Permutation: Thinking Backwards And Inside-Out


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 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.


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.


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.

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.

Adam Moore