The Schillinger System: Permutations

[ashbyanderson]

One of the great things I love about the Schillinger System of Musical Composition are the Permutations. They are a great way to develop existing material in your compositions or work in progress

General Permutation Procedure

1. Choose two elements from pitches, rhythms, or melodic phrases. To start, our elements will be two rhythmic values: a half-note and a quarter-note.
2. Assign the letters A and B to each element.
3. Permute (A+B) and (B+A)
4. This yields only two permutations. See examples 1a and 1b, where the permutations are shown on both a grand staff and a single staff.
5. Expanding the permutation to three elements (A+B+C) will yield six possible permutations:
A B C
A C B
C A B
B A C
B C A
C B A

Berklee College of music has a great article with more examples on using permutations: Berklee Article

ASHBY ANDERSON

[ashbyanderson]

To find out the number of permutations available for any number of musical elements. use this formula

for 3 elements:

1x2x3= 6 permutations

for 4 elements
1x2x3x4 = 24 permutations

for 5 elements

1x2x3x4x5=120 permutations

Enjoy Your Journey in Music,

ASHBY ANDERSON

[dogbite]

Originally Posted by ashbyanderson

To find out the number of permutations available for any number of musical elements. use this formula

for 3 elements:

1x2x3= 6 permutations

for 4 elements
1x2x3x4 = 24 permutations

for 5 elements

1x2x3x4x5=120 permutations

Enjoy Your Journey in Music,

ASHBY ANDERSON

i use the 6 permutations to show students with the first three notes in a blues scale that there are possibilities you haven't thought of...

and for the 24, i know a player who teaches 24 finger combinations on the guitar:

1234
1243
1324
1342
etc...

thanks for this ashby. math may make some squeemish but you have demonstrated a very real practical application

[d2leo]

Thanks db for the invite back. Got to tell you I am a bit gun shy.
Ashby great to meet you here.

The next great part of the System is to group your permutations as Ashy said
(A B C) A1
(A C B) B1
(C A B) C1
(B A C) D1
(B C A) E1
(C B A) F1

Now you can permute the groups of 3 like you just did the original groups. So you can see very quickly how a small amount of material (pitches, durations) how you can build a piece.

The next step is to build patterns with this material. After all that is what the Schillinger System is all about.

This is done by what Schillinger calls Coefficients of reoccurrence.
You take the permutations you choose and then repeat them in a pattern.
for example:
Using 3-1-2
A1 C1 E1
you get 3A1 + C1 + 2E1

phil

[ashbyanderson]

Thanks DB and Phil for your input. I love this stuff. I think the methods outlined by you both are a great way to expand any material that a musician has at hand. The other thing I love about math is that you can apply numbers in many different ways to get different results. I'll post more examples over the weekend if time permits.

Enjoy Your Journey In Music,
ASHBY ANDERSON

[ashbyanderson]

For those composing today, try creating the Rhythmic permutations using Schillinger's approach then add notes of your preference later.

Examples of Rhythmic Permutations within the Schillinger System of Music Compositions can be viewed here http://www.berklee.edu/bt/211/images/ex2a.jpg

The above is only an example, let your rhythmic preferences be your guide.

Enjoy your journey in music,

ASHBY ANDERSON

[ashbyanderson]

For those searching for and interesting phrase,theme or melody, I generally right out the melody and look at the rhythm of my idea. When I need something different, permutations of the original theme are the way to go. The example below outlines the concept.

Rhythmic Permutations with notes added

Although the examples are simple, the concept is what you want to want to grasp when learning Schillinger's Approach. As his concept of Rhythmic Permutations are the first chapter in his book, this concept alone yield's great results. I used this approach on a lot on music that I compose.Readers can hear a sample of this approach using trumpet, trombone and tenor on a work called Span-African that composed a while back.


Enjoy your journey in Music
ASHBY ANDERSON

[ashbyanderson]

Below is a more complex example that has 5 note values that are permutated with notes added
http://www.berklee.edu/bt/211/images/ex3a.jpg

Starting from the small, then progressing to the more complex is a reoccurring theme of the Schillinger System of Music Composition.

ASHBY ANDERSON

[d2leo]

Ashby,
Those clips are from my Berklee Today article The Power of Permutations.
It is this way that Jimmy Heath wrote his tune 'Changes'. Staring with a 4 bar phrase he expanded it into a complete song and arrangement.
Amazing stuff.

Now permuting scales 1,2,3,4, etc.. unit scales into phrases cool stuff.
or symmetric scales splitting the octave by 2, 4 6 or 12 and creating scales that way.
pd

[ashbyanderson]

Originally Posted by d2leo

Ashby,
Those clips are from my Berklee Today article The Power of Permutations.

Hey Phil, I know- I placed the link to the whole article at the beginning of this thread-did not know you wrote this though. This is one of the best articles I've ever read on Schillinger. Why aren't you posting more of your knowledge here?

Originally Posted by d2leo

Now permuting scales 1,2,3,4, etc.. unit scales into phrases cool stuff.

Please explain a bit-do you mean the diads, triads and tetrads as explained in Schillinger's book "Kaleidophone"?

Enjoy your journey in Music,

ASHBY ANDERSON

[ashbyanderson]

Originally Posted by d2leo

Jimmy Heath wrote his tune 'Changes'. Staring with a 4 bar phrase he expanded it into a complete song and arrangement.
Amazing stuff.

Thanks for educating me on that- did'nt have a clue. I'll have to anaylze the the tune and find the phases.

Please inform of any other jazz artists that use the system- I suspect Duke Ellington due to a small reference in an album liner note - but I'm not sure.


Enjoy your journey in Music,

ASHBY ANDERSON

[ashbyanderson]

Other Concepts within Schillinger method are the permutation of the intervals used to construct chords. I love this- it shows you the relationships between types of chord qualities. For instance, C ,Eb, Ab, B have the intervals (starting from C ) 3,5,3 which is a C harmonic Minor Chord. by permutating these numbers you get 5,3,3 which is a Csus Maj. 7 b6 chord(C,F,Ab,B) and 3,3,5 which is a C Diminished Major 7 chord (C,Eb, Gb, B)

This info is also present in Schillingers Book " Kaleidophone "

Enjoy your journey in Music,

ASHBY ANDERSON

[ashbyanderson]

Originally Posted by d2leo

Now permuting scales 1,2,3,4, etc.. unit scales into phrases cool stuff.

Ok... I found it in Chapter 7 PD. This is COOL stuff. Schillinger never ceases to amaze me!

Enjoy your journey in Music,

ASHBY ANDERSON

[d2leo]

Ashby,
Thank you for your kind words.
I haven't been on these boards for years after quite a flaming from some of the close minded people on these boards. I have used my energies in more positive ways.
db told me of the positive Schillinger discussion so I came on.

I give free Speaking Schillinger talks on the web live on Thursday evenings 7:30 edt on Wiziq.com. We have been getting together for almost three years and have a great discussion.
If you would like to join let me know and send me an email address and I will send you an invitation.

Phil

[d2leo]

Ashby
What reference to Schillinger is there on the Ellington Album?

Mercer Ellington studied the System,
Earth Wind and Fire's Composer Arranger Charles Stepney used the System.
The AACM was founded by Muhal Richard Abrams a Schillinger practitioner. I believe the other members Roscoe Mitchel et all used the System.
Jason Moran, Toshiko Akyoshi, Jimmy Heath, Yusef Lateef just to name a few.

pd