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OT: The RHYTHM INSTENSIVE The use of RHYTHMIC SUBSETS (or SKELETILIZATIONS) in arrangemet and improvisation

 The classical composer and theoretician Arnold Schoenberg
has been credited as saying that all composition is just very slow 
It stands to reason , then that improvisation can be thought of as
very fast composition.

The use of Rhythmic Subsets when responding to another persons rhythm
is a very powerful, real time strategy for improvising (or real time 
arranging as it
can be thought of in this sense) and for composition and arrangement in 
real time playing.

Here is an examples of what I'm talking about and a powerful way of

In a question about the double stroke exercise, someone
asked me about the relationship of the
Tresillo rhythm (two beat syncopation combination I C)
to the Cinquillo rhythm. (two beat syncopation combination  M F).

Both rhythms were carried with the West Africans that the Moors
enslaved into Spain when the Moors conquered Spain and then
later were brought to the New World when the Spanish Christians
defeated the Moors.    They are the African rhythmic basis of Afro Cuban
music.   This creative legacy of the horrible practice of  slavery also 
brought with it, the rhythmic
basis of blues, jazz and, later, r&b and rock n' roll in American music 

Tresillo is, literally, a subset or a skeletilization (reduction) of the 
rhythm Cinquillo

X * * X * * X *
X * X X * X X *

If you analyze rhythm sections in pop music from around the world, 
frequently rhythms are played that
are subsets of the dominant ostinato rhythm in the parts that make up the 
whole ensemble.
This is particularly true in the African Diaspora model of groove playing 
for dancing.

A really wonderful exercise is to play only subsets of a particular 
You can get incredible results using this
technique and it is astonishingly how many measure you can play without 
repeating yourself.

In a way, this is a kind of negative improvisation but the results it give 
you are always consonant, rhythmically speaking
with whatever ostinato forms the basis of the rhythm or groove you are 

The formula for determining how many possible subsets there are internal 
a rhythm is 2 to the N power where N = the number of notes in a rhythm.

As an example, the number of subsets in this rhythm

X X * X = 2 to the 3rd power (2 X 2 X 2)

so the rhythms internal to this rhythm are, including the very important 
last rhythm which is a rest on all 4 16th notes

1)   synco A   X * * *          first single audible note
2)   synco  B  * X * *          second single audible note
3)   synco  D  * * * X          third single audible note
4)   synco  E  X X * *          first double audible combination
5)   synco  I   X * * X          first two note 'apart' combination
6)   synco  J  * X * X          second two note 'apart' combination
7)   synco  N  X X * X        first triple note combination
8)   synco  P   * * * *          the ever important and frequently 
null set.

When you take a rhythm like Cinquillo (M F)
X * X X * X X *

there are 32 possible rhythms internal to is (2 to the 5th power = 32)
Tresillo is one of them

This is a really powerful and complex game if you start playing with 
as complex
as Cascara from Cuban Rumba music

X * X X * X * X X * X * X X * X

where there are an astonishing 1,024 possible measure of music you could 
utilizing subsets of the rhythm and never once repeating yourself

Mastery of all the possible combinations of ALL 16 notes is
close to impossible  (there are 65, 536 subsets of 16 notes -   2 to the 
16th power)
unless we realize that any 16 note pattern is merely the addition of
two 8 note patterns.   Buy memorizing the 256 two beat Syncopation 
we have not learned some of the possibilities of skeletilization but ALL 
the possibilities.
This is really, really powerful rhythmically and worth the 1 to 6 months 
work it takes
to master all these exercises.   Ones rhythmic ear will grow immeasurably 
through the 256 16th note combinations and the 64 triplet 8th note 

If you use this way of thinking when you are improvising it forms a very 
way of moving the rhythm and yet never being what the Cubans call CRUZADO
or crossed with the rhythm.

Just for starters, try improvising with only the subsets of Cinquillo to 
how powerful this is.

Below is a list of all of the subset possibilities of any combination of 
notes up to 16.

1   note rhythm   =                2 subsets
2   note rhythm  =                 4 subsets
3   note rhythm  =                 8 subsets
4   note rhythm  =               16 subsets
5   note rhythm  =               32 subsets
6   note rhythm  =               64 subsets
7   note rhythm  =             128 subsets
8   note rhythm  =             256 subsets
9   note rhythm  =             512 subsets
10 note rhythm  =          1,024 subsets
11 note rhythm  =          2,048 subsets
12 note rhythm  =          4,096 subsets
13 note rhythm  =          8,192 subsets
14 note rhythm  =        16,384 subsets
15 note rhythm  =        32,768 subsets
16 note rhythm  =        65,536 subsets