What are permutations? A permutation is a method of finding all the possible combinations of a set of anything. This could be a set of numbers, a set of musical notes a set of musical forms or a set of musical phrases. Anything that you can combine into a set number of objects, can be permutated to reveal all the possible combinations within the original set.
What does this have to do with music, with jazz improvisation, jazz composition or Music theory? Generally in music, we use 12 notes, at least those of us that use the even tempered system. Because we only have 12 notes, musician are already creating permutations of scales chords, musical phrases, intervals etc. With this in mind it helps to have a system to aid in creating permutations.
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Why are permutations important? Permutations are important because they allow us to determine how many variations there are based on a set number of items or in this instance notes.for example, if we have the notes A, B and C, there are six permutations to the original set of the notes A,B and C. In order to determine the number of permutations of any set of notes we simply number how many notes we have in our set. In this instance we have three different notes. To determine the number of permutations simply multiply 1 x 2 x 3. This equals the number 6 And informs us that for any set of three noted, there are six permutations or six different ways that we can arrange the original set. If you had four items or notes, you would end up with 24 permutations of the original set of notes.
How are permutations created? There are two methods for generating permutations. One is called mechanical permutations and the other is called circular permutations. Both methods generate the same number of permutations but, the difference is in how the arrangement of the permutations are presented.
Using the mechanical permutations method, our original notes consisting of notes A,B and C would be processed as follows. Take each note and interchange the remaining two notes. Following this process, our permutations would look like this:ABC, ACB, BAC, BCA, CAB, CBA. Using the circular permutations method, our original notes consisting of notes A,B and C would be processed as follows. Take each note and interchange the remaining two notes. Following this process, our permutations would look like this:ABC, BCA, CAD, ACB, CBA, BAC.
Why is this approach useful for music composition? As a composer, improvisor, or music theorist, this process aids in determining the breath and width of your melodic ideas. it is nice to know that you are not completely dependent upon your own creativity when composing a piece of music. The fact that there may be a musical phrase consisting of five to six notes, informs the composer that he or she has 120 to 720 variations of a melodic idea. This method is extremely helpful when composing extended jazz compositions and very practical when composing shorter jazz works like a 12-32 bar composition. This method can be also be applied to chords, to the permutation of sections within a musical work, to dynamics to textures or to anything that you want to assemble into a set of something.
Depending on the number of notes, this process can become quite complex and time consuming. However, due to today's technology, we can overcome the limits of our minds by using tools designed to calculate permutations in a matter of seconds. Please refer to the Permutations Generator
This is an extremely time saving device and will permutate up to 10 musical notes or numbers. You can save the patterns generated for later use.