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Re: [sc-users] Pitch Class sets

Your Welcome Fabrice,

    I hope you find James and my lists as helpful as I have.

Bruce Arnold


> From: Fabrice Mogini <fabrice.mogini@xxxxxxxxxx>
> Reply-To: SuperCollider users mailing list <sc-users@xxxxxxxxxxxxxxx>
> Date: Sun, 28 Dec 2003 14:43:32 +0000
> To: SuperCollider users mailing list <sc-users@xxxxxxxxxxxxxxx>
> Subject: 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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