Composers work with patterns, which is another way of saying we work with repetition. Thus, if I have three elements, A, B, and C, it would be useful to know how I can reorder them.
Now, assuming musical time is hierarchical, the patterns in music will also have that property. Consequently, I won’t need to know all the permutations of my smallest repeated element. (Thank goodness, because that could easily represent hundreds or thousands of repetitions, and an astronomically large number of permutations.) Instead, I can usually nest patterns into groups of 2-5 elements.
When we consider that most repetition isn’t literal (the subject of my next post), thinking in terms of hierarchies of repetition quickly becomes an easy way both to image quickly large swaths of music and to consider when we may want to vary the repetitions and how.
A Big Long List
All that background aside, I wrote this post as an excuse to post all the possible groups of 2-5 elements. They’re not just useful for composers. Any discipline that uses applied patterns could find these useful. Say you’re a poet or a rapper who wants come up with a new rhyme scheme (which got me thinking about this specific question). Or a visual artist or graphic designer or architect working with linear patterns (although spatial patterns quickly expand into the realm of gestalt theory).
Whatever your need, here are the first five permutations for you to mix, match, and nest.
A is always whatever’s first; B, whatever’s second; and so on.