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Re: [sc-users] Pitch Class sets



Thanks for doing and sending this!
Fabrice
On Saturday, December 20, 2003, at 08:51 AM, BRUCE ARNOLD wrote:

Thanks James,

Great to see someone else is interested in all those notes. Here is a
list I made back in SC2 days of all the prime forms in arrays.  I added
references to these prime forms in your list for comparison.

Thanks

Bruce Arnold


 //3 note Trichords 12 prime forms

[0,1,2],
[0,1,3],
[0,1,4],
[0,1,5],
[0,1,6],
[0,2,4],
[0,2,5],
[0,2,6],
[0,2,7],
[0,3,6],
[0,3,7],
[0,4,8],

//4 note tetrachords 29 prime forms

[0,1,2,3],
[0,1,2,4],
[0,1,2,5],
[0,1,2,6],
[0,1,2,7],
[0,1,3,4],
[0,1,3,5],
[0,1,3,6],
[0,1,3,7],
[0,1,4,5],
[0,1,4,6],
[0,1,4,7],
[0,1,4,8],
[0,1,5,6],
[0,1,5,7],
[0,1,5,8],
[0,1,6,7],
[0,2,3,5],
[0,2,3,6],
[0,2,3,7],
[0,2,4,6],
[0,2,4,7],
[0,2,4,8],
[0,2,5,7],
[0,2,5,8],
[0,2,6,8],
[0,2,4,7],
[0,2,5,8],
[0,2,6,9],

//5 note Pentachords 38 prime forms

[0,1,2,3,4],
[0,1,2,3,5],
[0,1,2,3,6],
[0,1,2,3,7],
[0,1,2,4,5],
[0,1,2,4,6],
[0,1,2,4,7],
[0,1,2,4,8],
[0,1,2,5,6],
[0,1,2,5,7],
[0,1,2,5,8],
[0,1,2,6,7],
[0,1,2,6,8],
[0,1,3,4,6],
[0,1,3,4,7],
[0,1,3,4,8],
[0,1,3,5,6],
[0,1,3,5,7],
[0,1,3,5,8],
[0,1,3,6,7],
[0,1,3,6,8],
[0,1,3,6,9],
[0,1,4,5,7],
[0,1,4,5,8],
[0,1,4,6,8],
[0,1,4,6,9],
[0,1,4,7,8],
[0,1,5,6,8],
[0,2,3,4,6],
[0,2,3,4,7],
[0,2,3,5,7],
[0,2,3,5,8],
[0,2,3,6,8],
[0,2,4,5,8],
[0,2,4,6,8],
[0,2,4,6,9],
[0,2,4,7,9],
[0,3,4,5,8],

//6 note Hexachords 35 prime forms

[0,1,2,3,4,5],
[0,1,2,3,4,6],
[0,1,2,3,4,7],
[0,1,2,3,4,8],
[0,1,2,3,5,7],
[0,1,2,3,5,8],
[0,1,2,3,6,7],
[0,1,2,3,6,8],
[0,1,2,3,6,9],
[0,1,2,3,7,8],
[0,1,2,4,5,8],
[0,1,2,4,6,8],
[0,1,2,4,6,9],
[0,1,2,4,7,8],
[0,1,2,4,7,9],
[0,1,2,5,6,9],
[0,1,2,5,7,8],
[0,1,2,5,7,9],
[0,1,2,6,7,8],
[0,1,3,4,5,7],
[0,1,3,4,5,8],
[0,1,3,4,6,9],
[0,1,3,4,7,9],
[0,1,3,5,7,9],
[0,1,4,5,7,9],
[0,1,3,6,7,9],
[0,2,3,6,7,9],
[0,1,4,5,6,8],
[0,1,4,5,8,9],
[0,2,3,4,5,7],
[0,2,3,4,6,8],
[0,2,3,4,6,9],
[0,2,3,5,7,9],
[0,2,4,5,7,9],
[0,2,4,6,8,10],

//7 note Septachords 38 prime forms

[0,1,2,3,4,5,6],
[0,1,2,3,4,5,7],
[0,1,2,3,4,6,7],
[0,1,2,3,5,6,7],
[0,1,2,3,4,5,8],
[0,1,2,3,4,6,8],
[0,1,2,3,5,6,8],
[0,1,2,4,5,6,8],
[0,1,2,3,4,7,8],
[0,1,2,3,5,7,8],
[0,1,2,4,5,7,8],
[0,1,2,3,6,7,8],
[0,1,2,4,6,7,8],
[0,1,2,3,4,6,9],
[0,1,2,3,5,6,9],
[0,1,2,4,5,6,9],
[0,1,2,3,4,7,9],
[0,1,2,3,5,7,9],
[0,1,2,4,5,7,9],
[0,1,2,3,6,7,9],
[0,1,2,4,6,7,9],
[0,1,3,4,6,7,9],
[0,1,4,5,6,7,9],
[0,1,2,4,5,8,9],
[0,1,2,4,6,8,9],
[0,1,3,4,6,8,9],
[0,1,2,5,6,8,9],
[0,1,2,5,6,7,9],
[0,2,3,4,5,6,8],
[0,1,3,4,5,6,8],
[0,2,3,4,5,7,9],
[0,2,3,4,6,7,9],
[0,1,3,5,6,7,9],
[0,1,3,4,5,7,9],
[0,1,2,4,6,8,10],
[0,1,3,4,6,8,10],
[0,1,3,5,6,8,10],
[0,1,3,4,5,7,8],

//8 note Octachords 29 prime forms

[0,1,2,3,4,5,6,7],
[0,1,2,3,4,5,6,8],
[0,1,2,3,4,5,7,8],
[0,1,2,3,4,6,7,8],
[0,1,2,3,5,6,7,8],
[0,1,2,3,4,5,6,9],
[0,1,2,3,4,5,7,9],
[0,1,2,3,4,6,7,9],
[0,1,2,3,5,6,7,9],
[0,1,2,3,4,5,8,9],
[0,1,2,3,4,6,8,9],
[0,1,2,3,5,6,8,9],
[0,1,2,4,5,6,8,9],
[0,1,2,3,4,7,8,9],
[0,1,2,3,5,7,8,9],
[0,1,2,4,5,7,8,9],
[0,1,2,3,6,7,8,9],
[0,2,3,4,5,6,7,9],
[0,1,3,4,5,6,7,9],
[0,1,2,4,5,6,7,9],
[0,1,2,3,4,6,8,10],
[0,1,2,3,5,6,8,10],
[0,1,2,4,5,6,8,10],
[0,1,2,3,5,7,8,10],
[0,1,2,4,5,7,8,10],
[0,1,2,4,6,7,8,10],
[0,1,3,4,5,6,8,9],
[0,1,3,4,5,7,8,10],
[0,1,3,4,6,7,9,10],

//9 note Nonachords 12 prime forms

[0,1,2,3,4,5,6,7,8],
[0,1,2,3,4,5,6,7,9],
[0,1,2,3,4,5,6,8,9],
[0,1,2,3,4,5,7,8,9],
[0,1,2,3,4,6,7,8,9],
[0,1,2,3,4,5,6,8,10],
[0,1,2,3,4,5,7,8,10],
[0,1,2,3,4,6,7,8,10],
[0,1,2,3,5,6,7,8,10],
[0,1,2,3,4,6,7,9,10],
[0,1,2,3,5,6,7,9,10],
[0,1,2,4,5,6,8,9,10],



From: James McCartney <asynth@xxxxxx>
Reply-To: SuperCollider users mailing list <sc-users@xxxxxxxxxxxxxxx>
Date: Fri, 19 Dec 2003 19:25:12 -0800
To: SuperCollider users mailing list <sc-users@xxxxxxxxxxxxxxx>
Subject: [sc-users] scales



I know no one cares about pitches any more, only beats.. but here's a
collection of scales.


// some of these names are the names that musicians give to the scales
// and have no accurate relation to their actual origin.
// no microtuning here, all equal tempered.
 // prime form pitch class references have been added

z = (
// 5 note scales prime form
minorPentatonic: [0,3,5,7,10], // major pentatonic mode
                               // prime form [0,2,4,7,9],
majorPentatonic: [0,2,4,7,9], // major pentatonic mode
                              // prime form [0,2,4,7,9],
ritusen: [0,2,5,7,9], // major pentatonic mode prime form [0,2,4,7,9],
egyptian: [0,2,5,7,10], // major pentatonic mode prime form [0,2,4,7,9],

kumoi: [0,2,3,7,9], prime form [0,1,3,6,8],
hirajoshi: [0,2,3,7,8], prime form [0,1,5,6,8],
iwato: [0,1,5,6,10], // mode of hirajoshi prime form [0,1,5,6,8],
chinese: [0,4,6,7,11], // mode of hirajoshi prime form [0,1,5,6,8],
indian: [0,4,5,7,10], // mode of kumoi prime form [0,1,3,6,8],
pelog: [0,1,3,7,8], // mode of kumoi prime form [0,1,3,6,8],

prometheus: [0,2,4,6,11], prime form [0,1,3,5,7],
scriabin: [0,1,4,7,9], prime form [0,1,4,6,9],

 // 6 note scales
whole: (0,2..10), //prime form [0,2,4,6,8,10],
augmented: [0,3,4,7,8,11], //prime form [0,1,4,5,8,9],
augmented2: [0,1,4,5,8,9], //mode of augmented prime form [0,1,4,5,8,9],

 // hexatonic modes with no tritone
hexMajor7: [0,2,4,7,9,11], prime form [0,2,4,5,7,9],
hexDorian: [0,2,3,5,7,10], hexMajor7 mode prime form [0,2,4,5,7,9],
hexPhrygian: [0,1,3,5,8,10], hexMajor7 mode prime form [0,2,4,5,7,9],
hexSus: [0,2,5,7,9,10], hexMajor7 mode prime form [0,2,4,5,7,9],
hexMajor6: [0,2,4,5,7,9], hexMajor7 mode prime form [0,2,4,5,7,9],
hexAeolian: [0,3,5,7,8,10], hexMajor7 mode prime form [0,2,4,5,7,9],

 // 7 note scales
ionian: [0,2,4,5,7,9,11], prime form [0,1,3,5,6,8,10],
dorian: [0,2,3,5,7,9,10], ionian mode prime form [0,1,3,5,6,8,10],
phrygian: [0,1,3,5,7,8,10], ionian mode prime form [0,1,3,5,6,8,10],
lydian: [0,2,4,6,7,9,11], ionian mode prime form [0,1,3,5,6,8,10],
mixolydian: [0,2,4,5,7,9,10], ionian mode prime form [0,1,3,5,6,8,10],
aeolian: [0,2,3,5,7,8,10], ionian mode prime form [0,1,3,5,6,8,10],
locrian: [0,1,3,5,6,8,10], ionian mode prime form [0,1,3,5,6,8,10],

harmonicMinor: [0,2,3,5,7,8,11], //prime form [0,1,3,4,6,8,9],
harmonicMajor:[0,2,4,5,7,8,11], //Retrograde of harmonicMinor at T7
                                //Prime form[0,1,3,4,6,8,9],

melodicMinor: [0,2,3,5,7,9,11],//Prime form[0,1,3,4,6,8,10],
bartok: [0,2,4,5,7,8,10], // jazzers call this the hindu scale
                           // mode of melodicMinor
                           // also called mixolydian b6 by jazzers
                            // Prime form[0,1,3,4,6,8,10],

// raga modes
todi: [0,1,3,6,7,8,11], // maqam ahar kurd Prime form[0,1,2,5,6,7,9],
purvi: [0,1,4,6,7,8,11],// mode of maqam ahar kurd
                        // Prime form[0,1,2,5,6,7,9],
marva: [0,1,4,6,7,9,11],// Prime form[0,1,2,4,6,7,9],
bhairav: [0,1,4,5,7,8,11],// Prime form[0,1,2,5,6,8,9],
ahirbhairav: [0,1,4,5,7,9,10], //harmonicMajor mode
                               //Prime form[0,1,3,4,6,8,9],

superLocrian: [0,1,3,4,6,8,10],// melodicMinor mode
                               // Prime form[0,1,3,4,6,8,10],
                               // also known as Dorianb2
romanianMinor: [0,2,3,6,7,9,10], // maqam nakriz also harmonicMajor mode
                                   //Prime form[0,1,3,4,6,8,9],
hungarianMinor: [0,2,3,6,7,8,11], //Prime form[0,1,2,5,6,8,9],
neapolitanMinor: [0,1,3,5,7,8,11],//Prime form[0,1,2,4,6,8,9]
enigmatic: [0,1,4,6,8,10,11], //Prime form[0,1,2,3,5,7,9],
spanish: [0,1,4,5,7,8,10], //romanianMinor mode Prime form[0,1,3,4,6,8,9],

// modes of whole tones with added note:
leadingWhole: [0,2,4,6,8,10,11], //Prime form[0,1,2,4,6,8,10]
lydianMinor: [0,2,4,6,7,8,10], //leadingWhole mode Prime
form[0,1,2,4,6,8,10]
neapolitanMajor: [0,1,3,5,7,9,11],//leadingWhole mode
                                  // Prime form[0,1,2,4,6,8,10]
locrianMajor: [0,2,4,5,6,8,10], //leadingWhole mode Prime
form[0,1,2,4,6,8,10]

// 8 note scales
diminished: [0,1,3,4,6,7,9,10],//jazzers call it symmetrical diminished too
diminished2: [0,2,3,5,6,8,9,11],

// 12 note scales
chromatic: (0..11)
);

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