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Old 26th March 2018, 09:24 AM   #241
calebprime
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What's that?

Oh, rhythm? I like rhythm.

A kind and helpful poster was suggesting that you could do a 12/8 groove, and get your syncopation pattern from the self-sim pattern above, what with its offbeat 5,7,9,11 thing.

Gradually fill it in. Assign notes to drum machine or something.




Heh. 12/8. The one thing in common between African music and Babbitt.
No one ever wrote: " The sly funkiness of All Set notwithstanding."

I recently located some articles in Perspectives of New Music that were about Stockhausen's serial derivation of rhythm. Not a particularly joyful topic. Will share once I've read.
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Old 27th March 2018, 04:32 AM   #242
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For today's nugget, a slightly different use for the same structure as the every-other square: all the columns are rotations of each other. The top row is the given series.

Hopefully each row/line will have some obvious relation to the others for this structure to be interesting.

Instead of an every-other square, we make a square where every column is a rotation of the same arbitrary series. Here that series is simply the inversion of the given series, Summer Train.

Summer Train has the rare quality that every contiguous 5-note group has no 012, and so is a viable harmony. We take advantage of that, and of our observation that there are groups of notes that are inversionally equivalent, by playing the top row (original) off the columns (inversion in rotation).

I don't know yet about the lines, but the chords are each 5-note wonders worthy of Ralph Towner, all good over a C pedal. Summer Train makes me feel fine.

today's nugget:

Code:

C,  D,  G,  E,  Ab, Bb, Db, Gb, F,  A,  Eb, B
Bb, B,  Eb, D,  E,  F,  C,  G,  Ab, Db, A,  Gb
F,  Gb, A,  B,  D,  Ab, Bb, Eb, E,  C,  Db, G
Ab, G,  Db, Gb, B,  E,  F,  A,  D,  Bb, C,  Eb
E,  Eb, C,  G,  Gb, D,  Ab, Db, B,  F,  Bb, A
-----------------------------------------------
C pedal
Ok, the lines are nothing, but I'm using this anyway.

Later I'll come up with some examples where the lines also have some resemblance.

eta: such as this one. columns are series transposed down a major third

Code:
C,  D,  G,  E,  Ab, Bb, Db, Gb, F,  A,  Eb, B
E,  Db, Ab, Gb, Bb, Eb, F,  A,  B,  D,  C,  G
Gb, F,  Bb, A,  Eb, C,  B,  D,  G,  Db, E,  Ab
A,  B,  Eb, D,  C,  E,  G,  Db, Ab, F,  Gb, Bb
D,  G,  C,  Db, E,  Gb, Ab, F,  Bb, B,  A,  Eb
Db, Ab, E,  F,  Gb, A,  Bb, B,  Eb, G,  D,  C
F,  Bb, Gb, B,  A,  D,  Eb, G,  C,  Ab, Db, E
B,  Eb, A,  G,  D,  Db, C,  Ab, E,  Bb, F,  Gb
G,  C,  D,  Ab, Db, F,  E,  Bb, Gb, Eb, B,  A
Ab, E,  Db, Bb, F,  B,  Gb, Eb, A,  C,  G,  D
Bb, Gb, F,  Eb, B,  G,  A,  C,  D,  E,  Ab, Db
Eb, A,  B,  C,  G,  Ab, D,  E,  Db, Gb, Bb, F

Last edited by calebprime; 27th March 2018 at 06:25 AM.
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Old 29th March 2018, 06:26 AM   #243
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Just this nugget for now, more later.

There is only one viable 4-voice chorale according to the computer.

Code:
ri/11/11:............B  C  Ab D  F# F  Bb C# Eb G  E  A  
i/5/6:...............E  B  C  Ab D  F# F  Eb Bb C# A  G  
r/6/5:...............G  E  D  Bb C# Ab F# F  A  Eb B  C  
p/0/0:...............C  D  G  E  Ab Bb C# F# F  A  Eb B
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Old 29th March 2018, 06:29 AM   #244
Ron_Tomkins
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Originally Posted by calebprime View Post
Yes, [twitches around mouth], little Bart Ron. During my, ah, period of...convalescence, we feel we worked really hard on our feelings of rage when we feel the gravity of our work is depreciated by others, indeed, whether they were our colleagues back at The Academy, or now, in humbler surroundings here at ISF.

And perhaps there is a trenchent point here after all that Ron wants to share with us --perhaps something about Pierre Boulez legendary aversion to dance rhythms such as waltes in Berg's music, or the whole French concept of ungrounded additive rhythm -- certainly what the little scamp could be referring to "undance-able" !

Because surely otherwise it would be out of place to be speaking of rhythm at this early point, when all we're doing is figuring out how to collect series!

Rhythm comes later!

Admittedly, it was also a point of criticism by Boulez of Schoenberg -- that his rhythm was like Brahms, too old-fashioned.

Whether serial techniques in the usual 12-tone sense would be very useful for generating memorable rhythms, I have my doubts.

But perhaps I've spoken too much.


At the time of my resignation, none of the allegations were substantiated.
So you can't dance to it then
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Old 29th March 2018, 08:15 AM   #245
calebprime
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Nope.
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Old 30th March 2018, 05:37 AM   #246
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Today I find myself bored with my plan -- to say a few things about each of the 24 series I chose.

Instead I think I'll shut up and mess around with the 24 series, maybe choose one and discuss that one in depth, maybe work it up into the beginnings of a piece.

Otherwise, If I'm worried about getting bored with the series themselves, maybe the worst thing to do is to say a few things about each series in turn. That is a boring, disinterested approach.
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Old 13th April 2018, 06:55 AM   #247
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I'm putting together a study of common-tones between (12EDO) scales -- something I've been contemplating since my 20's, but never accomplished.

After working with materials with more of an exotic reputation like microtonal tunings and 12-tone series, it's like coming home to an old neighborhood.

So far so good -- the ratio of insight to tedium is high at first.

I've never conducted a study of exactly this, so I have only a few sketchy opinions yet how it should be done. Constructive suggestions welcome if you have some understanding of the purpose in the first place.

IMO, the interesting cases are the ones with 4 common-tones or fewer, especially 3 and 2 common-tone situations.

Now, since the definition of scales I'm working with is logical and exhaustive, there is a built-in nullity to this study: What it will show is simply everything, unless the study is biased toward what is interesting.

The goal is to have some new insights that might spark some new (neo-old-age-late-style) composition.

example entry:

Code:
Scale Group 1 (major) with Scale Group 2 (melodic minor)

1		C,D,E,F#,G,A,B        C lydian       
with
2
C,D,E,F#,g#,A,B				C lydian #5

f,G,A,B,c#,D,E
bb,C,D,E,F#,G,A
eb,f,G,A,B,C,D
ab,bb,C,D,E,f,G
db,eb,f,G,A,bb,C  (no Ab)		common: G,A,C    (025)
Gb,ab,bb,C,D,eb,f (no Db)     common: Gb,C,D	(026)
B,A,c#,d#,f,G,g#,a# - (all)   common: G,A,B	(024)
E,F#,g#,a#,C,c#,d# (no F) 	common: C,E,F#	(026)                                       
A,B,c#,d#,f,F#,g# (no a#)		common: A,B,F#	(025)
D,E,F#,g#,a#,B,c#
G,A,B,c#,d#,E,F#

Last edited by calebprime; 13th April 2018 at 06:59 AM.
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Old 13th April 2018, 09:42 AM   #248
calebprime
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Originally Posted by calebprime View Post
...
example entry:

Code:
Scale Group 1 (major) with Scale Group 2 (melodic minor)

1		C,D,E,F#,G,A,B        C lydian       
with
2
C,D,E,F#,g#,A,B				C lydian #5

f,G,A,B,c#,D,E
bb,C,D,E,F#,G,A
eb,f,G,A,B,C,D
ab,bb,C,D,E,f,G
db,eb,f,G,A,bb,C  (no Ab)		common: G,A,C    (025)
Gb,ab,bb,C,D,eb,f (no Db)     common: Gb,C,D	(026)
B,A,c#,d#,f,G,g#,a# - (all)   common: G,A,B	(024)
E,F#,g#,a#,C,c#,d# (no F) 	common: C,E,F#	(026)                                       
A,B,c#,d#,f,F#,g# (no a#)		common: A,B,F#	(025)
D,E,F#,g#,a#,B,c#
G,A,B,c#,d#,E,F#
Code:
Scale Group 1 (major) with Scale Group 2 (melodic minor)

1		C,D,E,F#,G,A,B        C lydian       
with
2
C,D,E,F#,g#,A,B				C lydian #5

f,G,A,B,c#,D,E
bb,C,D,E,F#,G,A
eb,f,G,A,B,C,D
ab,bb,C,D,E,f,G
db,eb,f,G,A,bb,C  (no Ab)		common: G,A,C    (025)
Gb,ab,bb,C,D,eb,f (no Db)     common: Gb,C,D	(026)
B,c#,d#,f,G,g#,a# - (all)   common: G,B	(04)
E,F#,g#,a#,C,c#,d# (no F) 	common: C,E,F#	(026)                                       
A,B,c#,d#,f,F#,g# (no a#)		common: A,B,F#	(025)
D,E,F#,g#,a#,B,c#
G,A,B,c#,d#,E,F#
fix 1 dumb mistake
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Old 16th April 2018, 10:13 AM   #249
calebprime
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square one of that study:



Code:
===========================================================

Scale Group 1 (major)  with Scale Group 1 (major)

1		C,D,E,F#,G,A,B		C lydian

G,A,B,c#,D,E,F#
D,E,F#,g#,A,B,c#
A,B,c#,d#,E,F#,g#
E,F#,g#,a#,B,c#,d# no F 	common: E,F#,B  (027)
B,c#,d#,f,F#,g#,a# all 	common:F#,B
F#,g#,a#,C,c#,d#,f all 	common:F#,C
db,eb,f,G,ab,bb,C  all 	common:G,C
ab,bb,C,D,eb,f,G   no Db  common:C,D,G   (027)
d#,f,G,A,a#,C,D
a#,C,D,E,a,G,A
f,G,A,B,C,D,E,



===========================================================
Scale Group 1 (major) with Scale Group 2 (melodic minor)

1		C,D,E,F#,G,A,B		C lydian       
with
2
C,D,E,F#,g#,A,B				C lydian #5

f,G,A,B,c#,D,E
bb,C,D,E,F#,G,A
eb,f,G,A,B,C,D
ab,bb,C,D,E,f,G
db,eb,f,G,A,bb,C  (no Ab)		common: G,A,C    (025)
Gb,ab,bb,C,D,eb,f (no Db)     common: Gb,C,D	(026)
B,A,c#,d#,f,G,g#,a# - (all)   common: G,A,B	(024)
E,F#,g#,a#,C,c#,d# (no F) 	common: C,E,F#	(026)                                       
A,B,c#,d#,f,F#,g# (no a#)		common: A,B,F#	(025)
D,E,F#,g#,a#,B,c#
G,A,B,c#,d#,E,F#

===========================================================
Scale Group 1 (major) with Scale Group 3 (harmonic minor)

1		C,D,E,F#,G,A,B		C lydian 

C,D,E,f,g#,A,B				A Harmonic Minor
E,F#,G,A,B,C,d#
B,c#,D,E,F#,G,a#
F#,g#,A,B,c#,D,f    
c#,d#,E,F#,g#,A,C
ab,bb,B,db,eb,E,G  (no f)  common:B,E,G  (037)
eb,f,Gb,ab,bb,B,D  (no db) common:Gb,B,D  (037)
bb,C,db,eb,f,Gb,A  (no ab) common:C,Gb,A  (036)
f,G,ab,bb,C,db,E   (no eb) common:G,C,E   (037)

===========================================================

Scale Group 1 (major) with Scale Group 4 (harmonic major)

1		C,D,E,F#,G,A,B		C lydian 

D,E,F#,G,A,bb,c#   			D Harmonic major
A,B,c#,D,E,f,g#
E,F#,g#,A,B,C,d#
B,c#,d#,E,F#,G,a#
F#,g#,a#,B,c#,D,f   (no Eb) common: F#,B,D (037)
db,eb,f,Gb,ab,A,C   (no Bb) common: Gb,A,C (036)
ab,bb,C,db,eb,E,G   (no F)  common: C,E,G (037)
eb,f,G,ab,bb,B,D    (no Db) common: G,B,D (037)
bb,C,D,eb,f,Gb,A
f,G,A,bb,C,db,E
C,D,E,f,G,ab,B
G,A,B,C,D,eb,F#




===========================================================

Scale Group 1 (major) with Scale Group 5 (whole tone)

1		C,D,E,F#,G,A,B		C lydian 

C,D,E,F#,G#,a#
c#,d#,f,g,A,B  no G#,Bb     none adequate

===========================================================

Scale Group 1 (major) with Scale Group 6 (hexatonic)

C,D,E,F#,G,A,B


C, c#, E, f, g#, A  		no D#,A#
G, g#, B, C, d#, E  		no A#  common: G,B,C,E (0158)
D, d#, F#, G, a#, B 		no F   common: D,F#,G,B (0158)
A, a#, c#, D, f, F#,  	no D#,G#

===========================================================

Scale Group 1 (major) with Scale Group 7 (octotonic)

C,D,E,F#,G,A,B

C,c#,d#,E,F#,G,A,bb 	no F,G#
f,F#,g#,A,B,C,D,eb	no C#,Bb
bb,B,c#,D,E,f,G,ab 	no D#   common:B,D,E,G (0358)

===========================================================

Scale Group 2 (melodic minor) with Scale Group 2 (melodic minor)

C,D,E,F#,G#,A,B      A melodic minor

g,A,B,c#,d#,E,F#     E melodic minor
D,E,F#,G#,a#,B,c#
A,B,C#,d#,f,F#,G#
E,F#,G#,a#,C,c#,d#
B,c#,d#,f,g,G#,a#  (all)    common: B,G#
F#,G#,a#,C,D,d#,f  no: C#,G common: C,D,F#,G# (0268)
c#,d#,f,g,A,a#,C   (all)    common: A,C
Ab,bb,C,D,E,f,g
eb,f,g,A,B,C,D
bb,C,D,E,F#,g,A
f,g,A,B,c#,D,E



===========================================================

Scale Group 2 (melodic minor) with Scale Group 3 (harmonic minor)

1) 		C,D,E,F#,G#,A,B		C lydian #5
with
3)	
C,D,E,f,G#,A,B				A Harmonic Minor

f,g,A,bb,c#,D,E	(no eb)	common: A,D,E (027)	D harmonic Minor
bb,C,D,eb,F#,g,A
eb,f,g,Ab,B,C,D
G#,bb,C,db,E,f,g (no eb) common:G#,C,E (048) F harmonic Minor
c#,d#,f,Gb,A,bb,C (no G) common:Gb,A,C (036) Bb harmonic Minor
F#,G#,a#,B,D,eb,f
B,c#,d#,E,g,G#,a#  (no F) common:B,E,G# (037) G# harmonic Minor
E,f#,G#,A,C,c#,d#
A,B,c#,D,f,F#,G#
D,E,F#,g,a#,B,c#
g,A,B,C,d#,e,F#  

===========================================================
Scale Group 2 (melodic minor) with Scale Group 4 (harmonic major)

1) 		C,D,E,F#,G#,A,B		C lydian #5/A melodic minor

D,E,F#,g,A,Bb,C#   			D Harmonic major
A,B,c#,D,E,f,G#
E,F#,G#,A,B,C,eb
B,c#,d#,E,F#,g,bb  no: F common:B,E,F#  (027) B harmonic major
F#,G#,a#,B,C#,D,f
c#,d#,f,F#,G#,A,C
Ab,bb,C,Db,eb,E,g
eb,f,g,Ab,bb,B,D  no: C# common:Ab,B,D (036) Eb harmonic major
bb,C,D,Eb,F,Gb,A
f,g,A,bb,C,db,E  no: Eb common: A,C,E (037)  F harmonic major
C,D,E,f,g,Ab,B
g,A,B,C,D,eb,F#


===========================================================
Scale Group 2 (melodic minor) with Scale Group 5 (whole tone)

1) 		C,D,E,F#,G#,A,B		C lydian #5/A melodic minor


C,D,E,F#,G#,a#

c#,d#,f,g,A,B   (no A#) common: A,B



===========================================================
Scale Group 2 (melodic minor) with Scale Group 6 (hexatonic)

1) 		C,D,E,F#,G#,A,B		C lydian #5/A melodic minor

C, c#, E, f, G#, A 
g,G#,B,C,d#,E
D,d#,F#,g,a#,B  
A,bb,c#,D,f,F#   no:Eb,G    none is adequate




===========================================================
Scale Group 2 (melodic minor) with Scale Group 7 (octotonic)

1) 		C,D,E,F#,G#,A,B		C lydian #5/A melodic minor


C,c#,d#,E,F#,g,A,bb 	 no: F  common:C,E,F#,A  (0258)
f,F#,G#,A,B,C,D,eb	 
bb,B,c#,D,E,f,g,Ab 	 no:Eb  common:B,D,E,Ab  (0258)  common to both: only E   



===========================================================
Scale Group 3 (harmonic minor)  with Scale Group 3 (harmonic minor)

C,D,E,F,G#,A,B				A Harmonic Minor
with:

E,f#,g,A,B,C,d#                                   E harm minor 
B,c#,D,E,f#,g,a#  no:d#  common: B,D,E (025)      B harm minor
c#,d#,E,f#,G#,A,C
Ab,bb,B,db,eb,E,g no:f#  common: Ab,B,E (037)     Ab harm minor 
eb,F,gb,Ab,bb,B,D
bb,C,db,eb,F,gb,A no:G   common: C,F,A  (037)     Bb harm minor
F,G,Ab,bb,C,db,E
C,D,eb,F,g,Ab,B
g,A,bb,C,D,eb,f#  no:C#  common: A,C,D  (025)     G harm minor/D Phryg. nat. 3
D,E,F,g,A,bb,c#
 





===========================================================
Scale Group 3 (harmonic minor) with Scale Group 4 (harmonic major)

C,D,E,F,G#,A,B				A harmonic Minor

D,E,f#,g,A,bb,c#   			D harmonic major
A,B,c#,D,E,F,G#
E,f#,G#,A,B,C,d#
B,c#,d#,E,f#,g,a#  (all) common:  B and E  B harmonic major
f#,G#,A#,B,c#,D,F
db,eb,F,gb,Ab,A,C  
Ab,bb,C,Db,eb,E,g
eb,F,g,Ab,bb,B,D
bb,C,D,Eb,F,gb,A
F,g,A,Bb,C,db,E
C,D,E,F,g,Ab,B
g,A,B,C,D,eb,f#


===========================================================
Scale Group 3 (harmonic minor) with Scale Group 5 (whole tone)

C,D,E,f,G#,A,B				A Harmonic Minor

C,D,E,f#,G#,a#       neither is adequate
c#,d#,F,g,A,B    


===========================================================
Scale Group 3 (harmonic minor) with Scale Group 6 (hexatonic)

C,D,E,f,G#,A,B				A Harmonic Minor


C, c#, E, F, G#, A 
g,G#,B,C,d#,E
D,d#,f#,g,a#,B           no:C#  common:D,B
A,bb,c#,D,F,f#



===========================================================
Scale Group 3 (harmonic minor) with Scale Group 7 (octotonic)

C,D,E,F,G#,A,B				A Harmonic Minor


C,c#,d#,E,f#,g,A,bb 	 (all) common:C,E,A (037)
F,f#,G#,A,B,C,D,eb	 
bb,B,c#,D,E,F,g,Ab 	 


===========================================================

Scale Group 4 (harmonic major) with Scale Group 4 (harmonic major)

D,E,F#,G,A,Bb,C#   			D Harmonic major


A,b,C#,D,E,F,g#
E,F#,g#,A,b,c,d#    no F     common:E,F#,A   (025)
F#,g#,A#,b,C#,D,f
Db,eb,f,Gb,ab,A,c   no B     common:Db,Gb,A  (037)
ab,Bb,c,Db,eb,E,G
eb,f,G,ab,Bb,b,D    no C     common:G,Bb,D   (037)
Bb,c,D,eb,f,Gb,A
f,G,A,Bb,c,Db,E
c,D,E,f,G,ab,b      no Eb    common:D,E,G    (025)
G,A,b,c,D,eb,F#




===========================================================
Scale Group 4 (harmonic major)   Scale Group 5 (whole tone)

D,E,F#,G,A,Bb,C#   			D Harmonic major

c,D,E,F#,g#,a#         none adequate  (common:D,E,F#  (024))
C#,d#,f,G,A,b                         (common:C#,G,A  (026))


===========================================================

Scale Group 4 (harmonic major) with Scale Group 6 (hexatonic)

D,E,F#,G,A,Bb,C#   			D Harmonic major


c, C#, E, f, g#, A 
G,g#,B,c,d#,E           none adequate
D,d#,F#,G,A#,b
A,Bb,C#,D,f,F#


===========================================================
Scale Group 4 (harmonic major) with Scale Group 7 (octotonic)

D,E,F#,G,A,Bb,C#   			D Harmonic major


c,C#,d#,E,F#,G,A,Bb 	 
f,F#,g#,A,B,c,D,eb	 (all) common:F#,A,B,D  (0358)
Bb,b,C#,D,E,f,G,ab 	 



===========================================================
Scale Group 5 (whole tone)  Scale Group 6 (hexatonic)

C,D,E,F#,G#,A#


C, c#, E, f, G#, a        none adequate
g,G#,b,C,d#,E
D,d#,F#,g,A#,b
a,Bb,c#,D,f,F#


===========================================================
Scale Group 5 (whole tone)  Scale Group 7 (octotonic)

C,D,E,F#,G#,a#

 
C,c#,d#,E,F#,g,a,Bb 	   no:f,b             none adequate
f,F#,G#,a,b,C,D,eb       no:g,c#	 
Bb,b,c#,D,E,f,g,Ab 	   no:eb,a


===========================================================
Scale Group 6 (hexatonic) with Scale Group 6 (hexatonic)

C, C#, E, F, G#, A 

 
G,G#,B,C,D#,E
D,D#,F#,G,A#,B   includes all, disjunct, no common tones
A,Bb,C#,D,F,F#


===========================================================
Scale Group 6 (hexatonic)  Scale Group 7 (octotonic)

C, C#, E, F, G#, A 


C,C#,d#,E,f#,g,A,bb 	 common:C,C#,E,A
F,f#,g#,A,b,C,D,eb	 common:F,A,C,D        no G,Bb
bb,b,C#,d,E,F,g,Ab     common:C#,E,F,G# 	 

===========================================================
Scale Group 7 (octotonic)

C,c#,d#,E,F#,G,A,bb 	 
f,F#,g#,A,B,C,D,eb	 
bb,B,c#,D,E,f,G,ab


There are a handful of approaches I want to add to this, including the use of the Microtonal Scales program.

I'm also thinking of a mod-60 study, to see if thinking of harmony as mod60 (5 octaves) rather than mod12 has any advantages.
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Old 16th April 2018, 12:50 PM   #250
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found a mistake. should be:

================================================== =========
Scale Group 6 (hexatonic) Scale Group 7 (octotonic)

C, C#, E, F, G#, A


C,C#,d#,E,f#,g,A,bb common:C,C#,E,A
F,f#,G#,A,b,C,d,eb common:F,G#,A,C no G,Bb
bb,b,C#,d,E,F,g,Ab common:C#,E,F,G#
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Old 17th April 2018, 05:21 AM   #251
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This scale stuff is more useful if you've spent a lot of time improvising with these scales. Then, a term like "Lydian b7" has a very vivid imaginary sound and associations. Roger Sessions of all people made a similar point.

Otherwise, if these names and shapes have no prior familiarity, there's no benefit to joining them up this way. I wouldn't recommend these studies to anyone except someone who has practiced scales, with what amounts to an informed jazz or mathematical approach.




It seems to me that the first scale study I posted above could be more useful from a tonal musician's pov. The way to do that would be to list, in some sensible order, all the 3 and and 2-note common-tone situations with disjunct scales in such a way that the common-tones form a progressive pattern across the tonal grid.

That pattern is 013, 014, 015, 016, 017, 018, 019, 01-10, then 023, 024, 025, etc.

Then, as a player, you can learn a situation. Such as, tonal center of C. Are there two max disjunct scales having in common only C,Eb,Bb? (1, minor 3, flat 7) (0,3,10), and together omitting only the pitch B? What are they -- quickly!

The first study would be all the situations with [common tone "Do", or scale-degree 1, or 0, or tonic-note] and 1 or 2 or 3 other common pitches. Always filling in either the complete 12 tones or leaving out no more than 1 of them.

The second would drop the requirement that 1 note always be 0 (or scale-degree 1.) The second scale might include 0 or not.

Last edited by calebprime; 17th April 2018 at 05:26 AM.
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Old 17th April 2018, 08:40 AM   #252
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Originally Posted by calebprime View Post
T...
That pattern is 013, 014, 015, 016, 017, 018, 019, 01-10, then 023, 024, 025, etc.

...
actually it's more restricted if you want only the situations where 1 pitch is excluded by both scales. You can't have any semitones in the the 3 pitches nor 2 adjacent seconds.

Here I think is the entire sequence. Next I'll post the study.

C,D,F
C,D,F#
C,D,G
C,D,Ab
C,D,A,


C,Eb,F
C,Eb,F#
C,Eb,G
C,Eb,Ab
C,Eb,A
C,Eb,Bb

C,E,F#
C,E,G
C,E,Ab
C,E,A
C,E,Bb


C,F,G
C,F,Ab
C,F,A
C,F,Bb

C,F#,G#
C,F#,A
C,F#,Bb

C,G,A
C,G,Bb

And perhaps surprisingly, every other 3-note combination with C is excluded. So these, in this sequence, are the common-tone situations we want to find the most disjunct scales for.

With the help of Microtonal Scales plus a bit of reductive theory, it's easily done.

Last edited by calebprime; 17th April 2018 at 08:42 AM.
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Old 21st April 2018, 11:51 AM   #253
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That took a whole lot longer than I thought. Worth doing.

Microtonal Scales helped but didn't automate the process.

Here's a rough first version with mistakes -- probably some duplicates and omissions. Just for backup and getting the basic idea out there.

Fixed version tomorrow.

The basic idea is that you pick a 3-note harmony in relation to your tonal center. Here it is given as C, but you transpose.

Then the pairs of scales are the most disjunct and complete (most complementary) scales given those 3 common tones, of which 1 tone is your tonal center.

The idea might be to get fluent to the point that you can chain transposed row-pairs to make larger patterns that give you tones outside of your original "Do."


Code:
==============================================================================

common: only C,D,F  omitted: only C#

C,D,E,F,G,A,B   c major --  scale group 1  
with
C,D,Eb,F,Gb,Ab,Bb C Aeolian b5 -- scale group 2


Solution expressed as pseudo 12-tone row or disjunct unordered sets:
([E,G,A,B,][C,D,F] [Eb,Gb,Ab,Bb] [Db])

================================

common: only C,D,F  omitted: only C#


C,D,E,F,G,Ab,Bb C Mixolydian b6 -- scale group 2
with
C,D,Eb,F,Gb,A,B  D octotonic subset  "C melodic minor b5"

pseudo 12-tone row or disjunct unordered sets:
([E,G,Ab,Bb] [C,D,F] [Eb,Gb,A,B] [Db])
pitches within brackets can be any order, but overall bracket ordering is fixed
================================

common: only C,D,F  omitted: only C#


C,D,E,F,G,Ab,B C Harmonic Major  -- scale group 4
with
C,D,Eb,F,Gb,A,Bb Bb Harmonic Major  -- scale group 4
"C dorian b5"

pseudo 12-tone row or disjunct unordered sets:
([E,G,Ab,B]) [C,D,F] [Eb,Gb,A,Bb] [Db])
================================
================================
common: only C,D,F#  omitted: only C# 

C,D,E,F#,G,A,B   			c lydian --  scale group 1
with
C,D,Eb,F,Gb,Ab,Bb 			Ab lydian b7 -- scale group 2
"C Aeolian b5"

pseudo 12-tone row or disjunct unordered sets:

================================
common: only C,D,F#  omitted: only C# 

C,D,E,F#,G,A,Bb   			C lydian b7
with
C,D,Eb,F,Gb,Ab,B  			D oct subset
"C harmonic minor b5"

pseudo 12-tone row or disjunct unordered sets:


================================
common: only D,F#   has all 12 tones, doesn't preserve  C

C,D,Eb,F,Gb,Ab,A  			D oct subset
with
C#,D,E,F#,G,A#,B  			B harmonic minor

pseudo 12-tone row or disjunct unordered sets:



================================
================================
common: C,D,G   omitted: only C#


group 1: Aeolian to Lydian


Aeolian  with Lydian
C,D,Eb,F,G,Ab,Bb  with C,D,E,F#,G,A,B  or losing C:  C#,D,E,F#,G,A,B (all 12)

pseudo 12-tone row or disjunct unordered sets:

([Eb,F,Ab,Bb]   [C,D,G]  [E,F#,A,B ]   [C#])

================================
bb,C,D,E,F#,G,A  -    plus 		C,D,Eb,F,G,Ab,B     C  harmonic minor
C Lydian b7			  plus			C harmonic minor

pseudo 12-tone row or disjunct unordered sets:


================================
ab,bb,C,D,E,f,G - plus C,D,Eb,F#,G,A,B harmonic major
C Mixo b6				  plus			C melodic minor #4


pseudo 12-tone row or disjunct unordered sets:

================================
================================
================================
common: C,D,Ab    enharmonic treatment of Ab

C Aeolian plus                C Lydian #5
C,D,Eb,F,G,Ab,Bb		  plus		C,D,E,F#,G#,A,B       omits only C#

pseudo 12-tone row or disjunct unordered sets:



================================


C,D,E,F,G,Ab,Bb       plus		C,D,Eb,F#,G#,A,B  oct subset    omits only C#
C mixo b6				  plus		C Lydian #5 b3


pseudo 12-tone row or disjunct unordered sets:


================================ 
================================ 
================================ 

common: C,D,A   typically no c#






Bb,C,D,E,F,G,A  	D Aeol.			plus 	 C,D,Eb,F#,G#,A,B  D oct subset

pseudo 12-tone row or disjunct unordered sets:

========
C,D,E,F#,G#,A,B  A melodic minor  plus 	 C,D,Eb,F,G,A,Bb   C dorian	
D lydian b7	/  C Lyd #5			 plus	 D Phryg./ C Dorian

pseudo 12-tone row or disjunct unordered sets:		
======== 
bb,C,D,E,F#,G,A  D mixo b6		    plus	 C,D,Eb,F,Ab,A,B   D oct subset

pseudo 12-tone row or disjunct unordered sets:

================================

C,D,E,f,g#,A,B					plus     	
Harmonic Minor  (0 2 3 6 7 9 10)
A Harmonic Minor 					 	   	
G,A,Bb,C,D,Eb,F#  G Harmonic Minor
	 

pseudo 12-tone row or disjunct unordered sets:


================================ 
================================ 
================================ 

common:  C,Eb,F (typically no E, and always keeping C)
============

common:  C,Eb,F 


locrian with melodic minor:  
0,1,3,5,6,8,10 with (0 2 3 5 7 9 11)

pseudo 12-tone row or disjunct unordered sets:

========
phrygian with (0 2 3 5 6 9 11) octotonic subset    
0,1,3,5,7,8,10 with 0,2,3,5,6,9,11 

pseudo 12-tone row or disjunct unordered sets:

========

============
========

common:  C,Eb,F#


C,D,Eb,F,F#,G#,B   oct sub with
C,Db,Eb,E,F#,G,A,Bb oct complete

pseudo 12-tone row or disjunct unordered sets:

========
Ab7 #11 (lydian b7) Gb,ab,bb,C,D,eb,f    
with  E har minor C,Eb,E,F#,G,A,B      no C#
C Aeol b5 with C Lydian #2

pseudo 12-tone row or disjunct unordered sets:


========
F#,g#,a#,C,c#,d#,f  
with E harmonic minor C,Eb,E,F#,G,A,B       no D
C locrian with c lydian #2

pseudo 12-tone row or disjunct unordered sets:

========
E,F#,g#,a#,C,c#,d#   
with oct subset C,D,Eb,F,Gb,A,B      no G
C Locrian b4 (Altered) with C Melodic Minor b5

pseudo 12-tone row or disjunct unordered sets:

========
========
G,A,B,C,D,eb,F# 
with C,Db,Eb,F,Gb,Ab,bb C locrian    no E

pseudo 12-tone row or disjunct unordered sets:


========
db,eb,f,Gb,ab,A,C    
without C in second scale:   (2 3 6 7 10 11)   augmented 1-3    no E

pseudo 12-tone row or disjunct unordered sets:



========
========
================================ 
================================ 

common:  C,Eb,G
 


db,eb,f,G,ab,bb,C  
with C,D,Eb,F#,G,A,B Harmonic Major  no E
C Phrygian with C melodic minor #4

pseudo 12-tone row or disjunct unordered sets:


========
ab,bb,C,D,eb,f,G 
with 0 3 4 6 7 9 11  C,Eb,E,F#,G,A,B  Harmonic Minor no C#
C Aeolian with C Lydian #2

pseudo 12-tone row or disjunct unordered sets:


========
eb,f,G,A,B,C,D 
with 0 1 3 4 7 8 10 harmonic major no F#   
C melodic minor with C Phryg b4
========
E,F#,G,A,B,C,d#   
with C,D,Eb,F,G,Ab,Bb 
C Lydian #2 with C Aeol.  no C#
========
C,D,eb,f,G,ab,B   
with 0 1 3 4 6 7 9 10  all   with only C,Eb,G  complete  
C harmonic minor with C octotonic

[D,F,Ab,B]  [C,Eb,G] [Db,E,F#,A,Bb]    
nb, the d,f,ab,b is not so great, the 0369


========
 

ab,bb,C,db,eb,E,G   
with either no F, (0 2 3 6 7 9 11)  or no F#  (0 2 3 5 7 9 11)  
========

G,A,B,C,D,eb,F#    
with no F  (0 1 3 4 7 8 10)   or no E  (0 1 3 5 7 8 10)  


========
================================ 
================================ 

common: C,Eb,Ab


db,eb,f,G,ab,bb,C    
with (0 2 3 6 8 9 11) 0ct- (no E)  
and (0 3 4 6 8 9 11) Harmonic Major  (no D)
========
ab,bb,C,D,eb,f,G    
with (0 1 3 4 6 8 9)  har minor (no B)  
and   (0 3 4 6 8 9 11) har major (no C#)
========
E,F#,g#,a#,C,c#,d#    
with (0 2 3 5 7 8 11) Harmonic Minor (no D)  
and Sadvid   (0 2 3 5 8 9 11)  (no G)
========
ab,bb,C,db,eb,E,G         
with (0 2 3 5 6 8 9 11)  Oct          all


================================ 
================================ 
================================ 


common: C,Eb,A


d#,f,G,A,a#,C,D    with (0 1 3 4 6 8 9) or  (0 3 4 6 8 9 11)

C Dorian with either
     C,Db,Eb,E,F#,G#,A         C locrian b4 bb7    no B     
or   C,Eb,E,F#,G#,A,B          C Lydian #2 #5      no C#
========
eb,f,G,A,B,C,D     with (0 1 3 4 6 9 10) or (0 1 3 4 6 8 9)

C melodic minor with either

C,Db,Eb,E,F#,A,Bb  C octotonic with no G (5th)
or
C,Db,Eb,E,F#,G#,A  C Locrian b4 bb7
========

db,eb,f,G,A,bb,C        (0 2 3 6 8 9 11)  or  (0 3 4 6 8 9 11) 


C Dorian b2   with C,D,Eb,F#,G#,A,B  C diminished with no F
or
C,D#,E,F#,G#,A,B  C Lydian #5 #2  (same as E harmonic major)
========


================================ 
================================ 
================================ 




common: C,Eb,Bb

ab,bb,C,D,eb,f,G 
with Sadvid  (0 1 3 4 6 9 10) C,Db,Eb,E,F#,A,Bb C oct- no fifth, no G.
========

d#,f,G,A,a#,C,D  C Dorian
with (0 1 3 4 6 8 10) C Altered
========
 
Gb,ab,bb,C,D,eb,f  C Aeol b5 
with C,Db,Eb,E,G,A,Bb    C oct- no F#
========
 

================================ 
================================ 
================================ 

common: C,E,F#

C,D,E,F#,G,A,B  with C,Db,Eb,E,Gb,Ab,Bb  Altered


================================ 
================================ 
================================ 

common: C,E,G

 
f,G,A,B,C,D,E,   (0 1 3 4 6 7 10)   and (0 1 3 4 7 8 10)
========
c,d,e,f#,g,a,b    (0 1 4 5 7 8 10)  and (0 1 3 4 7 8 10)
========

ab,bb,C,D,E,f,G  with (0 3 4 6 7 9 11) and sadvid (0 1 3 4 6 7 9)
========
E,F#,G,A,B,C,d#  (0 1 4 5 7 8 10)    (0 2 4 5 7 8 10)
========


========
C,D,E,f,G,ab,B    with C octotonic


================================ 
================================ 
================================ 

common: C,E,Ab


ab,bb,C,D,E,f,G   with    (0 1 3 4 6 8 9)  or  (0 3 4 6 8 9 11)

E,F#,g#,a#,C,c#,d#    (0 2 4 5 8 9 11)   (0 2 4 5 7 8 11)

c,d,e,f#,g#,a,b  (0 1 4 5 7 8 10)   (0 1 3 4 7 8 10) 

C,D,E,f,g#,A,B        (0 1 3 4 6 8 10)   (0 1 3 4 7 8 10) 

 

================================ 
================================ 
================================ 

common: C,E,A

a#,C,D,E,f,G,A   (0 1 3 4 6 8 9)   (0 3 4 6 8 9 11)
========
f,G,A,B,C,D,E,   (0 1 3 4 6 9 10)  (0 1 3 4 6 8 9)
======== 
c,d,e,f#,g#,a,b  (0 1 3 4 7 9 10) (0 1 4 5 7 9 10)
========
C,D,E,f,g#,A,B     (0 1 3 4 6 7 9 10)   oct   all
========
c#,d#,E,F#,g#,A,C  (0 2 4 5 7 9 10)  (0 2 4 5 7 9 11)
========
E,F#,g#,A,B,C,d#   (0 1 4 5 7 9 10)  (0 2 4 5 7 9 10)
========
f,G,A,bb,C,db,E     (0 2 4 6 8 9 11) (0 3 4 6 8 9 11)


================================ 
================================ 
================================ 

common: C,E,Bb

a#,C,D,E,f,G,A     with (0 1 3 4 6 8 10) 
 
ab,bb,C,D,E,f,G         (0 1 3 4 6 9 10) 
E,F#,g#,a#,C,c#,d#      (0 2 4 5 7 9 10) 
 

================================ 
================================ 
================================ 


common: C,F,G


db,eb,f,G,ab,bb,C   with  (0 2 4 5 7 9 11)
   
eb,f,G,A,B,C,D      (0 1 4 5 7 8 10)
 
db,eb,f,G,A,bb,C      (0 2 4 5 7 8 11) 

C,D,eb,f,G,ab,B       (0 1 4 5 7 9 10) 
 
 
 
================================ 
================================ 
================================ 

common: C,F,Ab


F#,g#,a#,C,c#,d#,f   with  (0 2 4 5 8 9 11)  or   (0 2 4 5 7 8 11) 
db,eb,f,G,ab,bb,C          (0 2 5 6 8 9 11)       (0 2 4 5 8 9 11)
 
ab,bb,C,D,E,f,G            (0 1 3 5 6 8 9)        (0 3 5 6 8 9 11)
 
C,D,E,f,g#,A,B             (0 1 3 5 6 8 10)
f,G,ab,bb,C,db,E           (0 2 3 5 6 8 9 11) 
db,eb,f,Gb,ab,A,C           (0 2 4 5 7 8 10)       (0 2 4 5 7 8 11) 
C,D,E,f,G,ab,B              (0 1 3 5 6 8 9)       (0 1 3 5 6 8 10) 



================================ 
================================ 
================================ 

common: C,F,A

f,G,A,B,C,D,E,       (0 1 3 5 6 9 10) 
a#,C,D,E,F,G,A       (0 3 5 6 8 9 11)     (0 1 3 5 6 8 9)         
db,eb,f,G,A,bb,C     (0 2 5 6 8 9 11)     (0 2 4 5 8 9 11)
 

f,G,A,bb,C,db,E      (0 2 3 5 6 8 9 11)   all



================================ 
================================ 
================================ 

common: C,F,Bb


F#,g#,a#,C,c#,d#,f          (0 2 4 5 7 9 10)    
a#,C,D,E,F,G,A			     (0 1 3 5 6 8 10)
ab,bb,C,D,E,f,G             (0 1 3 5 6 9 10)
    
Gb,ab,bb,C,D,eb,f           (0 1 4 5 7 9 10)
bb,C,db,eb,f,Gb,A           (0 2 4 5 7 8 10)  
f,G,ab,bb,C,db,E            (0 2 3 5 6 9 10) 
bb,C,D,eb,f,Gb,A            (0 1 4 5 7 8 10)
f,G,A,bb,C,db,E             (0 2 3 5 6 8 10
 


================================ 
================================ 
================================ 


common: C,F#,G#


F#,g#,a#,C,c#,d#,f    with (0 2 4 6 8 9 11) 
E,F#,g#,a#,C,c#,d#         (0 2 5 6 8 9 11)



================================ 
================================ 
================================ 

common: C,F#,A

C,D,E,F#,G,A,B    	  (0 1 3 5 6 9 10)   or  (0 1 3 5 6 8 9)
bb,C,D,E,F#,G,A       (0 1 3 5 6 8 9) 
C,D,E,F#,G,A,Bb       (0 3 5 6 8 9 11)       (0 1 3 5 6 8 9)
bb,C,db,eb,f,Gb,A     (0 2 4 6 8 9 11)       (0 2 4 6 7 9 11) 
  



================================ 
================================ 
================================ 


common: C,F#,Bb


F#,g#,a#,C,c#,d#,f         (0 2 4 6 7 9 10)
bb,C,D,E,F#,G,A            (0 1 3 5 6 8 10) 
c,d,e,f#,g,a,bb            (0 1 3 5 6 8 10)  
Gb,ab,bb,C,D,eb,f          (0 1 4 6 7 9 10)
F#,g#,a#,B,c#,D,f          (0 3 4 6 7 9 10) 




================================ 
================================ 
================================ 


common: C,G,A

c,d,e,f#,g,a,b        (0 1 3 5 7 9 10) 

f,g,a,b,c,d,e         (0 1 3 6 7 9 10)  
 
eb,f,G,A,B,C,D        (0 1 4 6 7 9 10) 

db,eb,f,G,A,bb,C      (0 2 4 6 7 9 11)

f,G,A,bb,C,db,E       (0 2 3 6 7 9 11)

G,A,B,C,D,eb,F#       (0 1 4 5 7 9 10) 




================================ 
================================ 
================================ 


common: C,G,Bb


db,eb,f,G,ab,bb,C         (0 2 4 6 7 9 10)

ab,bb,C,D,eb,f,G          (0 1 4 6 7 9 10)  

bb,C,D,E,F#,G,A           (0 1 3 5 7 8 10)

ab,bb,C,D,E,f,G           (0 1 3 6 7 9 10)

f,G,ab,bb,C,db,E          (0 2 3 6 7 9 10)

 


================================ 
================================ 
================================

Last edited by calebprime; 21st April 2018 at 12:02 PM.
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Old 25th April 2018, 08:14 AM   #254
calebprime
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Of course it took 5 times longer than I thought.

Here's Version 0.1 -- probably still has major mistakes and omissions, and the formatting sucks, but it should be more or less consistent and correct all the way from beginning to end.

Soon to begin practicing this, then I'll have a better idea how it all works.

Code:
Sequence of 3-note common-tones:
C,D,F 		C,D,F#	 	C,D,G		C,D,Ab		C,D,A,

C,Eb,F		C,Eb,F#	C,Eb,G		C,Eb,Ab	C,Eb,A    C,Eb,Bb

C,E,F#		C,E,G		C,E,Ab		C,E,A		C,E,Bb

C,F,G		C,F,Ab		C,F,A		C,F,Bb

C,F#,G#	C,F#,A		C,F#,Bb

C,G,A		C,G,Bb


disjunct unordered sets:
pitches within brackets can be any order, but overall bracket ordering is fixed

==============================================================================
common: C,D,F   

[C Major]               [C Aeolian b5]
C,D,E,F,G,A,B     with  C,D,Eb,F,Gb,Ab,Bb            no C#
 
disjunct unordered sets:

([E,G,A,B,][C,D,F] [Eb,Gb,Ab,Bb] [Db])

================================


[C Mixolydian b6]       [C Melodic Minor b5]   
C,D,E,F,G,Ab,Bb   with  C,D,Eb,F,Gb,A,B              no C#   

disjunct unordered sets:

([E,G,Ab,Bb] [C,D,F] [Eb,Gb,A,B] [Db])

================================
  

[C Harmonic Major]       [C Dorian b5]
C,D,E,F,G,Ab,B   with    C,D,Eb,F,Gb,A,Bb            no C#

disjunct unordered sets:

([E,G,Ab,B]) [C,D,F] [Eb,Gb,A,Bb] [Db])

================================
================================
common: C,D,F#  

[C Lydian]               [C Aeolian b5]
C,D,E,F#,G,A,B   with    C,D,Eb,F,Gb,Ab,Bb            no C# 						
disjunct unordered sets:

([E,G,A,B]  [C,D,F#]  [Eb,F,Ab,Bb]  [C#])

===============================
  
[C Lydian b7]       	  [C Dim- subset, no A]
C,D,E,F#,G,A,Bb   with	  C,D,Eb,F,Gb,Ab,B             no C#

disjunct unordered sets:

([E,G,A,Bb]   [C,D,F#]   [Eb,F,Ab,B]  [C#])

================================
common: only D,F#    doesn't preserve  C


[C Dim subset]             [B Harmonic Minor]
C,D,Eb,F,Gb,Ab,A  	with   C#,D,E,F#,G,A#,B            all tones  		     
disjunct unordered sets:

([C,Eb,F,Ab,A]   [D,F#]    [C#,E,G,A#,B])

================================
================================
common: C,D,G    

[C Aeolian]           with 		[C Lydian]
C,D,Eb,F,G,Ab,Bb    		    C,D,E,F#,G,A,B            no C#

disjunct unordered sets:

([Eb,F,Ab,Bb]   [C,D,G]  [E,F#,A,B]   [C#])

-----------------

with no  C:  C#,D,E,F#,G,A,B (all 12)   [D major]        all tones

disjunct unordered sets:

([Eb,F,Ab,Bb,C]   [D,G]  [Db,E,F#,A,B] )

================================
[C Lydian b7]			       [C harmonic minor]
Bb,C,D,E,F#,G,A   with 		 C,D,Eb,F,G,Ab,B               no C#


disjunct unordered sets:

([Bb,E,F#,A]    [C,D,G]   [Eb,F,Ab,B]  [C#])

================================

[C Mixo b6]				  	 [C Mel min #4]
Ab,Bb,C,D,E,F,G   with      C,D,Eb,F#,G,A,B              no C#
 

disjunct unordered sets:

([Ab,Bb,E,F]  [C,D,G]   [Eb,F#,A,B]  [C#])

================================
================================
================================
common: C,D,Ab    


[C Aeolian]           with    [C Lydian #5]
C,D,Eb,F,G,Ab,Bb		  plus		C,D,E,F#,G#,A,B              no C#


disjunct unordered sets:

([Eb,F,G,Bb]  [C,D,Ab]  [E,F#,A,B]  [C#])

================================

[C mixo b6]                   [C Dim- subset no F]
C,D,E,F,G,Ab,Bb       plus		C,D,Eb,F#,G#,A,B              no C#
					


disjunct unordered sets:

([E,F,G,Bb]    [C,D,Ab]    [Eb,F#,A,B]   [C#])

================================ 
================================ 
================================ 

common: C,D,A   



[C Mixo]				with    [C dim with no F]
Bb,C,D,E,F,G,A  	     	     C,D,Eb,F#,G#,A,B                 no C#

disjunct unordered sets:

([Bb,E,F,G]	[C,D,A]   [Eb,F#,G#,B]  [C#])

========
      	
[C Lyd #5]			with  		[C Dorian]
C,D,E,F#,G#,A,B    		     	 C,D,Eb,F,G,A,Bb                no C#

disjunct unordered sets:

([E,F#,G#,B] [C,D,A]   [Eb,F,G,Bb]  [C#])
		
======== 
[C Lydian b7]         with     [C dim- subset no F#]
Bb,C,D,E,F#,G,A          	     C,D,Eb,F,Ab,A,B                no C#

disjunct unordered sets:

([Bb,E,F#,G]  [C,D,A]  [Eb,F,Ab,B]  [C#])

========= 
[C Harmonic Major]      with   	[C Dorian #4]
C,D,E,F,G#,A,B	                 G,A,Bb,C,D,Eb,F#             no C#	
					 	   	
disjunct unordered sets:

([E,F,G#,B]  [C,D,A]  [G,Bb,Eb,F#]  [C#])


================================ 
================================ 
================================ 

common:  C,Eb,F  


[C Locrian]      with     [C Melodic Minor]  
0,1,3,5,6,8,10            (0 2 3 5 7 9 11)                     no E  

disjunct unordered sets:

([Db,Gb,Ab,Bb]  [C,Eb,F]  [D,Eb,G,A,B]  [E])

========
[C phrygian]     with     [C Dim- no G#]    
0,1,3,5,7,8,10   with     0,2,3,5,6,9,11                        no E  

disjunct unordered sets:

([Db,G,Ab,Bb]  [C,Eb,F] [D,Gb,A,B]  [E])

========

============
========

common:  C,Eb,F#

[C dim- no A]          with           [C octotonic]  
C,D,Eb,F,F#,G#,B                      C,Db,Eb,E,F#,G,A,Bb    complete
 

disjunct unordered sets:

([D,F,G#,B]   [C,Eb,F#]   [Db,E,G,A,Bb])

========
     
 
[C Aeol b5]            with           [C Lydian #2]
C,D,Eb,F,Gb,Ab,Bb                     C,D#,E,F#,G,A,B           no C#

disjunct unordered sets:

([D,F,Ab,Bb]  [C,Eb,Gb]   [E,G,A,B]   [C#])

========
[C Locrian]             with            [C Lydian #2]
Gb,Ab,Bb,C,Db,Eb,F                      C,Eb,E,F#,G,A,B          no D
        
disjunct unordered sets:

([Ab,Bb,Db,F]   [C,Eb,Gb]  [E,G,A,B]   [D])

========
[C Locrian b4]          with             [C Dim-  no Ab]
E,Gb,Ab,Bb,C,Db,Eb                       C,D,Eb,F,Gb,A,B          no G
               

disjunct unordered sets:

([E,Ab,Bb,Db]  [C,Eb,Gb]   [D,F,A,B]   [G])

========
========
[C Lydian b3]              with          [C Locrian]
G,A,B,C,D,Eb,F#                          C,Db,Eb,F,Gb,Ab,Bb        no E
 
disjunct unordered sets:

([G,A,B,D]    [C,Eb,F#]   [Db,F,Ab,Bb]  [E])

========
Eb F# common only:

[C Locrian bb7]           with         [D augmented 1-3]
Db,Eb,F,Gb,Ab,A,C    	                D,Eb,F#,G,Bb,B
                                       no C                         no E

disjunct unordered sets:

([Db,F,Ab,A,C]  [Eb,F#]  [D,G,Bb,B] [E])

========
========
================================ 

common:  C,Eb,G
 
[C Phrygian]               with                [C melodic minor #4]
C,Db,Eb,F,G,Ab,Bb          with                C,D,Eb,F#,G,A,B       no E
  
disjunct unordered sets:

([Db,F,Ab,Bb]    [C,Eb,G ]      [D,F#,A,B]     [E])

========
[C Aeolian]                 with               [C Lydian #2]
C,D,Eb,F,G,Ab,Bb                               C,D#,E,F#,G,A,B       no C#
 
disjunct unordered sets:

([D,F,Ab,Bb]   [C,Eb,G]   [E,F#,A,B]   [C#])

========
[C Melodic Minor]           with               [C Phryg b4]
Eb,F,G,A,B,C,D                                 C,Db,Eb,E,G,Ab,Bb      no F#
    
disjunct unordered sets:

([F,A,B,D]    [C,Eb,G]    [Db,E,Ab,Bb]  [F#])

========
 
[C Phryg b4]               with          [C Lydian b3]
Ab,Bb,C,Db,Eb,E,G          with          C,D,Eb,F#,G,A,B               no F

disjunct unordered sets:

([Ab,Bb,Db,E]   [C,Eb,G]  [D,F#,A,B]  [F])

========
[C harmonic minor ]        with              [C octotonic]
C,D,Eb,F,G,Ab,B                              C,Db,Eb,E,F#,G,A,Bb       complete 

disjunct unordered sets:

[D,F,Ab,B]  [C,Eb,G] [Db,E,F#,A,Bb]    
nb. the d,f,ab,b is not so great, the 0369


========
================================ 
================================ 

common: C,Eb,Ab

[C Phrygian] 				  with          [C dim- no F]
C,Db,Eb,F,G,Ab,Bb,                     (C,D,Eb,F#,G#,A,B)            no E

disjunct unordered sets:     

([Db,F,G,Bb]  [C,Eb,Ab]   [D,F#,A,B]  [E]) 
 ========
                                          [C Lydian #2 #5]
                        or with            (C,D#,E,F#,G#,A,B)       (no D)

disjunct unordered sets:

([Db,F,G,Bb]  [C,Eb,Ab]   [E,F#,A,B]   [D])

========
[C Aeol ]             with                 [C Locr. b4 bb7]
C,D,Eb,F,G Ab,Bb,     with                 C,Db,Eb,E,Gb,Ab,A           (no B)
 
disjunct unordered sets:

([D,F,G,Bb]   [C,Eb,Ab]   [Db,E,F#,A]    [b])
========
 
                  or with                [C Lydian #5 #2]             (no C#)
                                         C,D#,E,F#,G#,A,B

disjunct unordered sets:

([D,F,G,Bb]   [C,Eb,Ab]   [B,E,F#,A]     [C#])

========

[C Locrian b4]  (Altered) with           [C Harmonic Minor ]  
C,Db,Eb,E,Gb,Ab,Bb,                      C,D,Eb,F,G,Ab,B             (no A)

disjunct unordered sets:

([Db,E,Gb,Bb]   [C,Eb,Ab]     [D,F,G,B]  [A])
======== 
                  or with                [Sadvid]                     (no G)
                                         C,D,Eb,F,Ab,A,B
disjunct unordered sets:

([Db,E,Gb,Bb]    [C,Eb,Ab]     [D,F,A,B]  [G])


========
[C Phryg. b4]                with       [C diminished ]                all
Ab,Bb,C,Db,Eb,E,G                       C,D,Eb,F,Gb,Ab,A,B     
                                       

disjunct unordered sets:

([Bb,Db,E,G]    [C,Eb,Ab]    [D,F,Gb,A,B])   
================================ 
================================ 
================================ 


common: C,Eb,A

[C Dorian]                       [C Locrian b4 bb7 ]                      no B
Eb,F,G,A,Bb,C,D    with          C,Db,Eb,E,Gb,Ab,A  

disjunct unordered sets:  

([F,G Bb,D]   [C,Eb,A]    [Db,E,Gb,Ab]   [b])
  

-------       
                   or with       [C Lydian #2 #5 ]              
                                 C,D#,E,F#,G#,A,B                         no C#

disjunct unordered sets:

([F,G,Bb,D  [C,Eb,A] [E,F#,G#,B]  [C#])
  
========
[C melodic minor]                [C octotonic  with no G (5th)]
Eb,F,G,A,B,C,D     with          C,Db,Eb,E,F#,A,Bb                        no G#

disjunct unordered sets:

([F,G,B,D]    [C,Eb,A]   [Db,E,F#,Bb]  [Ab])

========

                                 [C Locrian b4 bb7]
                or with          C,Db,Eb,E,Gb,Ab,A                        no Bb


disjunct unordered sets:

([F,G,B,D]    [C,Eb,A]   [Db,E,F#,A]  [Bb])                               

========
[C Dorian b2]      with         [C diminished with no F]                  no E
Db,Eb,F,G,A,Bb,C                  C,D,Eb,F#,G#,A,B  

disjunct unordered sets: 

([Db,F,G,Bb]  [C,Eb,A]  [D,F#,G#,B]  [E])

   
                  or with        [C Lydian #5 #2]            
                                 C,D#,E,F#,G#,A,B

disjunct unordered sets:

([Db,F,G,Bb]  [C,Eb,A]  [E,F#,G#,B]   [D])                               no  D
================================ 
================================ 
================================ 


common: C,Eb,Bb



[C Aeol ]          with             [Sadvid]  or [C oct- no fifth], no G         No B
Ab,Bb,C,D,Eb,F,G                    C,Db,Eb,E,F#,A,Bb 

disjunct unordered sets:

([Ab,D,F,G]    [C,Eb,Bb]  [Db,E,F#,A]   [b])
   
========
[C Dorian]         with              [C Altered]                                 No B
Eb,F,G,A,Bb,C,D                      C,Db,Eb,E,Gb,Ab,Bb

disjunct unordered sets:

([F,G,A,D] [C,Eb,Bb] [Db,E,F#,Ab] [b])

========
[C Aeol b5]                        [C oct- no F#]                                No B
Gb,Ab,Bb,C,D,Eb,F   with           C,Db,Eb,E,G,A,Bb

disjunct unordered sets:

([Gb,Ab,D,F]   [C,Eb,Bb]  [Db,E,G,A]    [b])
    
========
 

================================ 
================================ 
================================ 

common: C,E,F#


[C Lydian]        with                 [C Altered]                                No F
C,D,E,F#,G,A,B    with                 C,Db,Eb,E,Gb,Ab,Bb  

disjunct unordered sets:
([D,G,A,B]  [C,E,F#] [Db,Eb,Ab,Bb]    [F])


================================ 
================================ 
================================ 

common: C,E,G

[C major]          with       [C oct- no A]            
F,G,A,B,C,D,E,     with       C,Db,Eb,E,F#,G,Bb                                    No Ab



disjunct unordered sets:   ([F,A,B,D]  [C,E,G]  [Db,Eb,F#,Bb]   [Ab])
--------------------

                             [C phryg b4]
or                with       C,Db,Eb,E,G,Ab,Bb


disjunct unordered sets:  C,E,G
([F,A,B,D]  [C,E,G]  [Db,Eb,Ab,Bb]   [Gb])

========
[C lyd ]           with       [C Mixo b6 b2]      
C,D,E,F#,G,A,B     with       C,Db,E,F,G,Ab,Bb                                    No Eb 


disjunct unordered sets:  ([D,F#,A,B]   [C,E,G]   [Db,F,Ab,Bb]  [Eb])          

-------------------- 
or                 with       [C Phryg b4]
                              C,Db,Eb,E,G,Ab,Bb                                   no  F

disjunct unordered sets:  ([D,F#,A,B]  [C,E,G]   [Db,Eb,Ab,Bb]   [F])

========

[C Mixo b6]                   [C Lydian #2]               
Ab,Bb,C,D,E,F,G  with         C,D#,E,F#,G,A,B                                     no  Db

disjunct unordered sets:  ([Ab,Bb,D,F]  [C,E,G]  [D#,F#,A,B] [Db])       
--------------------
or                 with       [sadvid]   [C oct- no Bb]
                              C,Db,Eb,E,F#,G,A                                    no B

disjunct unordered sets:  ([Ab,Bb,D,F]   [C,E,G]   [Db,Eb,F#,A] [b])   

========
[C har maj. (b6)]    with     [C octotonic]
C,D,E,F,G,Ab,B       with      C,Db,Eb,E,F#,G,A,Bb                                all

disjunct unordered sets:  ([D,F,Ab,B]   [C,E,G]     [Db,Eb,F#,A,Bb])


================================ 
================================ 
================================ 

common: C,E,Ab


[C mixo b6]                 [C Locr. b4 bb7]                                    no B              
Ab,Bb,C,D,E,F,G    with     C,Db,Eb,E,Gb,Ab,A 

disjunct unordered sets:  ([Bb,D,F,G]  [C,E,Ab]  [Db,Eb,Gb,A]   [b])
--------------------
                           [C Lyd #5 #2]                                         no Db
or                 with    C,D#,E,F#,G#,A,B

disjunct unordered sets:   ([Bb,D,F,G]   [C,E,Ab]    [D#,F#,A,B]   [C#])
--------------------

[C Locr b4]                   [C Ion #5]                      
E,Gb,Ab,Bb,C,Db,Eb   with     C,D,E,F,G#,A,B                                   No   G   


disjunct unordered sets:  ([Gb,Bb,Db,Eb]   [C,E,Ab]     [D,F,A,B]    [G])
--------------------
               [C Ion b6]
or             C,D,E,F,G,Ab,B                                                  no  A

disjunct unordered sets:  ([Gb,Bb,Db,Eb]   [C,E,Ab]     [D,F,G,B]    [A])         
--------------------


[C Lyd #5 ]                 [C Mixo b6 b2]                        
C,D,E,F#,G#,A,B             C,Db,E,F,G,Ab,Bb                                    no Eb

disjunct unordered sets:  ([D,F#,A,B]  [C,E,Ab]   [Db,F,G,Bb]   [Eb])    
--------------------
                [C Phryg b4]
or              C,Db,Eb,E,G,Ab,Bb                                              no   F

 
disjunct unordered sets:  ([D,F#,A,B]  [C,E,Ab]  [Db,Eb,G,Bb]  [F] )               

================================ 
================================ 
================================ 

common: C,E,A


[C mixo]                  [C Locrian b4 bb7]
Bb,C,D,E,F,G,A    with    C,Db,Eb,E,Gb,Ab,A                                       No   B

disjunct unordered sets:     ([Bb,D,F,G]  [C,E,A]   [Db,Eb,Gb,Ab]  [b])    

========

C Mixo b2                 Lydian #5 #2
C,Db,E,F,G,A,Bb           C,D#,E,F#,G#,A,B                        all

disjunct unordered sets:  ([Bb,D,F,G]   [C,E,A]  [Db,Eb,Gb,Ab]   [b])


========

[C major]                 [C oct- no G]
F,G,A,B,C,D,E,    with    C,Db,Eb,E,F#,A,Bb                                      no   Ab

disjunct unordered sets:   ([F,G,B,D]  [C,E,A]  [Db,Eb,F#,Bb]  [Ab])

                          [C Locrian b4 bb7]
                  or      C,Db,Eb,E,F#,G#,A                                     no   Bb

disjunct unordered sets:  ([F,G,B,D]   [C,E,A]  [Db,Eb,F#,G#]    [Bb])

======== 

[C Lyd #5]                  [C oct- no F#]
C,D,E,F#,G#,A,B    with   C,Db,Eb,E,G,A,Bb                                         no  F

disjunct unordered sets:   ([D,F#,G#,B]  [C,E,A]  [Db,Eb,G,Bb]     [F])
 
                          [C Mixo b2]
                   or     C,Db,E,F,G,A,Bb


disjunct unordered sets:   ([D,F#,G#,B]   [C,E,A]   [Db,F,G,Bb]     [Eb])
========
  
[C Ion #5]                  [oct]
C,D,E,F,G#,A,B      with  C,Db,Eb,E,F#,G,A,Bb                     all

disjunct unordered sets:  ([D,F,G#,B]   [C,E,A]   [Db,Eb,F#,G,Bb])
========

================================ 
================================ 
================================ 

common: C,E,Bb


[C Mixo]                      [C Locr b4]
Bb,C,D,E,F,G,A     with     C,Db,Eb,E,Gb,Ab,Bb                                No   B

disjunct unordered sets:    ([D,F,G,A]   [C,E,Bb]    [Db,Eb,Gb,Ab]   [b])



-------------------- 
[C Mixo b6 ]                  [C Oct- No G]
Ab,Bb,C,D,E,F,G             C,Db,Eb,E,Gb,A,Bb

disjunct unordered sets:  ([D,F,G,Ab]   [C,E,Bb]    [Db,Eb,Gb,A]   [b])
 
 

================================ 
================================ 
================================ 


common: C,F,G


[C Phryg ]                   [C Ion ]{Major]
Db,Eb,F,G,Ab,Bb,C   with   C,D,E,F,G,A,B                          no  F#

disjunct unordered sets:  ([Db,Eb,Ab,Bb]  [C,F,G] [D,E,A,B]  [F#])
--------------------   
[C Mel Min ]                 [C Mixo b6 b2]
Eb,F,G,A,B,C,D             C,Db,E,F,G,Ab,Bb

disjunct unordered sets:  ([Eb,A,B,D] [C,F,G]  [Db,E,Ab,Bb]  [F#])
-------------------- 
[C Dorian b2 ]               [C Ion b6]
Db,Eb,F,G,A,Bb,C           C,D,E,F,G,Ab,B

disjunct unordered sets:  ([Db,Eb,A,Bb]  [C,F,G ] [D,E,Ab,B]  [F#])
--------------------
[C Har Minor ]               [C Mixo b2]
C,D,Eb,F,G,Ab,B            C,Db,E,F,G,A,Bb

disjunct unordered sets:  ([D,Eb,Ab,B]  [C,F,G]  [Db,E,A,Bb]  [F#])
 
 
 
================================ 
================================ 
================================ 

common: C,F,Ab


[C Locrian ]                 [ C Ion #5]
Gb,Ab,Bb,C,Db,Eb,F   with   C,D,E,F,G#,A,B                                    no   G 

disjunct unordered sets:  ([Gb,Bb,Db,Eb]  [C,F,Ab]   [D,E,A,B]  [G])   
--------------------
                           [C Ion b6]
                    or     C,D,E,F,G,Ab,B                                      no    A
disjunct unordered sets:  ([Gb,Bb,Db,Eb]   [C,F,Ab]  [D,E,G,B]  [A] )               

--------------------
[C Phryg]                    [C dim- no Eb]
Db,Eb,F,G,Ab,Bb,C           C,D,F,Gb,Ab,A,B                                    no    E 
disjunct unordered sets:  ([Db,Eb,G,Bb]   [C,F,Ab]  [D,Gb,A,B]   [E])

 
                           [C Ion #5]
                    or     C,D,E,F,G#,A,B                                      no   F#
disjunct unordered sets:  ([Db,Eb,G,Bb]   [C,F,Ab]  [D,E,A,B]   [F#])
 --------------------
[C Mixo b6]                   [C Locrian bb7]
Ab,Bb,C,D,E,F,G             C,Db,Eb,F,Gb,Ab,A                                  no    B
disjunct unordered sets:  ([Bb,D,E,G]   [C,F,Ab]  [Db,Eb,Gb,A]  [b])

                            [C dim- no D]
                     or     C,Eb,F,Gb,Ab,A,B                                   no    C#
disjunct unordered sets:  ([Bb,D,E,G]  [C,F,Ab]  [Eb,Gb,A,B]  [C#])
--------------------
C Mixo b6 b2                 C Dim
F,G,Ab,Bb,C,Db,E             C,D,Eb,F,Gb,Ab,A,B                            all

disjunct unordered sets:   ([Bb,Db,E,G]  [C,F,Ab]   [D,Eb,Gb,A,B])        

================================ 
================================ 
================================ 

common: C,F,A


F,G,A,B,C,D,E,         C,Db,Eb,F,Gb,A,Bb                                 no   Ab

disjunct unordered sets:  ([G,B,D,E]   [C,F,A]  [Db,Eb,Gb,Bb]   [Ab])           

--------------------
Bb,C,D,E,F,G,A          C,Eb,F,Gb,Ab,A,B                                 no   Db
 
disjunct unordered sets:  ([Bb,D,E,G]  [C,F,A ]  [Eb,Gb,Ab,B]  [Db])

-------------------- 
                  or   C,Db,Eb,F,Gb,Ab,A                                 no  B
disjunct unordered sets:  ([Bb,D,E,G]   [C,F,A]  [Db,Eb,Gb,Ab] [b])

--------------------
Db,Eb,F,G,A,Bb,C        C,D,F,Gb,Ab,A,B                                  no  E

disjunct unordered sets: ([Db,Eb,G,Bb]   [C,F,A]   [D,Gb,Ab,B]   [E])



                   or   C,D,E,F,Ab,A,B                                   no   F#
disjunct unordered sets:  ([Db,Eb,G,Bb] [C,F,A] [D,E,Ab,B] [F#])
 


--------------------

F,G,A,Bb,C,Db,E         C,D,Eb,F,Gb,Ab,A,B   all

disjunct unordered sets:  ([G,Bb,Db,E]  [C,F,A]   [D,Eb,Gb,Ab,B])



================================ 
================================ 
================================ 

common: C,F,Bb


[C Locrian]              with    [C Mixolydian]
Gb,Ab,Bb,C,Db,Eb,F               C,D,E,F,G,A,Bb           no B

disjunct unordered sets:  

([Gb,Ab,Db,Eb]  [C,F,Bb]   [D,E,G,A]   [b])  

----------

[C Mixo b6]              with    	[C Dor b5 b2]
Ab,Bb,C,D,E,F,G                	C,Db,Eb,F,Gb,A,Bb
 
disjunct unordered sets:  ([Gb,Ab,Db,Eb]   [C,F,Bb]   [D,E,G,A]  [b])



 
--------------------  
[C Aeol b5]              with 	[C Mixo b2] 
Gb,Ab,Bb,C,D,Eb,F           		C,Db,E,F,G,A,Bb 

disjunct unordered sets:  ([Gb,Ab,D,Eb]  [C,F,Bb]  [Db,E,G,A]  [b])


--------------------
[C Mixo b6 b2]           with		[C Dor b5]
F,G,Ab,Bb,C,Db,E            		C,D,Eb,F,Gb,A,Bb

disjunct unordered sets:  ([G,Ab,Db,E]   [C,F,Bb]   [D,Eb,Gb,A]   [b])



 
 


================================ 
================================ 
================================ 


common: C,F#,G#


C Locrian                  		C Lydian #5
Gb,Ab,Bb,C,Db,Eb,F    		with 	C,D,E,F#,G#,A,B                          no  G

disjunct unordered sets:  
([Bb,Db,Eb,F]  [C,F#,G#]  [D,E,A,B]  [G])

--------------------
C Locrian b4 (Altered)           C dim- no Eb
E,Gb,Ab,Bb,C,Db,Eb         		C,D,F,F#,G#,A,B                          no   G

disjunct unordered sets:  C,F#,G#


([E,Bb,Db,Eb]  [C,F#,G#]   [D,F,A,B]  [G])

================================ 
================================ 
================================ 

common: C,F#,A


C Lydian                          C Dor b5 b2
C,D,E,F#,G,A,B    with	  			C,Db,Eb,F,Gb,A,Bb                         no   Ab
 
disjunct unordered sets:  ([D,E,G,B]   [C,F#,A]    [Db,Eb,F,Bb]  [Ab]) 

--------------------
                                
                                 C Locrian bb7
					 or					C,Db,Eb,F,Gb,Ab,A

disjunct unordered sets:  ([D,E,G,B]   [C,F#,A]    [Db,Eb,F,Ab]  [Bb])

--------------------

C Lydian b7                      C Locrian bb7
Bb,C,D,E,F#,G,A						C,Db,Eb,F,Gb,Ab,A    

disjunct unordered sets:  ([Bb,D,E,G]   [C,F#,A]   [Db,Eb,F,Ab]   [b])

--------------------

                                 C dim- No D
					  or				C,Eb,F,Gb,Ab,A,B                          No    Db 
 
disjunct unordered sets:  ([Bb,D,E,G])  ([C,F#,A])  ([Eb,F,Ab,B])    ([Db])

--------------------
 
C Lyd #5                         C Dor b5 b2           
C,D,E,F#,G#,A,B          			C,Db,Eb,F,Gb,A,Bb                         No     G 

disjunct unordered sets:  ([D,E,G#,B]   [C,F#,A]  [Db,Eb,F,Bb]   [G])

--------------------
                               	C Oct- No E
					or    			   C,Db,Eb,F#,G,A,Bb                         No     F
 
disjunct unordered sets:  ([D,E,G#,B]   [C,F#,A]   [Db,Eb,G,Bb]  [F])

 



================================ 
================================ 
================================ 


common: C,F#,Bb


C Locrian                      C Lydian b7
Gb,Ab,Bb,C,Db,Eb,F   with      C,D,E,F#,G,A,Bb         no B

disjunct unordered sets:  [Ab,Db,Eb,F]  [C,F#,Bb]  [D,E,G,A]  [b]
 
--------------------

C Aeol b5                      C Lydian b7 b2
Gb,Ab,Bb,C,D,Eb,F              C,Db,E,F#,G,A,Bb        no B

disjunct unordered sets:  ([Ab,D,Eb,F]  [C,F#,Bb]  [Db,E,G,A]   [b])

--------------------

Common:  F#,Bb


no C:
B Lyd b3                       C Oct- No C#
F#,G#,A#,B,C#,D,F              C,D#,E,F#,G,A,Bb        all tones  

disjunct unordered sets:   F#,Bb

([G#,B,C#,D,F]  [F#,Bb]  [C,D#,E,G,A])


================================ 
================================ 
================================ 


common: C,G,A


[C Lydian]            [C Phryg]
[C,D,E,F#,G,A,B]        [C,Db,Eb,F,G,A,Bb]           No Ab

disjunct unordered sets:  

([D,E,F#,A,B]  [C,G,A]   [Db,Eb,F,Bb]  [Ab])
-----------------
[C major]             [C oct- no E]
F,G,A,B,C,D,E         C,Db,Eb,F#,G,A,Bb              No Ab

disjunct unordered sets:   
 
([D,E,F,A,B] [C,G,A]  [Db,Eb,F#,Bb]   [Ab])
-----------------

[C Ion. b3] [Mel Min] [C oct- no Eb]
Eb,F,G,A,B,C,D        C,Db,E,F#,G,A,Bb               No Ab

disjunct unordered sets:   
([Eb,F,B,D]   [C,G,A]     [Db,E,F#,Bb]   [Ab])
-----------------
[C Mixo. b2]          [C Lyd b3]
F,G,A,Bb,C,Db,E       C,D,Eb,F#,G,A,B                No Ab

disjunct unordered sets:  ([F,Bb,Db,E]  [C,G,A]  [D,Eb,F#,B]   [Ab])
 





================================ 
================================ 
================================ 


common: C,G,Bb


 

[C Phryg.]							[C Lydian b7]
Db,Eb,F,G,Ab,Bb,C    with         C,D,E,F#,G,A,Bb      no B

disjunct unordered sets:
([Ab,Db,Eb,F]   [C,G,Bb]  [D,E,F#,A]  [b])

-----------------

[C Aeol].                        [C Oct. no Eb]
Ab,Bb,C,D,Eb,F,G                 C,Db,E,F#,G,A,Bb

disjunct unordered sets:
([Ab,D,Eb,F]   [C,G,Bb]  [Db,E,F#,A]  [b])

------------------
[C Mixo. b6 ]                    [C Oct  no E]
Ab,Bb,C,D,E,F,G                  C,Db,Eb,F#,G,A,Bb

disjunct unordered sets:
([Ab,D,E,F]   [C,G,Bb]   [Db,Eb,F#,A]   [b])


------------------
 
[C Phryg. maj3 ]                 [C Dorian #4]
F,G,Ab,Bb,C,Db,E                 C,D,Eb,F#,G,A,Bb
[C Mixo b6 b2]

disjunct unordered sets:
([F,Ab,Db,E]    [C,G,Bb] [D,F#,A,Bb]  [b])
 


================================ 
================================ 
================================
eta: swapped in this version which finished all the "disjunct unordered sets"

Last edited by calebprime; 25th April 2018 at 10:11 AM.
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Old 27th April 2018, 04:49 AM   #255
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Originally Posted by calebprime View Post
...

The basic idea is that you pick a 3-note harmony in relation to your tonal center. Here it is given as C, but you transpose.

Then the pairs of scales are the most disjunct and complete (most complementary) scales given those 3 common tones, of which 1 tone is your tonal center.

The idea might be to get fluent to the point that you can chain transposed row-pairs to make larger patterns that give you tones outside of your original "Do."
I'm not smart enough to transpose these scales and have any room for anything else in my little noggin. It's too hard.

A solution might be to display all the transpositions in some concise way -- the good ol' inversion square to the rescue.

There are three possible "scale situations" with the first trichord -- C,D,F. I can just fit three squares on one (large) screen vertically with a 14-point font.

Beyond that difficulty, there is the slight melancholy of secretly wanting a clear path forward, but having only just completed a little dictionary that gives no such path forward at all. It's just a complete list of situations.

You can't see it, but I've also colored all the C-D-F's red in these three squares.


Code:
E,  G,  G#, B, |C,  D,  F, |Eb, F#, A,  Bb,|Db
Db, E,  F,  G#, A,  B,  D,  C,  Eb, F#, G,  Bb
C,  Eb, E,  G,  G#, Bb, Db, B,  D,  F,  F#, A
A,  C,  Db, E,  F,  G,  Bb, G#, B,  D,  Eb, F#
----------------------------------------------------
G#, B,  C,  Eb, E,  F#, A,  G,  Bb, Db, D,  F
F#, A,  Bb, Db, D,  E,  G,  F,  G#, B,  C,  Eb
Eb, F#, G,  Bb, B,  Db, E,  D,  F,  G#, A,  C
----------------------------------------------------
F,  G#, A,  C,  Db, Eb, F#, E,  G,  Bb, B,  D
D,  F,  F#, A,  Bb, C,  Eb, Db, E,  G,  G#, B
B,  D,  Eb, F#, G,  A,  C,  Bb, Db, E,  F,  G#
Bb, Db, D,  F,  F#, G#, B,  A,  C,  Eb, E,  G
----------------------------------------------------
G,  Bb, B,  D, |Eb, F,  G#,|F#, A,  C,  Db,|E





E,  G,  G#, Bb,|C,  D,  F | Eb, F#, A,  B, |Db
Db, E,  F,  G, |A,  B,  D,| C,  Eb, F#, G#,|Bb
C,  Eb, E,  F#,|G#, Bb, Db| B,  D,  F,  G, |A
Bb, Db, D,  E, |F#, G#, B,| A,  C,  Eb, F, |G
---------------|----------|----------------|-----
G#, B,  C,  D, |E,  F#, A,| G,  Bb, Db, Eb,|F
F#, A,  Bb, C, |D,  E,  G,| F,  G#, B,  Db,|Eb
Eb, F#, G,  A, |B,  Db, E,| D,  F,  G#, Bb,|C
---------------|----------|----------------|-----
F,  G#, A,  B, |Db, Eb, F#| E,  G,  Bb, C, |D
D,  F,  F#, G#,|Bb, C,  Eb| Db, E,  G,  A, |B
B,  D,  Eb, F, |G,  A,  C,| Bb, Db, E,  F#,|G#
A,  C,  Db, Eb,|F,  G,  Bb| G#, B,  D,  E, |F#
---------------|----------|----------------|---
G,  Bb, B,  Db, Eb, F,  G#| F#, A,  C,  D, |E






E,  G,  A,  B, |C,  D,  F, |Eb, F#, G#, Bb, db
db, E,  F#, G#,|A,  B,  D, |C,  Eb, F,  G,  Bb
B,  D,  E,  F#,|G,  A,  C, |Bb, db, Eb, F,  G#
A,  C,  D,  E, |F,  G,  Bb,|G#, B,  db, Eb, F#
---------------------------|-------------------------
G#, B,  db, Eb,|E,  F#, A, |G,  Bb, C,  D,  F
F#, A,  B,  db,|D,  E,  G, |F,  G#, Bb, C,  Eb
Eb, F#, G#, Bb,|B,  db, E, |D,  F,  G,  A,  C
-----------------------------------------------------
F,  G#, Bb, C, |db, Eb, F#,|E,  G,  A,  B,  D
D,  F,  G,  A, |Bb, C,  Eb,|db, E,  F#, G#, B
C,  Eb, F,  G, |G#, Bb, db,|B,  D,  E,  F#, A
Bb, db, Eb, F, |F#, G#, B, |A,  C,  D,  E,  G
G,  Bb, C,  D, |Eb, F,  G#,|F#, A,  B,  db, E
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Old 3rd May 2018, 06:47 AM   #256
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I've completed the first draft of a document with an inversion square for every "situation" -- every intersection of scales as described above. The squares had to be hand-assembled for formatting reasons and there were around a hundred plus.

I don't have the quick chops to make this document display well here or in preview in Box, but it should be 3 squares across by some 38, each a 12 by 12 square, but with additional lines to show partitions.


https://app.box.com/s/k95trxdba7wrmfefljmaw4xqwm3ttmz6
Download here.
Took a lot of work, anyone's welcome to it.

The idea is that if you want to see 4 different situations that aren't adjacent here, you can simply open up 4 copies of the same document. Easy Peasy. Four windows.
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Old 3rd May 2018, 06:57 AM   #257
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And now we jam.
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Old 26th June 2018, 07:26 AM   #258
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As schemas go, that last one has turned out to be fairly useful and fun to improvise with. The notes you fall upon with this way of displaying things are fresh combinations of the less-usual-but-conventional scales.

Your hands seem to find good-sounding things fairly easily with this method.

And now, back to multiple-order function series -- MOFs.

mof3 in particular. A,C#,D#,C,F,G#,G,D,B,E,Bb,F#

This is an old series for me, a favorite. Gunther Schuller wrote every piece with a series that he considered magical. This "MOF3" would be my candidate.

It's not strictly a dual-property series as I've defined it, but it is a good MOF series in unusually numerous ways.

Details next post.
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Old 26th June 2018, 07:36 AM   #259
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The idea is that notes can be added to the series, interpolating between the original notes. The result, with the right MOF series, is not junk, but another version of the series.

Instead of a strict definition, I'm choosing relationships that are good-enough. That is, all or mostly good with a few exceptions.

With a loose definition, some ten or eleven new series might be formed by adding notes to the original series.

Code:
Mof3, starting on A

    ?   yes            #7                   gd?
    |   |       ^       ^                   ^
....v...v.......|.......|...................|
A,  C#, D#, C,  F,  G#, G,  D,  B,  E,  A#, F#
F,  A,  B,  G#, C#, E,  D#, A#, G,  C,  F#, D     --> p/8
D#, G,  A,  F#, B,  D,  C#, G#, F,  A#, E,  C
F#, A#, C,  A,  D,  F,  E,  B,  G#, C#, G,  D#    --> p/9
C#, F,  G,  E,  A,  C,  B,  F#, D#, G#, D,  A#    <-- r/4
A#, D,  E,  C#, F#, A,  G#, D#, C,  F,  B,  G
B,  D#, F,  D,  G,  A#, A,  E,  C#, F#, C,  G#
E,  G#, A#, G,  C,  D#, D,  A,  F#, B,  F,  C#    --> p/7  1 wrong
G,  B,  C#, A#, D#, F#, F,  C,  A,  D,  G#, E
D,  F#, G#, F,  A#, C#, C,  G,  E,  A,  D#, B     <-- r/5  
G#, C,  D,  B,  E,  G,  F#, C#, A#, D#, A,  F
C,  E,  F#, D#, G#, B,  A#, F,  D,  G,  C#, A     <-- r/3  2 reversals at end
I've indicated these with arrows, pointing in the direction you read the series.
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Old 26th June 2018, 07:42 AM   #260
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The project here, once some basics have been established, is to find many of the basic chains of rows-in-sequence that go from the original series in a strange loop back to the original series.

That work would come before composition, because you would want the overview of possible moves, instead of just going by the seat of your pants. (Just as you would with chess.)

Once the abstract possibilities have been figured out, it will probably turn out that some sound much better than others, but I have to hear them before I know.

The contiguous scale segments, the 012-free segments, the tonal associations, are absolutely essential to this. This is not supposed to sound like Schoenberg.


Here are some examples of viable chains of adding notes that return to the original or in a few cases, the backwards version, the retrograde, or r/0.

Code:
p/0 -> i/6   -> p/0

p/0 -> p/8   -> p/4  -> p/0

p/0 -> r/3   -> p/6  -> r/9 -> p/0

r/0 -> p/4   -> r/8  -> p/0

p/0 -> r/4   -> p/8  -> r/0

p/0 -> r/5   -> p/10 -> r/3 -> p/8 -> r/1 -> p/6 -> r/11 -> p/4 -> r/9 -> p/2 -> r/7 -> p/0

p/0 -> ri/10 -> r/6  -> i/4 -> p/0

p/0 -> ri/9  -> p/0

p/0 -> ri/6 -> i/3  -> p/10 -> i/4 -> p/0

p/0 -> ri/6 -> i/3  -> p/10 -> r/3 -> p/6  -> r/9 -> p/0
Next post, I'll explain that, fill it in.

Last edited by calebprime; 26th June 2018 at 07:48 AM.
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Old 26th June 2018, 08:31 AM   #261
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The first two loops from above.

Code:
p/0 -> i/6   -> p/0


A,  C#, D#, C,  F,  G#, G,  D,  B,  E,  A#, F#      p/0
a...........c...........g...........e...........    i/6  
................f.......................a#......
....c#..............g#......d...............f#..



A,  C,  G,  E,  F,  A#,  C#,  G#,  D,  F#,  D#, B   i/6
a........................c#.................d#..... p/0
....c...........f.............g#...................
........g..........................d............b..
............e.......a#.................f#..........




p/0 -> p/8   -> p/4  -> p/0

A,  C#, D#, C,  F,  G#, G,  D,  B,  E,  A#, F#     p/0
....c#..........f.......g...........e...........   p/4
a...........c...................b...........f#..
........d#..........g#......d...........a#......


C#, F,  G,  E,  A,  C,  B,  F#, D#, G#, D,  A#     p/4
....f...........a.......b...........g#..........   p/8
c#..........e...................d#..........a#..
........g...........c.......f#..........d.......



F,  A,  B,  G#, C#, E,  D#, A#, G,  C,  F#, D      p/8
....a...........c#......d#..........c...........   p/0
f...........g#..................g...........d...
........b...........e.......a#..........f#......

next few posts, 2 examples per post, same kind of thing
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Old 26th June 2018, 08:51 AM   #262
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Code:
p/0 -> r/3   -> p/6  -> r/9 -> p/0


A,  C#, D#, C,  F,  G#, G,  D,  B,  E,  A#, F#     p/0
........d#..............g.......................   r/9
....c#..............g#..........b...e...........
................f...........d...................
a...........c...........................a#..f#..


D#, G,  C#, G#, B,  E,  F,  D,  A,  C,  A#, F#     r/9
eb..g...........................a...........f#..   p/6
................b...........d...................
........c#..g#..........f...............a#......
....................e...............c...........


Eb, G,  A,  F#, B,  D,  C#, G#, F,  A#, E,  C,     p/6
........a...............c#......................   r/3
....g...............d...........f...a#..........
................b...........g#..................
d#..........f#..........................e...c...


A,  C#, G,  D,  F,  A#, B,  G#, D#, F#, E,  C.     r/3
a...c#..........................d#..........c...   p/0
................f...........g#..................
........g...d...........b...............e.......
....................a#..............f#..........

Adding notes:
p/0 --> r/3 --> p/6 --> r/9 --> p/0

------------------------------------------------------

A,  C#, D#, C,  F,  G#, G,  D,  B,  E,  A#, F#     p/0
............c.......................e.......f#..   p/3
........d#..........g#..........b.......a#......
................f.......g...d...................
a...c#



C,  E,  F#, D#, G#, B,  A#, F,  D,  G,  C#, A      p/3
............eb......................g.......a...   p/6
........f#..........b...........d.......c#......
................g#......a#..f...................
c...e




Eb, G,  A,  F#, B,  D,  C#, G#, F,  A#, E,  C,     p/6
............f#......................a#......c...   p/9
........a...........d...........f.......e.......
................b.......c#..g#..................
eb..g




F#, A#, C,  A,  D,  F,  E,  B,  G#, C#, G,  D#     p/9
............a.......................c#......d#...  p/0
........c...........f...........g#......g........
................d.......e...b....................
f#..a#



r/0 -> p/4   -> r/8  -> p/0

Reversal of direction in a few steps, I suppose:


A,  C#, D#, C,  F,  G#, G,  D,  B,  E,  A#, F#     p/0 
............................d...............f#...  r/8
............c...........g...............a#.......
........d#..........................e............
....c#..............g#..........b................
a...............f..........



D,  F#, C,  G,  A#, D#, E,  C#, G#, B,  A,  F      r/8     
............................c#..............f...   p/4
............g...........e...............a.......
........c...........................b...........
....f#..............d#..........g#..............
d...............a#.........


C#, F,  G,  E,  A,  C,  B,  F#, D#, G#, D,  A#     p/4
............................f#..............a#..   r/0
............e...........b...............d.......
........g...........................g#..........
....f...............c...........d#..............
c#..............a
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Old 26th June 2018, 09:26 AM   #263
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Code:
A,  C#, D#, C,  F,  G#, G,  D,  B,  E,  A#, F#     p/0
a.......................g...............a#......   i/4 but not from first note, from second note
................f...........d...................
........eb..........g#..........b...........f#..
............c.......................e...........
....c#.......       the last note c# goes beyond the loop boundary


A,  G,  A#, F,  D,  Eb, G#, B,  F#, C,  E,  C#     i/4 from second note
....................................c...e.......   r/6
........a#..f...........g#..................c#..
................d...........b...f#..............
a...g...............d#.............


C,  E,  A#, F,  G#, C#, D,  B,  F#, A,  G,  D#     r/6
........a#......................f#..............   ri/10
c...........f...........d...........a...........
................g#..........b...................
....e...............c#..................g...d#..



A#, F#, C,  F,  D,  A,  G#, B,  E,  C#, G,  D#     ri/10
....................a...............c#......d#...  p/0
........c...f...........g#..............g.......
................d...........b...e...............
a#..f#..............................


adding notes:

p/0 --> ri/10 --> r/6 --> i/4 --> p/0



------------------------------------------------------


A,  C#, D#, C,  F,  G#, G,  D,  B,  E,  A#, F#     P/0
a...............f...............b...e............  RI/9
....c#..............g#..g...............a#.......
........d#..c...............d...............f#...  


A,  F,  B,  E,  C#, G#, G,  A#, D#, C,  D,  F#     RI/9
a...............c#..............d#..c..........    p/0
....f...............g#..g...............d......
........b...e...............a#..............f#.

adding notes:

p/0 --> ri/9 -->  p/0 



------------------------------------------------------
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Old 27th June 2018, 01:47 PM   #264
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Originally Posted by calebprime View Post
The first two loops from above.

Code:
p/0 -> i/6   -> p/0


A,  C#, D#, C,  F,  G#, G,  D,  B,  E,  A#, F#      p/0
a...........c...........g...........e...........    i/6  
................f.......................a#......
....c#..............g#......d...............f#..
........d#......................b


A,  C,  G,  E,  F,  A#,  C#,  G#,  D,  F#,  D#, B   i/6
a........................c#.................d#..... p/0
....c...........f.............g#...................
........g..........................d............b..
............e.......a#.................f#..........




p/0 -> p/8   -> p/4  -> p/0

A,  C#, D#, C,  F,  G#, G,  D,  B,  E,  A#, F#     p/0
....c#..........f.......g...........e...........   p/4
a...........c...................b...........f#..
........d#..........g#......d...........a#......


C#, F,  G,  E,  A,  C,  B,  F#, D#, G#, D,  A#     p/4
....f...........a.......b...........g#..........   p/8
c#..........e...................d#..........a#..
........g...........c.......f#..........d.......



F,  A,  B,  G#, C#, E,  D#, A#, G,  C,  F#, D      p/8
....a...........c#......d#..........c...........   p/0
f...........g#..................g...........d...
........b...........e.......a#..........f#......

next few posts, 2 examples per post, same kind of thing
In my haste, I omitted the two notes d# and b, hilited.

Last edited by calebprime; 27th June 2018 at 01:48 PM.
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Old 29th June 2018, 05:34 AM   #265
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To construct loops of chains of series, we need only think about valid connections between series, and we can list them. I mean that it is possible to ignore the content, what the series sound like. This might be the best spirit for generating possible chains.

Or maybe, each choice of series yields very different musical results, and we might hear that as we work, and those preferences (which are not part of the lists below) ought to be one of the main things that guides us. This might be the best spirit for finally writing some music.

As resourceful arrangers, we may be able to make different series work, ones that don't seem attractive at first.

With any series in a schema like this, there would be a different set of series it could go to based on whether it is a prime form, an inversion, a retrograde, or a retrograde inversion.

Here's the list for "Mof 3":
From P/0: p/8, p/9 r/4, p/7, r/5, r/3, i/4, i/6, ri/8, ri/10, ri/9

From R/0: r/8, r/9, p/4, r/7, p/5, p/3, ri/4, ri/6, i/8, i/10, i/9,

From I/0: I/4, I/3(-), ri/8, p/6, r/3, r/2, p/5, I/6, ri/3, r/9

From RI/0: RI/4, RI/3(-), i/8, R/6, p/3, p/2, r/5, RI/6, i/3, p/9


Armed with such a list, I can blithely and wantonly construct an arbitrary chain of series that progress according to the rules, and starts and ends on p/0.

Something like this:
p/0 r/5 p/8 ri/4 r/10 r/6 i/4 p/10 p/6 ri/3 p/0



Next post, I'll report on whether that was right or whether I made mistakes. As someone who frequently makes careless errors, I shouldn't be too optimistic. Checking this is just a matter of making those loop diagrams as in the posts above.

Last edited by calebprime; 29th June 2018 at 06:31 AM.
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Old 29th June 2018, 07:02 AM   #266
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Something is wrong with the list from I, I think. Further research needed.

In any case, it worked up to the end, where it needed a tweak.

Code:
p/0
A,  C#, D#, C,  F,  G#, G,  D,  B,  E,  A#, F#

r/5
B,  D#, A,  E,  G,  C,  C#, A#, F,  G#, F#, D
........a...............c#.....................
....d#..............c...........f...g#.........
................g...........................d..
b...........e...............a#..........f#.....



p/8
F,  A,  B,  G#, C#, E,  D#, A#, G,  C,  F#, D
........b...............d#.....................
....a...........................g...c..........
................c#..........a#.................
f...........g#..........................f#..d..


ri/4
E,  C,  F#, B,  G#, D#, D,  F,  A#, G,  A,  C#
............................f...........a........
............b...g#..........................c#...
e...................d#..........a#..g............
....c...f#..............d...



r/10
E,  G#, D,  A,  C,  F,  F#, D#, A#, C#, B,  G
e...............c.......f#..............b......
....g#......................d#.................
........d...........f...........a#..........g..
............a.......................c#.........



r/6
C,  E,  A#, F,  G#, C#, D,  B,  F#, A,  G,  D#
....e...........g#......d...........a............
c...........f...................f#..........d#...
........a#..........c#......b...........g........


i/4
C#, A,  G,  A#, F,  D,  D#, G#, B,  F#, C,  E
........................................c...e....
............a#..f...........g#...................
c#..................d...........b...f#...........
....a...g...............d#..............


p/10
G,  B,  C#, A#, D#, F#, F,  C,  A,  D,  G#, E
........c#......................a................
g...........a#..........f...........d............
................d#......................g#.......
....b...............f#......c...............e....



p/6
D#, G,  A,  F#, B,  D,  C#, G#, F,  A#, E,  C
........a.......................f...............
d#..........f#..........c#..........a#..........
................b.......................e.......
....g...............d.......g#..............c


i/0
A,  F,  D#, F#, C#, A#, B,  E,  G,  D,  G#, C
........d#..............b.......................
....f...............a#..........g...d...........
................c#..........e...................
a...........f#..........................g#..c...



ri/3
D#, B,  F,  A#, G,  D,  C#, E,  A,  F#, G#, C
............................e...............c...
............a#..........c#..............g#......
........f...........................f#..........
....b...............d...........a...............
d#..............g




i/7
E,  C,  A#, C#, G#, F,  F#, B,  D,  A,  D#, G
........a#..............f#.....................
....c...............f...........d...a..........
................g#..........b..................
e...........c#..........................d#..g




ri/10  
A#, F#, C,  F,  D,  A,  G#, B,  E,  C#, D#, G
....................a...............c#..d#......
........c...f...........g#..................g...
................d...........b...e...............
a#..f#
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Old 29th June 2018, 11:17 AM   #267
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For a long time, I've been meaning to post at least a sketchy summary of all the ways I know of generating series with the kinds of self-similarity I've been talking about. Call it embedded self-similarity or call it multiple order function, mof.

They are:

1) power residue index series -- example index of 2 ^ n mod 13.

2) first 12 values of any longer power residue index series

3) mod 12 or mod 13 residues of all power res index series, rarely, with cherry-picking.

4) the "handalg" technique that was probably worked out by Robert Morris first.

a) find a complete incrementing series that makes a complete orbit with some version of a chromatic series ( 0,1,2,3,4,5,6,7,8,9,10,11 ), in the usual meaning of orbit in permutation theory. Make the one-line permutation. For each number, now swap position and value. This will be self-simllar in the Mallalieu way at the interval of 1, or a semitone, in a pattern that you chose in the first step.

5) Use my Microtonal Scales application, which has a whole section

6) Given a series, re-order the pitches using the 2 ^ n mod 13 formula that Varwoche implemented in his spreadsheet -- this will give self-similarity of the "every other" square kind, and in rare instances will yield series with both kinds of self-sim.

Last edited by calebprime; 29th June 2018 at 11:21 AM.
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Old 30th June 2018, 08:31 AM   #268
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Hopefully corrected. If not, the lesson is the same -- this the way to build up a chain of moves between series.


From P/0: p/8, p/9 r/4, p/7, r/5, r/3, i/4, i/6, ri/8, ri/10, ri/9

From R/0: r/8, r/9, p/4, r/7, p/5, p/3, ri/4, ri/6, i/8, i/10, i/9,
from i/0: i/4, i/3, ri/8, ri/7 ri/9, p/6, p/9, r/4, r/2, p/7, r/3

from ri/0: ri/4, ri/3, i/8, i/7, i/9, r/6, r/9, p/4, p/2, r/7, p/3


That is, the particulars would be different for every series, so the above is just an example of the working-out for this particular series. The moves on the chess board would be different for every series.

If this theory is extravagent at all, it's that probably you need only fairly short, simple chains for a composition. I don't have an accurate feel at present for how much time these transformations need, and it varies according to the spacing.

And of course, the style. A minimalist unfolding might take hours.

Last edited by calebprime; 30th June 2018 at 08:36 AM.
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Old 3rd July 2018, 05:01 AM   #269
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I defend the process, the intent, the basic viability. All ok. But I'm making some careless errors persistently when I try to get to the level of thinking in terms of abstract "row successions." I'm a little frustrated with myself.

If a Tesla were reading this, he or she might sense some intellectual weakness. I'm weak at this level until I get it right. That's today's project. I intend to slow way down and to try to figure out why I'm still making errors in something that should be fairly easy.

I suspect it's not Tesla that's reading this, but Yortuk Festrunk. Not a genius who sees my weakness, but a wild and crazy guy who doesn't see the point of making this kind of effort.

What shouldn't need defending is the project of trying to write music based on techniques developed in past centuries.

I'm no Bach, but Bach, absurdly, was considered outmoded and old-fashioned with his stodgy preoccupation with all that counterpoint stuff. Who needs counterpoint?
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Old 3rd July 2018, 06:33 AM   #270
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Originally Posted by calebprime View Post
I defend the process, the intent, the basic viability. All ok. But I'm making some careless errors persistently when I try to get to the level of thinking in terms of abstract "row successions." I'm a little frustrated with myself.

If a Tesla were reading this, he or she might sense some intellectual weakness. I'm weak at this level until I get it right. That's today's project. I intend to slow way down and to try to figure out why I'm still making errors in something that should be fairly easy.

I suspect it's not Tesla that's reading this, but Yortuk Festrunk. Not a genius who sees my weakness, but a wild and crazy guy who doesn't see the point of making this kind of effort.

What shouldn't need defending is the project of trying to write music based on techniques developed in past centuries.

I'm no Bach, but Bach, absurdly, was considered outmoded and old-fashioned with his stodgy preoccupation with all that counterpoint stuff. Who needs counterpoint?
I've confused myself and probably any potential reader by not being consistent and clear about when I re-label a row -- for the purpose of showing relative moves -- and when I keep all the labels the same -- for the purpose of keeping overall track. Very boring error, but I can't afford to make it.
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Old 12th July 2018, 09:00 AM   #271
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Thanks to Hevneren, I now have a computer app that chains sequences of row-forms. Here's a verified example with mof3:


P/0 ->P/8 ->RI/6 ->I/2 ->RI/10 ->RI/2 ->P/6 ->RI/4 ->RI/8 ->P/11 ->RI/9 ->I/6 ->P/0


A C# D# C F G# G D B E A# F# P/0
D# B A C G E F A# C# G# D F# I/6
A F B E C# G# G A# D# C D F# Ri/9
G# C D B E G F# C# A# D# A F p/11
G# E A# D# C G F# A D B C# F ri/8
E C F# B G# D# D F A# G A C# ri/4
D# G A F# B D C# G# F A# E C p/6
D A# E A F# C# C D# G# F G B ri/2
A# F# C F D A G# B E C# D# G RI/10
B G F G# D# C C# F# A E A# D i/2
F# D G# C# A# F E G C A B D# ri/6
F A B G# C# E D# A# G C F# D p/8
A C# D# C F G# G D B E A# F# P/0

Moves from Bottom upward to Top.


We may be able to print the source code for this.

The next step for me as an exercise will be to take one of the stable of series I found previously, and build up similar chains using the new app. Mof3, the series I just used, has unusually fecund branching and I wonder what success I'll have with the other series.

Last edited by calebprime; 12th July 2018 at 09:02 AM.
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Old 13th July 2018, 11:53 AM   #272
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Yes, with series named summer train.

Code:
P/0 ->R/9 ->P/6 ->RI/6 ->I/9 ->RI/0 ->I/3 ->I/11 ->I/8 ->RI/11 ->I/2 ->R/2 ->P/0

C,  Db, Eb, Ab, F,  A,  B,  D,  G,  F#, Bb, E.  P/0
F#, C,  Ab, A,  E,  Db, B,  G,  Bb, F,  Eb, D.  R/2
D,  Db, B,  F#, A,  F,  Eb, C,  G,  Ab, E,  Bb. i/2
G,  Db, F,  E,  A,  C,  D,  F#, Eb, Ab, Bb, B.  RI/11
Ab, G,  F,  C,  Eb, B,  A,  F#, Db, D,  Bb, E.  I/8
B,  Bb, Ab, Eb, F#, D,  C,  A,  E,  F,  Db, G.  I/11
Eb, D,  C,  G,  Bb, F#, E,  Db, Ab, A,  F,  B.  I/3
Ab, D,  F#, F,  Bb, Db, Eb, G,  E,  A,  B,  C.  Ri/0
A,  Ab, F#, Db, E,  C,  Bb, G,  D,  Eb, B,  F.  I/9
D,  Ab, C,  B,  E,  G,  A,  Db, Bb, Eb, F,  F#. RI/6
F#, G,  A,  D,  B,  Eb, F,  Ab, Db, C,  E,  Bb. p/6
Db, G,  Eb, E,  B,  Ab, F#, D,  F,  C,  Bb, A.  R/9
C,  Db, Eb, Ab, F,  A,  B,  D,  G,  F#, Bb, E.  P/0
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Old 15th July 2018, 05:04 AM   #273
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Future posts of mine will explain why the goal of "dual" properties is not such a great one. Basically, one kind of self-similarity is adequate, and two different kinds is unnecessary, like having two, um, phalluses.

These posts should include what exactly each kind of self-sim is good for. I've done enough work with this material to have a good idea, now. It's more restrictive, less forgiving, than I would have thought.

Freed from the obligation to only discuss the freakish dual-property series, I can look at different populations of series.

For instance, there are around 8k series that have four shows with a spacing of 5, 1 exception, no 012's per 4 note fields, no 0369 per 4-note field, and no self-equivalence. I think only one or two series from that 8k currently have names, or qualify as "dual property."

So, henceforth and hitherto and forthwith, the subject of this thread is self-similar 12-tone series, the new beginning, or some such. Not dual.

Different kind of numerical series are good for writing different kinds of piece, I'll fill in later. This isn't merely empty truism. I've tried it.
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Old 15th July 2018, 06:25 AM   #274
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Source Code for Row Chainer

...



Code:
/*
 * To change this license header, choose License Headers in Project Properties.
 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */
package calebschainer;

import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.File;
import java.io.FileReader;
import java.io.FileWriter;
import java.io.IOException;
import java.util.Collection;
import java.util.EnumMap;
import java.util.EnumSet;
import java.util.HashSet;
import java.util.Map;
import java.util.Map.Entry;
import java.util.Scanner;
import java.util.Set;
import java.util.Stack;

/**
 *
 * @author Test
 */
public class CalebsChainer {

    private static Map<RowForm, Set<TransposedRowForm>> rowFormMap;
    private static int minNumberOfRowsInChain = 1;
    private static int maxNumberOfRowsInChain = Integer.MAX_VALUE;
    private static int maxNumbersOfSolutions = Integer.MAX_VALUE;
    private static Set<String> printedSolutions;
    private static Set<RowForm> requiredForms;
    private static Set<TransposedRowForm> requiredTransposedForms;

    public static void main(String[] args) {
        String filename = null;
        rowFormMap = new EnumMap<>(RowForm.class);
        printedSolutions = new HashSet<>();
        requiredForms = EnumSet.noneOf(RowForm.class);
        requiredTransposedForms = new HashSet<>();
        if (args.length > 0) {
            filename = args[0];
            try {
                parseArgumentsInFile(filename);
            } catch (IOException | FormatException ex) {
                ex.printStackTrace();
            }
        } else {
            System.out.println("Enter go-to row-forms");
            try {
                String[] p0Forms = promptForTransposedForms("from P/0: ");
                rowFormMap.put(RowForm.P, new HashSet<>(TransposedRowForm.fromStrings(p0Forms)));
                String[] i0Forms = promptForTransposedForms("from I/0: ");
                rowFormMap.put(RowForm.I, new HashSet<>(TransposedRowForm.fromStrings(i0Forms)));
                String[] r0Forms = promptForTransposedForms("from R/0: ");
                rowFormMap.put(RowForm.R, new HashSet<>(TransposedRowForm.fromStrings(r0Forms)));
                String[] ri0Forms = promptForTransposedForms("from RI/0: ");
                rowFormMap.put(RowForm.RI, new HashSet<>(TransposedRowForm.fromStrings(ri0Forms)));
            } catch (FormatException | NumberFormatException ex) {
                ex.printStackTrace();
                return;
            }

            String[] requiredClasses = promptForForms("Required form classes: ");
            for (String s : requiredClasses) {
                if (s != null && s.length() > 0) {
                    requiredForms.add(RowForm.valueOf(s.trim().toUpperCase()));
                }
            }

            String[] requiredTransposed = promptForForms("Required forms: ");
            try {
                requiredTransposedForms.addAll(TransposedRowForm.fromStrings(requiredTransposed));
            } catch (FormatException | NumberFormatException ex) {
                ex.printStackTrace();
                return;
            }

            try {
                minNumberOfRowsInChain = promptForNumber("Minimum number of series in chain: ");
                maxNumberOfRowsInChain = promptForNumber("Maximum number of series in chain: ");
                maxNumbersOfSolutions = promptForNumber("Maximum number of solutions to print: ");
            } catch (NumberFormatException ex) {
                System.out.println(ex.getMessage());
                return;
            }
            if (minNumberOfRowsInChain > maxNumberOfRowsInChain) {
                System.out.println("Max should be greater than or equal to min.");
                return;
            }
        }

        Stack<TransposedRowForm> lst = new Stack<>();
        lst.push(new TransposedRowForm(RowForm.P, 0));
        while (filename == null) {
            System.out.print("Enter a filename to save arguments, or [ENTER] to skip saving: ");
            Scanner scanner = new Scanner(System.in);
            filename = scanner.nextLine();
            //filename = System.console().readLine("Enter a filename to save arguments, or [ENTER] to skip saving: ");
            if (filename != null && filename.length() > 0) {
                try {
                    saveArgumentsToFile(filename);
                } catch (IOException ex) {
                    System.out.println(ex);
                    filename = null;
                }
            } else {
                break;
            }
        }
        traverseFrom(lst);
    }

    private static void parseArgumentsInFile(String filename) throws IOException, FormatException {
        File file = new File(filename);
        try (BufferedReader sr = new BufferedReader(new FileReader(file))) {
            String line = sr.readLine();
            while (line != null) {
                //var line = sr.ReadLine().Trim();
                if (line.startsWith("#")) {
                    line = sr.readLine();
                    continue;
                }
                String[] parts = line.split("=");
                String key = parts[0].trim();
                String value = parts[1].trim();
                switch (key) {
                    case "minNumberOfRowsInChain":
                        minNumberOfRowsInChain = Integer.parseInt(value);
                        break;
                    case "maxNumberOfRowsInChain":
                        maxNumberOfRowsInChain = Integer.parseInt(value);
                        break;
                    case "maxNumbersOfSolutions":
                        maxNumbersOfSolutions = Integer.parseInt(value);
                        break;
                    case "requiredTransposedForms":
                        {
                            String[] forms = value.split(" ");
                            requiredTransposedForms.addAll(TransposedRowForm.fromStrings(forms));
                            break;
                        }
                    case "requiredForms":
                        {
                            String[] forms = value.split(" ");
                            requiredForms.addAll(RowForm.fromStrings(forms));
                            break;
                        }
                    default:
                        try {
                            RowForm form = RowForm.valueOf(key);
                            Collection<TransposedRowForm> list = TransposedRowForm.fromStrings(value.split(" "));
                            rowFormMap.put(form, new HashSet<>(list));
                        } catch (IllegalArgumentException ex) {
                            // If no match, ignore the argument
                        }   break;
                }
                line = sr.readLine();
            }
        }
    }

    private static void saveArgumentsToFile(String filename) throws IOException {
        File file = new File(filename);
        try (BufferedWriter sw = new BufferedWriter(new FileWriter(file))) {
            sw.write("minNumberOfRowsInChain=" + minNumberOfRowsInChain + "\r\n");
            sw.write("maxNumberOfRowsInChain=" + maxNumberOfRowsInChain + "\r\n");
            sw.write("maxNumbersOfSolutions=" + maxNumbersOfSolutions + "\r\n");

            for (Entry<RowForm, Set<TransposedRowForm>> entry : rowFormMap.entrySet()) {
                sw.write(entry.getKey() + "=" + TransposedRowForm.toString(entry.getValue()) + "\r\n");
            }

            if (requiredTransposedForms.size() > 0) {
                sw.write("requiredTransposedForms=" + TransposedRowForm.toString(requiredTransposedForms, " "));
            }
        }
    }

    private static void traverseFrom(Stack<TransposedRowForm> transposedRowForms) {
        if (printedSolutions.size() >= maxNumbersOfSolutions) {
            return;
        }
        if (transposedRowForms.size() >= maxNumberOfRowsInChain) {
            return;
        }
        TransposedRowForm last = transposedRowForms.peek();
        Set<TransposedRowForm> allowed = rowFormMap.get(last.RowForm);
        for (TransposedRowForm form : allowed) {
            int transposedSteps = (last.Steps + form.Steps) % 12;
            TransposedRowForm newForm = new TransposedRowForm(form.RowForm, transposedSteps);

            if (transposedRowForms.contains(newForm) && ((newForm.RowForm != RowForm.P) || (newForm.Steps != 0))) {
                continue;
            }
            transposedRowForms.push(newForm);
            if (isValidSolution(transposedRowForms)) {
                String toPrint = TransposedRowForm.toString(transposedRowForms, " ->");
                if (!printedSolutions.contains(toPrint)) {
                    System.out.println(toPrint);
                    printedSolutions.add(toPrint);
                }
            }
            traverseFrom(transposedRowForms);
            transposedRowForms.pop();
        }
    }

    private static Set<RowForm> extractRowFormClasses(Iterable<TransposedRowForm> transposedRowForms) {
        Set<RowForm> usedFormClasses = EnumSet.noneOf(RowForm.class);
        for (TransposedRowForm trf : transposedRowForms) {
            usedFormClasses.add(trf.RowForm);
        }
        return usedFormClasses;
    }

    private static String[] promptForTransposedForms(String prompt) {
        System.out.print(prompt);
        Scanner scanner = new Scanner(System.in);
        String input = scanner.nextLine();
        return input.split(" ");
    }

    private static String[] promptForForms(String prompt) {
        System.out.print(prompt);
        Scanner scanner = new Scanner(System.in);
        String input = scanner.nextLine();
        return input.split(" ");
    }

    private static int promptForNumber(String prompt) throws NumberFormatException {
        System.out.print(prompt);
        Scanner scanner = new Scanner(System.in);
        String input = scanner.nextLine();
        return Integer.parseInt(input);
    }

    private static boolean isValidSolution(Stack<TransposedRowForm> transposedRowForms) {
        if (transposedRowForms.size() < minNumberOfRowsInChain) {
            return false;
        }
        TransposedRowForm lastForm = transposedRowForms.peek();
        if (lastForm.RowForm != RowForm.P || lastForm.Steps != 0) {
            return false;
        }
        int numberOfP0s = 0;
        for (TransposedRowForm trf : transposedRowForms) {
            if (trf.RowForm == RowForm.P && lastForm.Steps == 0) {
                ++numberOfP0s;
                if (numberOfP0s >= 3) {
                    return false;
                }
            }
        }
        if (!transposedRowForms.containsAll(requiredTransposedForms)) {
            return false;
        } else if (!extractRowFormClasses(transposedRowForms).containsAll(requiredForms)) {
            return false;
        }
        return true;
    }
}





Code:
/*
 * To change this license header, choose License Headers in Project Properties.
 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */
package calebschainer;

/**
 *
 * @author Test
 */
public class FormatException extends Exception {

    public FormatException() {
    }
    
}





Code:
/*
 * To change this license header, choose License Headers in Project Properties.
 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */
package calebschainer;

import java.util.ArrayList;
import java.util.Collection;
import java.util.List;

/**
 *
 * @author Test
 */
enum RowForm {
    P,
    I,
    R,
    RI;

    public static Collection<RowForm> fromStrings(String[] source) throws FormatException {
        List<RowForm> ret = new ArrayList<>();
        for (String s : source) {
            if (s.length() > 0) {
                ret.add(valueOf(s));
            }
        }
        return ret;
    }
}






Code:
/*
 * To change this license header, choose License Headers in Project Properties.
 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */
package calebschainer;

import java.util.ArrayList;
import java.util.Collection;
import java.util.List;
import java.util.Objects;

/**
 *
 * @author Test
 */
class TransposedRowForm {

    public RowForm RowForm;
    public int Steps;

    public TransposedRowForm(String s) throws FormatException {
        String[] parts = s.toUpperCase().split("/");
        if (parts.length != 2) {
            throw new FormatException();
        }
        RowForm = RowForm.valueOf(parts[0]);
        Steps = Integer.parseInt(parts[1]);
    }

    public TransposedRowForm(RowForm rowForm, int steps) {
        RowForm = rowForm;
        Steps = steps;
    }

    public static Collection<TransposedRowForm> fromStrings(String[] source) throws FormatException {
        List<TransposedRowForm> ret = new ArrayList<>();
        for (String s : source) {
            if (s.length() > 0) {
                ret.add(new TransposedRowForm(s));
            }
        }
        return ret;
    }

    public static String toString(Iterable<TransposedRowForm> transposedRowForms) {
        return toString(transposedRowForms, " ");
    }

    public static String toString(Iterable<TransposedRowForm> transposedRowForms, String separator) {
        StringBuilder sb = new StringBuilder();
        for (TransposedRowForm form : transposedRowForms) {
            sb.append(form.RowForm.toString());
            sb.append('/');
            sb.append(form.Steps);
            sb.append(separator);
        }
        if (sb.length() > 0) {
            sb.setLength(sb.length() - separator.length());
        }
        return sb.toString();
    }

    @Override
    public boolean equals(Object other) {
        if (other == null || !(other instanceof TransposedRowForm)) {
            return super.equals(other);
        }
        TransposedRowForm otherForm = (TransposedRowForm) other;
        return otherForm.RowForm == this.RowForm && otherForm.Steps == this.Steps;
    }

    @Override
    public int hashCode() {
        int hash = 5;
        hash = 61 * hash + Objects.hashCode(this.RowForm);
        hash = 61 * hash + this.Steps;
        return hash;
    }

}

Last edited by calebprime; 15th July 2018 at 06:32 AM.
calebprime is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 16th July 2018, 05:02 AM   #275
calebprime
moleman
 
calebprime's Avatar
 
Join Date: Jul 2006
Posts: 12,166
If we now require slightly different parameters, the program finds some thirty+ groups of series, or some 330+. Here we require no spacing exceptions, a 12-note motif, a maximum spacing of 6, and 4 occurrences of the motif embedded in the series.

Of these, I've studied one, and found that it works just fine with the row chainer. The work involves finding where each form of the row can go based on embedding. In this scheme, it can go to a new series when relatively few pitches are needed to be added between each of the original pitches.


Search


Code:
                                        modulus: 12
         wolf intervals (between any two notes): ()
                     display multiple spellings: #f
    acceptable error when naming scales (cents): 0
                                     sort order: (rotation packing)
             abbreviated multiple-column output: #t
                                  output format: numbers
                       number of output columns: 3
                                     row length: 12
                                      bad cells: ((4 0 3 6 9) (4 0 1 2))
                    maximum number of bad cells: 0
                                     good cells: ()
                   minimum number of good cells: 0
      bad intervals (between consecutive notes): ()
                maximum number of bad intervals: 0
     good intervals (between consecutive notes): ()
               minimum number of good intervals: 0
          minimum number of different intervals: 3
   maximum number of same consecutive intervals: 2
             self-equivalence filter - standard: #f
                   self-equivalence filter - 5m: #f
              self-equivalence filter tolerance: 0
                         remove near-duplicates: #f
                       near-duplicate tolerance: 0
         wrap when counting cells and intervals: #t
      virtual row length, for computing spacing: 12
                                   motif length: 12
     look for standard transformations of motif: #t
           look for 5m transformations of motif: #f
                                minimum spacing: 1
                                maximum spacing: 6
minimum number of violations of min/max spacing: 0
maximum number of violations of min/max spacing: 0
                     minimum number of 1-spaces: 0
                     maximum number of 1-spaces: 3
  minimum number of occurrences of motif in row: 4
                    wrap when computing spacing: #t
              maximum number of rows to display: 6000
               file of results to search within: 

finding rows.............................................................................................................................................................................................................................................................done

number of rows found: 332

(0 1 3 6 8 9 11 2 4 5 7 10)  (0 1 3 7 10 5 4 11 2 6 8 9)  (0 1 4 8 5 9 3 11 2 10 7 6)  
(0 2 3 5 8 10 11 1 4 6 7 9)  (0 1 4 5 7 11 2 9 8 3 6 10)  (0 3 7 4 8 2 10 1 9 6 5 11)  
(0 2 5 7 8 10 1 3 4 6 9 11)  (0 2 3 6 7 9 1 4 11 10 5 8)  (0 3 11 8 7 1 2 5 9 6 10 4)  
(0 3 5 6 8 11 1 2 4 7 9 10)  (0 2 6 9 4 3 10 1 5 7 8 11)  (0 4 1 5 11 7 10 6 3 2 8 9)  
                             (0 3 4 6 10 1 8 7 2 5 9 11)  (0 4 10 6 9 5 2 1 7 8 11 3)  
                             (0 3 7 9 10 1 2 4 8 11 6 5)  (0 6 2 5 1 10 9 3 4 7 11 8)  
                             (0 3 10 9 4 7 11 1 2 5 6 8)  (0 6 7 10 2 11 3 9 5 8 4 1)  
                             (0 4 6 7 10 11 1 5 8 3 2 9)  (0 8 5 4 10 11 2 6 3 7 1 9)  
                             (0 4 7 2 1 8 11 3 5 6 9 10)  (0 8 11 7 4 3 9 10 1 5 2 6)  
                             (0 7 6 1 4 8 10 11 2 3 5 9)  (0 9 1 7 3 6 2 11 10 4 5 8)  
                             (0 7 10 2 4 5 8 9 11 3 6 1)  (0 9 8 2 3 6 10 7 11 5 1 4)  
                             (0 11 6 9 1 3 4 7 8 10 2 5)  (0 11 5 6 9 1 10 2 8 4 7 3)  

(0 1 4 8 6 11 3 10 2 7 5 9)  (0 1 5 10 4 11 7 6 9 2 8 3)  (0 1 6 3 11 9 8 5 4 2 10 7)  
(0 3 4 7 11 9 2 6 1 5 10 8)  (0 3 8 2 9 6 7 11 4 10 5 1)  (0 5 2 10 8 7 4 3 1 9 6 11)  
(0 3 7 5 10 2 9 1 6 4 8 11)  (0 4 9 3 10 6 5 8 1 7 2 11)  (0 5 6 11 8 4 2 1 10 9 7 3)  
(0 4 2 7 11 6 10 3 1 5 8 9)  (0 5 11 6 2 1 4 9 3 10 7 8)  (0 8 5 10 11 4 1 9 7 6 3 2)  
(0 4 7 8 11 3 1 6 10 5 9 2)  (0 5 11 6 3 4 8 1 7 2 10 9)  (0 8 6 5 2 1 11 7 4 9 10 3)  
(0 4 9 7 11 2 3 6 10 8 1 5)  (0 6 1 9 8 11 4 10 5 2 3 7)  (0 9 2 3 8 5 1 11 10 7 6 4)  
(0 4 11 3 8 6 10 1 2 5 9 7)  (0 6 1 10 11 3 8 2 9 5 4 7)  (0 9 5 3 2 11 10 8 4 1 6 7)  
(0 5 3 7 10 11 2 6 4 9 1 8)  (0 7 3 2 5 10 4 11 8 9 1 6)  (0 9 8 6 2 11 4 5 10 7 3 1)  
(0 5 9 4 8 1 11 3 6 7 10 2)  (0 7 4 5 9 2 8 3 11 10 1 6)  (0 10 6 3 8 9 2 11 7 5 4 1)  
(0 7 11 4 2 6 9 10 1 5 3 8)  (0 8 7 10 3 9 4 1 2 6 11 5)  (0 10 9 6 5 3 11 8 1 2 7 4)  
(0 10 2 5 6 9 1 11 4 8 3 7)  (0 9 10 2 7 1 8 4 3 6 11 5)  (0 11 8 7 5 1 10 3 4 9 6 2)  
(0 10 3 7 2 6 11 9 1 4 5 8)  (0 11 2 7 1 8 5 6 10 3 9 4)  (0 11 9 5 2 7 8 1 10 6 4 3)  

(0 1 7 5 10 2 8 6 11 3 9 4)  (0 1 7 6 3 11 2 10 4 8 5 9)  (0 1 7 6 9 2 5 4 10 11 8 3)  
(0 4 10 5 1 2 8 6 11 3 9 7)  (0 3 4 10 9 6 2 5 1 7 11 8)  (0 1 10 5 2 3 9 8 11 4 7 6)  
(0 4 10 8 1 5 11 6 2 3 9 7)  (0 3 11 5 9 6 10 1 2 8 7 4)  (0 3 2 8 9 6 1 10 11 5 4 7)  
(0 5 9 3 1 6 10 4 11 7 8 2)  (0 4 1 5 8 9 3 2 11 7 10 6)  (0 3 8 11 10 4 5 2 9 6 7 1)  
(0 5 9 3 10 6 7 1 11 4 8 2)  (0 4 7 8 2 1 10 6 9 5 11 3)  (0 5 8 7 1 2 11 6 3 4 10 9)  
(0 6 1 9 10 4 2 7 11 5 3 8)  (0 6 5 2 10 1 9 3 7 4 8 11)  (0 6 5 8 1 4 3 9 10 7 2 11)  
(0 6 4 9 1 7 2 10 11 5 3 8)  (0 6 10 7 11 2 3 9 8 5 1 4)  (0 6 7 4 11 8 9 3 2 5 10 1)  
(0 6 4 9 1 7 5 10 2 8 3 11)  (0 8 2 6 3 7 10 11 5 4 1 9)  (0 7 4 5 11 10 1 6 9 8 2 3)  
(0 7 3 4 10 8 1 5 11 9 2 6)  (0 8 11 7 1 5 2 6 9 10 4 3)  (0 9 4 1 2 8 7 10 3 6 5 11)  
(0 8 9 3 1 6 10 4 2 7 11 5)  (0 9 1 4 5 11 10 7 3 6 2 8)  (0 9 10 4 3 6 11 2 1 7 8 5)  
(0 10 3 7 1 8 4 5 11 9 2 6)  (0 9 5 8 4 10 2 11 3 6 7 1)  (0 11 2 7 10 9 3 4 1 8 5 6)  
(0 10 3 7 1 11 4 8 2 9 5 6)  (0 11 8 4 7 3 9 1 10 2 5 6)  (0 11 5 6 3 10 7 8 2 1 4 9)  

(0 1 8 5 10 3 7 6 11 2 9 4)  (0 1 9 4 10 2 7 5 11 3 8 6)  (0 1 9 4 11 2 7 6 10 3 8 5)  
(0 3 10 5 1 2 9 6 11 4 8 7)  (0 4 9 7 1 2 10 5 11 3 8 6)  (0 3 8 7 11 4 9 6 1 2 10 5)  
(0 4 3 8 11 6 1 9 10 5 2 7)  (0 4 9 7 1 5 10 8 2 3 11 6)  (0 4 9 2 11 6 7 3 10 5 8 1)  
(0 5 8 3 10 6 7 2 11 4 9 1)  (0 5 3 9 1 6 4 10 11 7 2 8)  (0 5 2 9 10 6 1 8 11 4 3 7)  
(0 5 9 8 1 4 11 6 2 3 10 7)  (0 5 3 9 10 6 1 7 11 4 2 8)  (0 5 4 8 1 6 3 10 11 7 2 9)  
(0 5 10 2 1 6 9 4 11 7 8 3)  (0 6 7 3 10 4 8 1 11 5 9 2)  (0 5 10 7 2 3 11 6 1 4 9 8)  
(0 7 2 10 11 6 3 8 1 5 4 9)  (0 6 10 3 1 7 8 4 11 5 9 2)  (0 7 2 5 10 9 1 6 11 8 3 4)  
(0 7 3 4 11 8 1 6 10 9 2 5)  (0 6 10 3 1 7 11 4 2 8 9 5)  (0 7 8 4 11 6 9 2 1 5 10 3)  
(0 7 4 9 2 6 5 10 1 8 3 11)  (0 7 1 5 10 8 2 6 11 9 3 4)  (0 7 10 3 2 6 11 4 1 8 9 5)  
(0 8 9 4 1 6 11 3 2 7 10 5)  (0 8 3 9 1 6 4 10 2 7 5 11)  (0 8 3 10 1 6 5 9 2 7 4 11)  
(0 9 2 7 11 10 3 6 1 8 4 5)  (0 10 4 5 1 8 2 6 11 9 3 7)  (0 9 4 5 1 8 3 6 11 10 2 7)  
(0 11 4 7 2 9 5 6 1 10 3 8)  (0 10 4 8 1 11 5 6 2 9 3 7)  (0 11 3 8 1 10 5 6 2 9 4 7)  

(0 1 10 5 11 4 7 6 2 9 3 8)  (0 2 4 7 11 3 6 8 10 1 5 9)  (0 2 7 3 5 10 6 8 1 9 11 4)  
(0 3 2 10 5 11 4 8 9 6 1 7)  (0 2 5 9 1 4 6 8 11 3 7 10)  (0 5 1 3 8 4 6 11 7 9 2 10)  
(0 4 5 2 9 3 8 11 10 6 1 7)  (0 3 5 7 10 2 6 9 11 1 4 8)  (0 8 10 3 11 1 6 2 4 9 5 7)  
(0 5 8 7 3 10 4 9 1 2 11 6)  (0 3 7 11 2 4 6 9 1 5 8 10)                               
(0 5 9 10 7 2 8 1 4 3 11 6)  (0 4 7 9 11 2 6 10 1 3 5 8)                               
(0 6 11 2 1 9 4 10 3 7 8 5)  (0 4 8 11 1 3 6 10 2 5 7 9)                               
(0 6 11 3 4 1 8 2 7 10 9 5)                                                            
(0 7 1 6 9 8 4 11 5 10 2 3)                                                            
(0 7 1 6 10 11 8 3 9 2 5 4)                                                            
(0 8 3 9 2 6 7 4 11 5 10 1)                                                            
(0 9 4 10 3 6 5 1 8 2 7 11)                                                            
(0 11 7 2 8 1 5 6 3 10 4 9)                                                            

(0 2 7 3 11 4 10 5 9 1 8 6)  (0 2 7 11 5 1 8 6 9 4 10 3)  (0 2 8 4 11 1 7 6 10 3 9 5)  
(0 4 8 3 1 7 9 2 10 6 11 5)  (0 3 10 4 9 6 8 1 5 11 7 2)  (0 2 8 7 11 4 10 6 1 3 9 5)  
(0 4 11 9 3 5 10 6 2 7 1 8)  (0 4 10 6 1 11 2 9 3 8 5 7)  (0 4 9 3 11 6 8 2 10 5 7 1)  
(0 5 1 9 2 8 3 7 11 6 4 10)  (0 5 2 4 9 1 7 3 10 8 11 6)  (0 5 11 7 2 4 10 6 1 3 9 8)  
(0 5 11 6 10 2 9 7 1 3 8 4)  (0 5 9 3 11 6 4 7 2 8 1 10)  (0 6 2 9 11 5 1 8 10 4 3 7)  
(0 6 1 5 9 4 2 8 10 3 11 7)  (0 6 2 9 7 10 5 11 4 1 3 8)  (0 6 2 9 11 5 4 8 1 7 3 10)  
(0 6 8 1 9 5 10 4 11 3 7 2)  (0 6 11 8 10 3 7 1 9 4 2 5)  (0 6 5 9 2 8 4 11 1 7 3 10)  
(0 7 5 11 1 6 2 10 3 9 4 8)  (0 7 1 6 3 5 10 2 8 4 11 9)  (0 7 9 3 2 6 11 5 1 8 10 4)  
(0 7 11 3 10 8 2 4 9 5 1 6)  (0 7 5 8 3 9 2 11 1 6 10 4)  (0 7 9 3 11 6 8 2 1 5 10 4)  
(0 8 1 7 2 6 10 5 3 9 11 4)  (0 8 3 1 4 11 5 10 7 9 2 6)  (0 8 3 5 11 7 2 4 10 9 1 6)  
(0 8 4 9 3 10 2 6 1 11 5 7)  (0 9 11 4 8 2 10 5 3 6 1 7)  (0 8 3 5 11 10 2 7 1 9 4 6)  
(0 10 4 6 11 7 3 8 2 9 1 5)  (0 10 1 8 2 7 4 6 11 3 9 5)  (0 11 3 8 2 10 5 7 1 9 4 6)  

(0 2 8 6 1 5 9 4 10 3 11 7)  (0 2 9 5 10 6 1 3 11 8 7 4)  (0 2 9 5 11 1 8 4 10 3 7 6)  
(0 4 8 3 9 2 10 6 11 1 7 5)  (0 2 10 7 6 3 11 1 8 4 9 5)  (0 2 9 5 11 4 8 7 1 3 10 6)  
(0 4 11 5 10 6 2 7 9 3 1 8)  (0 5 1 8 10 6 3 2 11 7 9 4)  (0 4 3 9 11 6 2 8 10 5 1 7)  
(0 5 1 9 2 4 10 8 3 7 11 6)  (0 7 3 8 4 11 1 9 6 5 2 10)  (0 5 9 8 2 4 11 7 1 3 10 6)  
(0 5 7 1 11 6 10 2 9 3 8 4)  (0 7 9 5 2 1 10 6 8 3 11 4)  (0 6 8 3 11 5 7 2 10 4 9 1)  
(0 6 4 11 3 7 2 8 1 9 5 10)  (0 8 1 9 4 6 2 11 10 7 3 5)  (0 6 8 3 11 5 10 2 1 7 9 4)  
(0 6 11 7 3 8 10 4 2 9 1 5)  (0 8 3 5 1 10 9 6 2 4 11 7)  (0 6 11 3 2 8 10 5 1 7 9 4)  
(0 7 1 6 2 10 3 5 11 9 4 8)  (0 8 5 4 1 9 11 6 2 7 3 10)  (0 7 3 9 2 6 5 11 1 8 4 10)  
(0 7 11 3 10 4 9 5 1 6 8 2)  (0 8 10 5 1 6 2 9 11 7 4 3)  (0 7 3 9 11 6 2 8 1 5 4 10)  
(0 8 1 3 9 7 2 6 10 5 11 4)  (0 9 5 7 2 10 3 11 6 8 4 1)  (0 8 2 4 11 7 1 6 10 9 3 5)  
(0 8 4 9 11 5 3 10 2 6 1 7)  (0 9 8 5 1 3 10 6 11 7 2 4)  (0 8 2 7 11 10 4 6 1 9 3 5)  
(0 10 5 9 1 8 2 7 3 11 4 6)  (0 11 8 4 6 1 9 2 10 5 7 3)  (0 11 5 7 2 10 4 6 1 9 3 8)  

(0 2 10 3 5 1 6 8 4 9 11 7)  (0 2 11 4 10 5 8 6 1 9 3 7)  (0 3 6 11 4 10 5 9 1 8 2 7)  
(0 5 7 3 8 10 6 11 1 9 2 4)  (0 3 1 8 4 10 2 7 9 6 11 5)  (0 3 8 1 7 2 6 10 5 11 4 9)  
(0 8 1 3 11 4 6 2 7 9 5 10)  (0 4 9 11 8 1 7 2 5 3 10 6)  (0 4 8 3 9 2 7 10 1 6 11 5)  
                             (0 5 7 4 9 3 10 1 11 6 2 8)  (0 4 11 5 10 3 6 9 2 7 1 8)  
                             (0 5 11 6 9 7 2 10 4 8 1 3)  (0 5 8 11 4 9 3 10 2 6 1 7)  
                             (0 6 1 4 2 9 5 11 3 8 10 7)  (0 5 10 1 4 9 2 8 3 7 11 6)  
                             (0 6 10 3 5 2 7 1 8 11 9 4)  (0 5 10 4 11 3 7 2 8 1 6 9)  
                             (0 7 3 9 1 6 8 5 10 4 11 2)  (0 5 11 6 10 2 9 3 8 1 4 7)  
                             (0 7 10 8 3 11 5 9 2 4 1 6)  (0 6 1 5 9 4 10 3 8 11 2 7)  
                             (0 8 2 6 11 1 10 3 9 4 7 5)  (0 6 11 4 7 10 3 8 2 9 1 5)  
                             (0 9 2 8 3 6 4 11 7 1 5 10)  (0 7 1 6 11 2 5 10 3 9 4 8)  
                             (0 10 5 1 7 11 4 6 3 8 2 9)  (0 7 11 3 10 4 9 2 5 8 1 6)  

(0 3 7 1 9 6 2 5 10 4 11 8)  (0 3 7 4 11 2 9 6 10 1 8 5)  (0 3 7 4 11 5 10 1 9 6 2 8)  
(0 3 8 2 9 6 10 1 5 11 7 4)  (0 3 10 7 2 5 9 6 1 4 11 8)  (0 3 11 8 4 10 2 5 9 6 1 7)  
(0 4 7 11 5 1 10 6 9 2 8 3)  (0 3 10 7 11 2 9 6 1 4 8 5)  (0 4 1 8 2 7 10 6 3 11 5 9)  
(0 4 10 6 3 11 2 7 1 8 5 9)  (0 4 1 8 11 6 3 7 10 5 2 9)  (0 4 7 11 8 3 9 2 5 1 10 6)  
(0 5 11 6 3 7 10 2 8 4 1 9)  (0 4 7 2 11 6 9 1 10 5 8 3)  (0 5 8 4 1 9 3 7 10 2 11 6)  
(0 6 1 10 2 5 9 3 11 8 4 7)  (0 7 4 8 11 6 3 10 1 5 2 9)  (0 6 10 1 5 2 9 3 8 11 7 4)  
(0 6 2 11 7 10 3 9 4 1 5 8)  (0 7 4 11 2 6 3 10 1 8 5 9)  (0 6 11 2 10 7 3 9 1 4 8 5)  
(0 7 4 8 11 3 9 5 2 10 1 6)  (0 7 10 2 11 6 9 4 1 5 8 3)  (0 7 1 6 9 5 2 10 4 8 11 3)  
(0 8 5 1 4 9 3 10 7 11 2 6)  (0 7 10 5 2 6 9 4 1 8 11 3)  (0 8 2 6 9 1 10 5 11 4 7 3)  
(0 8 11 4 10 5 2 6 9 1 7 3)  (0 9 1 4 11 8 3 6 10 7 2 5)  (0 8 5 1 7 11 2 6 3 10 4 9)  
(0 9 1 4 8 2 10 7 3 6 11 5)  (0 9 4 7 2 11 3 6 1 10 5 8)  (0 9 4 10 3 6 2 11 7 1 5 8)  
(0 9 5 8 1 7 2 11 3 6 10 4)  (0 9 4 7 11 8 3 6 1 10 2 5)  (0 9 5 11 3 6 10 7 2 8 1 4)  

(0 3 8 5 1 4 9 6 11 2 10 7)  (0 4 2 9 1 11 6 10 8 3 7 5)  (0 4 11 9 1 8 6 10 5 3 7 2)  
(0 3 8 5 10 1 9 6 11 2 7 4)  (0 7 11 9 4 8 6 1 5 3 10 2)  (0 7 5 9 4 2 6 1 11 3 10 8)  
(0 3 11 8 1 4 9 6 2 5 10 7)  (0 10 5 9 7 2 6 4 11 3 1 8)  (0 10 2 9 7 11 6 4 8 3 1 5)  
(0 5 2 7 10 6 3 8 11 4 1 9)                                                            
(0 5 2 10 1 6 3 8 11 7 4 9)                                                            
(0 5 8 1 10 6 9 2 11 4 7 3)                                                            
(0 5 8 4 1 6 9 2 11 7 10 3)                                                            
(0 8 5 10 1 6 3 11 2 7 4 9)                                                            
(0 8 11 4 1 6 9 5 2 7 10 3)                                                            
(0 9 2 5 1 10 3 6 11 8 4 7)                                                            
(0 9 2 5 10 7 3 6 11 8 1 4)                                                            
(0 9 5 8 1 10 3 6 2 11 4 7)                                                            

(0 5 1 9 2 8 3 10 7 4 11 6)  (0 8 4 1 11 9 6 2 10 7 5 3)  (0 9 7 6 4 1 11 10 8 5 3 2)  
(0 5 11 6 1 10 7 2 9 3 8 4)  (0 8 5 3 1 10 6 2 11 9 7 4)  (0 10 7 5 4 2 11 9 8 6 3 1)  
(0 6 1 8 5 2 9 4 10 3 11 7)  (0 9 5 1 10 8 6 3 11 7 4 2)  (0 10 9 7 4 2 1 11 8 6 5 3)  
(0 6 11 7 3 8 2 9 4 1 10 5)  (0 9 7 5 2 10 6 3 1 11 8 4)  (0 11 9 6 4 3 1 10 8 7 5 2)  
(0 7 1 6 2 10 3 9 4 11 8 5)  (0 10 7 3 11 8 6 4 1 9 5 2)                               
(0 7 2 8 1 9 5 10 4 11 6 3)  (0 10 8 5 1 9 6 4 2 11 7 3)                               
(0 7 2 11 8 3 10 4 9 5 1 6)                                                            
(0 7 4 1 8 3 9 2 10 6 11 5)                                                            
(0 8 1 7 2 9 6 3 10 5 11 4)                                                            
(0 8 4 9 3 10 5 2 11 6 1 7)                                                            
(0 9 4 11 5 10 6 2 7 1 8 3)                                                            
(0 9 6 1 8 2 7 3 11 4 10 5)



Study


Code:
(0 1 7 5 10 2 8 6 11 3 9 4) 

C,Db,G,F,Bb,D,Ab,Gb,B,Eb,A,E


1,6,10,5,4,6,10,5,4,6,7,8     1,4,5,6,7,8,10    meh

P/0
        v       ^               ^
C,  Db, G,  F,  Bb, D,  Ab, Gb, B,  Eb, A,  E
B,  C,  Gb, E,  A,  Db, G,  F,  Bb, D,  Ab, Eb
F,  Gb, C,  Bb, Eb, G,  Db, B,  E,  Ab, D,  A
G,  Ab, D,  C,  F,  A,  Eb, Db, Gb, Bb, E,  B
D,  Eb, A,  G,  C,  E,  Bb, Ab, Db, F,  B,  Gb
Bb, B,  F,  Eb, Ab, C,  Gb, E,  A,  Db, G,  D
E,  F,  B,  A,  D,  Gb, C,  Bb, Eb, G,  Db, Ab
Gb, G,  Db, B,  E,  Ab, D,  C,  F,  A,  Eb, Bb
Db, D,  Ab, Gb, B,  Eb, A,  G,  C,  E,  Bb, F
A,  Bb, E,  D,  G,  B,  F,  Eb, Ab, C,  Gb, Db
Eb, E,  Bb, Ab, Db, F,  B,  A,  D,  Gb, C,  G        <--  r/3
Ab, A,  Eb, Db, Gb, Bb, E,  D,  G,  B,  F,  C    --> 1 wrong




I/0
        v       ^               ^
C,  B,  F,  G,  D,  Bb, E,  Gb, Db, A,  Eb, Ab
Db, C,  Gb, Ab, Eb, B,  F,  G,  D,  Bb, E,  A
G,  Gb, C,  D,  A,  F,  B,  Db, Ab, E,  Bb, Eb
F,  E,  Bb, C,  G,  Eb, A,  B,  Gb, D,  Ab, Db
Bb, A,  Eb, F,  C,  Ab, D,  E,  B,  G,  Db, Gb
D,  Db, G,  A,  E,  C,  Gb, Ab, Eb, B,  F,  Bb
Ab, G,  Db, Eb, Bb, Gb, C,  D,  A,  F,  B,  E
Gb, F,  B,  Db, Ab, E,  Bb, C,  G,  Eb, A,  D
B,  Bb, E,  Gb, Db, A,  Eb, F,  C,  Ab, D,  G
Eb, D,  Ab, Bb, F,  Db, G,  A,  E,  C,  Gb, B
A,  Ab, D,  E,  B,  G,  Db, Eb, Bb, Gb, C,  F      <---
E,  Eb, A,  B,  Gb, D,  Ab, Bb, F,  Db, G,  C   --> 1 wrong




R/0

E,  A,  Eb, B,  Gb, Ab, D,  Bb, F,  G,  Db, C
B,  E,  Bb, Gb, Db, Eb, A,  F,  C,  D,  Ab, G
F,  Bb, E,  C,  G,  A,  Eb, B,  Gb, Ab, D,  Db
A,  D,  Ab, E,  B,  Db, G,  Eb, Bb, C,  Gb, F
D,  G,  Db, A,  E,  Gb, C,  Ab, Eb, F,  B,  Bb
C,  F,  B,  G,  D,  E,  Bb, Gb, Db, Eb, A,  Ab
Gb, B,  F,  Db, Ab, Bb, E,  C,  G,  A,  Eb, D
Bb, Eb, A,  F,  C,  D,  Ab, E,  B,  Db, G,  Gb
Eb, Ab, D,  Bb, F,  G,  Db, A,  E,  Gb, C,  B
Db, Gb, C,  Ab, Eb, F,  B,  G,  D,  E,  Bb, A
G,  C,  Gb, D,  A,  B,  F,  Db, Ab, Bb, E,  Eb
Ab, Db, G,  Eb, Bb, C,  Gb, D,  A,  B,  F,  E




RI/0

Ab, Eb, A,  Db, Gb, E,  Bb, D,  G,  F,  B,  C
Db, Ab, D,  Gb, B,  A,  Eb, G,  C,  Bb, E,  F
G,  D,  Ab, C,  F,  Eb, A,  Db, Gb, E,  Bb, B
Eb, Bb, E,  Ab, Db, B,  F,  A,  D,  C,  Gb, G
Bb, F,  B,  Eb, Ab, Gb, C,  E,  A,  G,  Db, D
C,  G,  Db, F,  Bb, Ab, D,  Gb, B,  A,  Eb, E
Gb, Db, G,  B,  E,  D,  Ab, C,  F,  Eb, A,  Bb
D,  A,  Eb, G,  C,  Bb, E,  Ab, Db, B,  F,  Gb
A,  E,  Bb, D,  G,  F,  B,  Eb, Ab, Gb, C,  Db
B,  Gb, C,  E,  A,  G,  Db, F,  Bb, Ab, D,  Eb
F,  C,  Gb, Bb, Eb, Db, G,  B,  E,  D,  Ab, A
E,  B,  F,  A,  D,  C,  Gb, Bb, Eb, Db, G,  Ab



p/0 to r/3   p/0 to i/7   p/0 to ri/10  p/0 to ri/11

R/0 to p/3  r/0 to ri/7  r/0 to i/10 r/0 to i/11

i/0 to ri/9  i/0 to p/5  i/0 to r/2  i/0 to r/1

ri/0 to i/9  ri/0 to r/5  ri/0 to p/2  ri/0 to p/1







java -jar CCU.jar
Enter go-to row-forms
from P/0: r/3 i/7 ri/10 ri/11
from I/0: ri/9 p/5 r/2 r/1
from R/0: p/3   ri/7 i/10 i/11
from RI/0: i/9 r/5 p/2 p/1
Required form classes: p r ri i
Required forms: i/7 ri/11 ri/10 r/9
Minimum number of series in chain: 13
Maximum number of series in chain: 13
Maximum number of solutions to print: 50000
Enter a filename to save arguments, or [ENTER] to skip saving: better
P/0 ->RI/10 ->R/3 ->I/2 ->RI/11 ->R/4 ->I/3 ->RI/0 ->P/1 ->I/8 ->R/9 ->I/7 ->P/0
P/0 ->RI/10 ->R/3 ->I/2 ->RI/11 ->R/4 ->P/7 ->RI/5 ->R/10 ->I/8 ->R/9 ->I/7 ->P/0
etc.
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Old 17th July 2018, 06:46 AM   #276
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Originally Posted by calebprime View Post
Future posts of mine will explain why the goal of "dual" properties is not such a great one. Basically, one kind of self-similarity is adequate, and two different kinds is unnecessary, like having two, um, phalluses.

These posts should include what exactly each kind of self-sim is good for. I've done enough work with this material to have a good idea, now. It's more restrictive, less forgiving, than I would have thought.

Freed from the obligation to only discuss the freakish dual-property series, I can look at different populations of series.

For instance, there are around 8k series that have four shows with a spacing of 5, 1 exception, no 012's per 4 note fields, no 0369 per 4-note field, and no self-equivalence. I think only one or two series from that 8k currently have names, or qualify as "dual property."

So, henceforth and hitherto and forthwith, the subject of this thread is self-similar 12-tone series, the new beginning, or some such. Not dual.

Different kind of numerical series are good for writing different kinds of piece, I'll fill in later. This isn't merely empty truism. I've tried it.

This can be boiled down to a few things. My hard-earned rules of thumb.


>Use a pure power-residue index series (3 ^ n mod 17 or something) when you're going to map some series to a grid of scales (instead of the usual all-12 chromatic scale.) This is because the mapping to the scale introduces some variability or distortion. Don't combine an imperfect series with a mapping-to-scale: Two kinds of imperfection or distortion is too much "fractal wrongness." Use a mathematically perfect series when mapping to a scale.

> Don't use the rapid-wheel pitch generation technique (in which notes are picked at regular intervals from a "wheel" or ostinato-pattern) with a mapping to a 12-tone grid or ordinary-all-12-mapping. Although the future may yield some exceptions, so far the results have been that slightly nauseating shade of color: the color of all 12 tones at once. Rapid-pitch-wheel techniques should be mapped to scales.

> Only the smallest deviation from perfect self-sim can be tolerated (in the every-other kind of pitch-approximate self-sim.) As the imperfection is amplified in each link of the chain of series, it has to be small to begin with.

> Minimalist textures with ostinato patterns that gradually change according to some serial scheme are very forgiving and almost write themselves.
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Old 17th July 2018, 08:00 AM   #277
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Perhaps it will be understood that this is a peculiar world where eight thousand becomes forty eight becomes four very quickly.


Code:
                                       modulus: 12
         wolf intervals (between any two notes): ()
                     display multiple spellings: #f
    acceptable error when naming scales (cents): 0
                                     sort order: (rotation packing)
             abbreviated multiple-column output: #t
                                  output format: numbers
                       number of output columns: 3
                                     row length: 12
                                      bad cells: ((4 0 3 6 9) (4 0 1 2))
                    maximum number of bad cells: 0
                                     good cells: ()
                   minimum number of good cells: 0
      bad intervals (between consecutive notes): ()
                maximum number of bad intervals: 0
     good intervals (between consecutive notes): ()
               minimum number of good intervals: 0
          minimum number of different intervals: 3
   maximum number of same consecutive intervals: 2
             self-equivalence filter - standard: #t
                   self-equivalence filter - 5m: #f
              self-equivalence filter tolerance: 0
                         remove near-duplicates: #f
                       near-duplicate tolerance: 0
         wrap when counting cells and intervals: #t
      virtual row length, for computing spacing: 12
                                   motif length: 12
     look for standard transformations of motif: #t
           look for 5m transformations of motif: #f
                                minimum spacing: 1
                                maximum spacing: 6
minimum number of violations of min/max spacing: 0
maximum number of violations of min/max spacing: 0
                     minimum number of 1-spaces: 0
                     maximum number of 1-spaces: 3
  minimum number of occurrences of motif in row: 4
                    wrap when computing spacing: #t
              maximum number of rows to display: 6000
               file of results to search within: 

finding rows...........................................done

number of rows found: 48

(0 1 7 5 10 2 8 6 11 3 9 4)  (0 1 9 4 10 2 7 5 11 3 8 6)  (0 2 8 4 11 1 7 6 10 3 9 5)  
(0 4 10 5 1 2 8 6 11 3 9 7)  (0 4 9 7 1 2 10 5 11 3 8 6)  (0 2 8 7 11 4 10 6 1 3 9 5)  
(0 4 10 8 1 5 11 6 2 3 9 7)  (0 4 9 7 1 5 10 8 2 3 11 6)  (0 4 9 3 11 6 8 2 10 5 7 1)  
(0 5 9 3 1 6 10 4 11 7 8 2)  (0 5 3 9 1 6 4 10 11 7 2 8)  (0 5 11 7 2 4 10 6 1 3 9 8)  
(0 5 9 3 10 6 7 1 11 4 8 2)  (0 5 3 9 10 6 1 7 11 4 2 8)  (0 6 2 9 11 5 1 8 10 4 3 7)  
(0 6 1 9 10 4 2 7 11 5 3 8)  (0 6 7 3 10 4 8 1 11 5 9 2)  (0 6 2 9 11 5 4 8 1 7 3 10)  
(0 6 4 9 1 7 2 10 11 5 3 8)  (0 6 10 3 1 7 8 4 11 5 9 2)  (0 6 5 9 2 8 4 11 1 7 3 10)  
(0 6 4 9 1 7 5 10 2 8 3 11)  (0 6 10 3 1 7 11 4 2 8 9 5)  (0 7 9 3 2 6 11 5 1 8 10 4)  
(0 7 3 4 10 8 1 5 11 9 2 6)  (0 7 1 5 10 8 2 6 11 9 3 4)  (0 7 9 3 11 6 8 2 1 5 10 4)  
(0 8 9 3 1 6 10 4 2 7 11 5)  (0 8 3 9 1 6 4 10 2 7 5 11)  (0 8 3 5 11 7 2 4 10 9 1 6)  
(0 10 3 7 1 8 4 5 11 9 2 6)  (0 10 4 5 1 8 2 6 11 9 3 7)  (0 8 3 5 11 10 2 7 1 9 4 6)  
(0 10 3 7 1 11 4 8 2 9 5 6)  (0 10 4 8 1 11 5 6 2 9 3 7)  (0 11 3 8 2 10 5 7 1 9 4 6)  

(0 2 9 5 11 1 8 4 10 3 7 6)                                                            
(0 2 9 5 11 4 8 7 1 3 10 6)                                                            
(0 4 3 9 11 6 2 8 10 5 1 7)                                                            
(0 5 9 8 2 4 11 7 1 3 10 6)                                                            
(0 6 8 3 11 5 7 2 10 4 9 1)                                                            
(0 6 8 3 11 5 10 2 1 7 9 4)                                                            
(0 6 11 3 2 8 10 5 1 7 9 4)                                                            
(0 7 3 9 2 6 5 11 1 8 4 10)                                                            
(0 7 3 9 11 6 2 8 1 5 4 10)                                                            
(0 8 2 4 11 7 1 6 10 9 3 5)                                                            
(0 8 2 7 11 10 4 6 1 9 3 5)                                                            
(0 11 5 7 2 10 4 6 1 9 3 8)

Last edited by calebprime; 17th July 2018 at 08:01 AM.
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Old 18th July 2018, 07:46 AM   #278
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Originally Posted by calebprime View Post
Perhaps it will be understood that this is a peculiar world where eight thousand becomes forty eight becomes four very quickly.


Code:
                                       modulus: 12
         wolf intervals (between any two notes): ()
                     display multiple spellings: #f
    acceptable error when naming scales (cents): 0
                                     sort order: (rotation packing)
             abbreviated multiple-column output: #t
                                  output format: numbers
                       number of output columns: 3
                                     row length: 12
                                      bad cells: ((4 0 3 6 9) (4 0 1 2))
                    maximum number of bad cells: 0
                                     good cells: ()
                   minimum number of good cells: 0
      bad intervals (between consecutive notes): ()
                maximum number of bad intervals: 0
     good intervals (between consecutive notes): ()
               minimum number of good intervals: 0
          minimum number of different intervals: 3
   maximum number of same consecutive intervals: 2
             self-equivalence filter - standard: #t
                   self-equivalence filter - 5m: #f
              self-equivalence filter tolerance: 0
                         remove near-duplicates: #f
                       near-duplicate tolerance: 0
         wrap when counting cells and intervals: #t
      virtual row length, for computing spacing: 12
                                   motif length: 12
     look for standard transformations of motif: #t
           look for 5m transformations of motif: #f
                                minimum spacing: 1
                                maximum spacing: 6
minimum number of violations of min/max spacing: 0
maximum number of violations of min/max spacing: 0
                     minimum number of 1-spaces: 0
                     maximum number of 1-spaces: 3
  minimum number of occurrences of motif in row: 4
                    wrap when computing spacing: #t
              maximum number of rows to display: 6000
               file of results to search within: 

finding rows...........................................done

number of rows found: 48

(0 1 7 5 10 2 8 6 11 3 9 4)  (0 1 9 4 10 2 7 5 11 3 8 6)  (0 2 8 4 11 1 7 6 10 3 9 5)  
(0 4 10 5 1 2 8 6 11 3 9 7)  (0 4 9 7 1 2 10 5 11 3 8 6)  (0 2 8 7 11 4 10 6 1 3 9 5)  
(0 4 10 8 1 5 11 6 2 3 9 7)  (0 4 9 7 1 5 10 8 2 3 11 6)  (0 4 9 3 11 6 8 2 10 5 7 1)  
(0 5 9 3 1 6 10 4 11 7 8 2)  (0 5 3 9 1 6 4 10 11 7 2 8)  (0 5 11 7 2 4 10 6 1 3 9 8)  
(0 5 9 3 10 6 7 1 11 4 8 2)  (0 5 3 9 10 6 1 7 11 4 2 8)  (0 6 2 9 11 5 1 8 10 4 3 7)  
(0 6 1 9 10 4 2 7 11 5 3 8)  (0 6 7 3 10 4 8 1 11 5 9 2)  (0 6 2 9 11 5 4 8 1 7 3 10)  
(0 6 4 9 1 7 2 10 11 5 3 8)  (0 6 10 3 1 7 8 4 11 5 9 2)  (0 6 5 9 2 8 4 11 1 7 3 10)  
(0 6 4 9 1 7 5 10 2 8 3 11)  (0 6 10 3 1 7 11 4 2 8 9 5)  (0 7 9 3 2 6 11 5 1 8 10 4)  
(0 7 3 4 10 8 1 5 11 9 2 6)  (0 7 1 5 10 8 2 6 11 9 3 4)  (0 7 9 3 11 6 8 2 1 5 10 4)  
(0 8 9 3 1 6 10 4 2 7 11 5)  (0 8 3 9 1 6 4 10 2 7 5 11)  (0 8 3 5 11 7 2 4 10 9 1 6)  
(0 10 3 7 1 8 4 5 11 9 2 6)  (0 10 4 5 1 8 2 6 11 9 3 7)  (0 8 3 5 11 10 2 7 1 9 4 6)  
(0 10 3 7 1 11 4 8 2 9 5 6)  (0 10 4 8 1 11 5 6 2 9 3 7)  (0 11 3 8 2 10 5 7 1 9 4 6)  

(0 2 9 5 11 1 8 4 10 3 7 6)                                                            
(0 2 9 5 11 4 8 7 1 3 10 6)                                                            
(0 4 3 9 11 6 2 8 10 5 1 7)                                                            
(0 5 9 8 2 4 11 7 1 3 10 6)                                                            
(0 6 8 3 11 5 7 2 10 4 9 1)                                                            
(0 6 8 3 11 5 10 2 1 7 9 4)                                                            
(0 6 11 3 2 8 10 5 1 7 9 4)                                                            
(0 7 3 9 2 6 5 11 1 8 4 10)                                                            
(0 7 3 9 11 6 2 8 1 5 4 10)                                                            
(0 8 2 4 11 7 1 6 10 9 3 5)                                                            
(0 8 2 7 11 10 4 6 1 9 3 5)                                                            
(0 11 5 7 2 10 4 6 1 9 3 8)

Because the program filtered out everything but those 4 series, it filtered out every self-identical series. These 4 remaining all happen to be self-identical in a strange way that wasn't part of the definition: They each have a common 6-note segment, or 5 consecutive common intervals but shifted by 4 places.

(0 1 7 5 10 2 8 6 11 3 9 4) has 1-7-5-10-2-8 and 2-8-6-11-3-9.
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Old 18th July 2018, 09:30 AM   #279
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That being too few, we can enlarge the possible spacing from 6 to 7 and get 32 or so new rows to study, which is more like it.


Code:
                                       modulus: 12
         wolf intervals (between any two notes): ()
                     display multiple spellings: #f
    acceptable error when naming scales (cents): 0
                                     sort order: (rotation packing)
             abbreviated multiple-column output: #t
                                  output format: numbers
                       number of output columns: 3
                                     row length: 12
                                      bad cells: ((4 0 3 6 9) (4 0 1 2))
                    maximum number of bad cells: 0
                                     good cells: ()
                   minimum number of good cells: 0
      bad intervals (between consecutive notes): ()
                maximum number of bad intervals: 0
     good intervals (between consecutive notes): ()
               minimum number of good intervals: 0
          minimum number of different intervals: 3
   maximum number of same consecutive intervals: 2
             self-equivalence filter - standard: #t
                   self-equivalence filter - 5m: #f
              self-equivalence filter tolerance: 0
                         remove near-duplicates: #t
                       near-duplicate tolerance: 0
         wrap when counting cells and intervals: #t
      virtual row length, for computing spacing: 12
                                   motif length: 12
     look for standard transformations of motif: #t
           look for 5m transformations of motif: #f
                                minimum spacing: 1
                                maximum spacing: 7
minimum number of violations of min/max spacing: 0
maximum number of violations of min/max spacing: 0
                     minimum number of 1-spaces: 0
                     maximum number of 1-spaces: 4
  minimum number of occurrences of motif in row: 5
                    wrap when computing spacing: #t
              maximum number of rows to display: 9000
               file of results to search within: /Users/caleb/Desktop/MOFs and Searches/39k?

finding rows.........done

number of rows found: 1536

removing near-duplicates...done

number of rows remaining: 32

(0 1 3 5 8 9 11 2 4 6 7 10)  (0 1 3 6 5 9 11 2 4 8 10 7)  (0 1 3 6 8 2 9 11 5 7 4 10)  

(0 1 3 6 8 2 11 9 4 5 7 10)  (0 1 3 6 8 9 11 2 7 5 4 10)  (0 1 3 8 9 5 2 10 11 7 4 6)  

(0 1 3 9 10 6 4 2 11 7 5 8)  (0 1 4 3 9 11 8 6 2 5 10 7)  (0 1 4 6 10 9 2 7 11 5 3 8)  

(0 1 4 7 2 6 10 5 8 11 3 9)  (0 1 5 9 10 7 4 8 2 11 6 3)  (0 1 5 10 4 8 11 3 2 6 9 7)  

mof3*                        (0 1 6 9 7 10 5 2 11 4 8 3)  (0 1 7 3 10 11 6 2 8 4 9 5)  
(0 1 6 9 4 10 2 11 7 5 8 3)                                                            

(0 1 7 5 10 2 8 6 11 3 9 4)  (0 1 8 3 11 5 7 2 9 6 10 4)  (0 1 8 4 6 11 7 2 10 5 9 3)  

(0 1 8 4 11 2 9 6 10 3 7 5)  (0 1 8 10 4 2 7 11 6 9 5 3)  (0 1 9 6 8 4 11 2 10 5 7 3)  

(0 1 9 6 11 4 8 5 10 2 7 3)  Where Do They All Belong?*   (0 2 4 9 7 11 5 8 1 3 10 6)  
                             (0 2 4 9 6 3 5 11 8 1 10 7)                               

(0 2 5 7 1 10 6 3 11 8 4 9)  (0 2 5 8 1 4 10 3 6 9 11 7)  (0 2 6 10 3 1 7 11 8 4 9 5)  

(0 2 7 5 11 3 8 4 10 1 9 6)  (0 2 8 3 11 6 10 1 7 5 9 4)  (0 2 8 4 7 11 6 1 10 3 9 5)  

(0 2 9 6 1 3 10 7 11 5 8 4)  (0 3 7 2 9 6 1 4 10 5 11 8)

Last edited by zooterkin; 20th July 2018 at 08:09 AM.
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Old 22nd July 2018, 05:24 AM   #280
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One of those series is studied and chained. New software takes the agony and shame out of the process.

The rows are chained starting from bottom and going to top.

A good link here is defined as not too many notes necessary to transform row below into row above.


P/0 ->I/0 ->I/11 ->P/11 ->R/2 ->R/3 ->P/6 ->P/3 ->I/3 ->RI/0 ->R/0 ->R/9 ->P/0




C, D, Ab, Gb, B, Eb, Bb, Db, A, G, E, F P/0
D, Db, E, Gb, Bb, G, C, Ab, Eb, F, B, A R/9
F, E, G, A, Db, Bb, Eb, B, Gb, Ab, D, C R/0
G, Ab, F, Eb, B, D, A, Db, Gb, E, Bb, C RI/0
Eb, Db, G, A, E, C, F, D, Gb, Ab, B, Bb I/3
Eb, F, B, A, D, Gb, Db, E, C, Bb, G, Ab P/3
Gb, Ab, D, C, F, A, E, G, Eb, Db, Bb, B P/6
Ab, G, Bb, C, E, Db, Gb, D, A, B, F, Eb R/3
G, Gb, A, B, Eb, C, F, Db, Ab, Bb, E, D R/2
B, Db, G, F, Bb, D, A, C, Ab, Gb, Eb, E P/11
B, A, Eb, F, C, Ab, Db, Bb, D, E, G, Gb I/11
C, Bb, E, Gb, Db, A, D, B, Eb, F, Ab, G I/0
C, D, Ab, Gb, B, Eb, Bb, Db, A, G, E, F P/0






The big surprise in using the new chainer software? With this particular series, there are no adequate solutions less than 13 series total! (No solutions of 10, or 11, or 12.)

Much more than 13 series, there are too many possibilities and you have to break it down into two or more separate chains that you put together for the final result.

So my choice of a 13-series form was a lucky guess, it seems.

Last edited by calebprime; 22nd July 2018 at 05:27 AM.
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