3</span><span style="">A1, thus ^</span><span style="vertical-align: super;">3</span>C equals C#. The enharmonically equivalent alternate generator is ^^m2. The genchain is
 <span style="">...^1 - M2 - vM3 - ^4 - P5 - vM6 - ^m7 - <u>'''P1'''</u> - vM2 - ^m3 - P4 - v5 - ^m6 - m7 - v8...</span>
@@ Line 142: / Line 142: @@
 <span style="">In C, this would be </span>
-<span style="">...C^ - D - Ev - F^ - G - Av - Bb^ - <u>'''C'''</u> - Dv - Eb^ - F - Gv - Ab^ - Bb - Cv...</span>
+<span style="">...^C - D - vE - ^F - G - vA - ^Bb - <u>'''C'''</u> - vD - ^Eb - F - vG - ^Ab - Bb - vC...</span>
-<span style="">Unlike the other proposals here, the notes without ups and downs still form the familiar chain of 5ths ...Eb Bb F C G D A E B F# C#..., and interval arithmetic remains unchanged. Staff notation is as usual, with the addition of up and down accidentals before certain notes.</span>
+<span style="">Unlike the other proposals on this page, the notes without ups and downs still form the familiar chain of 5ths ...Eb Bb F C G D A E B F# C#..., and interval arithmetic remains unchanged. Staff notation is as usual, with the addition of up and down accidentals before certain notes.</span>
-<span style="">Porcupine[8] in A is A Bv C</span>^ D Ev F^ G Av A. Porcupine[7] would omit Av.
+<span style="">Porcupine[8] in A is A vB ^C</span> D vE <span style="">^</span>F G vA A. Porcupine[7] would omit vA.
 <span style="">Example comma pump, with brackets indicating an enharmonic equivalence:</span>
-<span style="">C.v -- Av.^m -- Dv.v -- [Bvv=Bb^].^m -- Eb^.v -- Ab^.v -- C.v</span>
+<span style="">Cv -- vA^m -- vDv -- [vvB=^Bb]^m -- ^Ebv -- ^Abv -- Cv</span>
 <span style="">See the ups and downs page for an explanation of the chord names.</span>
-This is the rank-2 notation,<span style=""> for a generator of indeterminate cents</span>. The edo notation uses ups and downs to represent one EDOstep. If an edo tempers out porcupine, it must be sharp-3, sharp-6, sharp-9, etc. (See the scale tree on the ups and downs page.) The notation is identical for sharp-3 edos<span style=""> (15, 22, 29, etc.). For sharp-6 edos (e.g. 30 or 72), simply double all ups and downs. The generator is vvM2. The genchain is P1 - vvM2 - ^^m3 - P4 - vv5... or C - Dvv - Eb^^ - F - Gvv... Sharp-9 edos are rarely used, but the generator would be v</span><span style="font-size: 14.4px; vertical-align: super;">3</span><span style="">M2. </span>
+This is the rank-2 notation,<span style=""> for a generator of indeterminate cents</span>. The edo notation uses ups and downs to represent one EDOstep. If an edo tempers out porcupine, it must be sharp-3, sharp-6, sharp-9, etc. (See the scale tree on the [[EDO|EDOs]] page.) The notation is identical for sharp-3 edos<span style=""> (15, 22, 29, etc.). For sharp-6 edos (e.g. 30 or 72), simply double all ups and downs. The generator is vvM2. The genchain is P1 - vvM2 - ^^m3 - P4 - vv5... or C - vvD - ^^Eb - F - vvG... Sharp-9 edos are rarely used, but the generator would be v</span><span style="font-size: 14.4px; vertical-align: super;">3</span><span style="">M2. </span>