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Vol. 13, No. 6: Dec.-Jan. 2008
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Permutation: Thinking Backwards And Inside-Out
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by Adam Moore
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Page added in
February, 2007
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About the Author
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England's Adam Moore, with more than fifteen years playing experience, is a perpetual student and continues to study music and its related philosophies, theory, the guitar and composition.
His latest CD is entitled "Curious Liquid", featuring heavy riffs, hard rock melodies and flashy solos.
You are invited to visit Adam's web site.
Send comments or questions to Adam Moore.
© Adam Moore
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Permutation
Thinking about permutation enables us to explore the wider implications
present within a limited set of material. By material we could mean a set of
notes, a rhythm, a picking pattern or any such fixed parameter. Once we have
mastered a piece of material we can look at it from a number of alternative
angles and then reinterpret it in various ways. This process gives us access
to new material. Numerous thoughtful individuals across the ages have
presented this in the form of an aphorism along the lines of 'from one thing
know many things'. We can hopefully see then that this idea has a great many
implications for the guitarist. We can apply it to our practice schedule,
when we compose new music and, indeed, we can apply it to life in general.
The three definitions of permutation offered by answers.com are:
1. A complete change; a transformation.
2. The act of altering a given set of objects in a group.
3. Mathematics. A rearrangement of the elements of a set.
The second and third are of most immediate use, but they generally lead us back to the first, which is ultimately the more valuable. These definitions
are by no means exhaustive, but reflect a general consensus on the meaning
of the word.
Musicians and musicologists of all sorts have been exploring permutation for
centuries. A great deal of the theory surrounding twentieth-century harmony
has focused on this subject and, at its extreme, generated such wonderfully
complex ideas as mirror harmony, projected set & pattern completion. These
ideas are based upon the concept of taking a small, fixed pattern of pitches
or values and unfixing it. Often, this involves looking at all the possible
options before completing a piece of music. Take, for example, the notes A,
B & C. If we play them in that order we can get a figure with a certain
musical quality. If we play them backwards we get another figure, if we plan
B, C then A, we get a third and so on. These figures are made from the same
material, the same stuff, but are different enough to count as separate
entities in which we can hear and feel different things.
For those who wish to know; if you want to find out how many combinations
there are of a given set of things, take the total amount and multiply it by
all the number below that in succession, e.g. there are 24 combinations of 4
things because 4 times 3 times 2 times 1 equals 24. (We will return to this
in a moment when we look at how many fingers you've got on your fretting
hand and what you can do with them.) These combinations stack up very fast
such that the possible permutation of eight things is 40,320.
Jazz players such as Parker, Miles and Coltrane made extensive use of
permutation when they played. They might take the same musical phrase and
expand and contract it rhythmically, move it to a new starting point, add
extra notes and so forth. Doing the same allows you to generate massive
amounts of material without needing to create totally new ideas. Why not
milk an idea for all its worth before going off in search of another one? A
good book for this kind of work is Steve Rochinski's "The Motivic Basis for
Jazz Guitar Improvisation" (Hal Leonard). Also, you might try recording a
phrase and moving it against a backing track to hear the many different
effects a figure can have just by being in a slightly different place. This
is also very helpful if you want to move a figure that is just too complex
to learn in a new place. You may find that nice, metrical figures can be
imagined in different places much easier than bluesy, rubato melodies, but
the effect of moving either can be equally striking. Thinking slightly
differently, listen to and play King Crimson's "Frame by Frame" to hear a
guitar figure in 7/8 moving against one in 13/16. This provides a great
example of the metrical permutations of two melodic patterns.
One of the most famous books based on these concepts is Nicolas Slonimsky's
"Thesaurus of Scales and Melodic Patterns". If you've read through the
instructional pages on Steve Vai's site you will probably recognise the
title. Frank Zappa was a fan of Slonimsky's work and the two met to talk
about its application at Zappa's house (nice bit of trivia for you there).
Slonimsky was a great experimental musicologist and composer who did
extensive work into the possibilities for mutating melodic phrases to
generate new ones. He gave the musical world such terms as ultrapolation and
infrapolation and the magnificent infra-inter-ultrapolation. These terms
mean, essentially, to put things in between other things, either a bit below
of a bit above. It's often been suggested that John Coltrane got the idea
for "Giant Steps" from this book. Worth checking out.
Practice
As we begin to develop a practice schedule we should think about what can be
learned from the little figures and patterns that are so often used. If we
take a C major scale and play it up and down over one or two octaves we have
learned one thing, hopefully we've learned it well and can appreciate the
quality of that particular group of relationships. But think about what else
one can do with this little set of notes. If we have picked it alternatively
starting on a down stroke, we can do the same but starting on an up stroke.
We can play it in ascending groups of two, three, four etc, play it in
thirds, fourths, fifths and so on. Then we can play it in thirds and ensure
we've covered starting on both an up and a downstroke. These ideas all
represent permutations, that is, we do different things with the same stuff,
in this case a C major scale. We learn many things from one thing. Indeed,
when practicing scales, you may well see all the major scales as just
permutations of the same interval values. It is much easier for a guitar
player to see scales as permutations of the same thing as they move so
uniformly around the guitar neck, it is less logically so for, say, a
pianist or a saxophonist.
Once we add a click (metronome pulse) to our practice, we have a new factor
against which to develop variations. Still using C major as an example, we
can begin our scale on the downbeat, or the upbeat, or any sixteenth note,
or triplet subdivision we can cope with. The point of this is getting our
ears and fingers to move away from the notion of having to begin a phrase
with the root note and on the downbeat. Try Guthrie Govan's "Creative Guitar
2: Advanced Techniques" for a good chapter on variations of a major scale for
practicing.
As a last point on practice, think about the four fingers on your fretting
hand. As we noted earlier, there are four fingers, which generates
twenty-four combinations - provided we use all four. The physical act of
putting then down on the guitar neck is different in each case, playing
1,2,3,4 is different to playing 3,1,2,4 and it's always worth thinking and
feeling your way through these permutations and getting to know what is easy
and difficult about each combination. You might find that putting finger 3
down first does not come naturally, or that following 3 with 2 is very
difficult. If we dig into the complexities of these permutations we can find
all sorts of answers without having to learn great rafts of new material.
Composition
I've touched on this already but it's worth treating as a separate topic.
The result of exploring variations on a small pattern of values is that it
leads to new ones that are different enough to be experienced as unique. The
process of exploration which permutation encourages is vital to the creative
process and can lead us away from the mimicry that dogs so many would-be
guitar heroes. Imagine how many of your favourite players use something like
a blues pentatonic riff. The chances are that the notes in the phrase are
not particularly original, but some fresh element in the delivery or the
ordering of tones is enough to make it quite clearly a Steve Morse lick or a
Jeff Beck lick or whatever. The more attention you can bring to bear upon
something simple like a blues riff and the more possible variations of you
can come up with, the more likely you will be to find your own sound within
something already as old as the hills. At this point it's probably worth
reading "The Origin of Species"!
To conclude, we can say that seeking out the musical and physical
variations, alterations and permutations within anything and everything we
come into contact with can provide the difference between real creative
development and stagnation. Furthermore, it can lead us to an understanding
of the principles that guide us over and above the laws that fasten us into
a single way of working and thinking.
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