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One of the Andy Warhol paintings displayed at the National Gallery of Art. That boy sure liked his soup. Perhaps that's because the painting "32 Campbell's Soup Cans" was his first successful exhibit at the Ferus Gallery in LA. His meaningless repetition of commercial goods identified Americans as consumers. Even his paintings of Marilyn Monroe (who died in 1962) represent the cultural change in values that had been taking place.

A Simple Trick To Think About Repetition in Music — or Anything

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.

2

AA
AB

 

3

AAA
AAB
ABA
ABB
ABC

 

4

AAAA
AAAB
AABA
AABB
AABC
ABAA
ABAB
ABAC
ABBA
ABBB
ABBC
ABCA
ABCB
ABCC
ABCD

5

AAAAA
AAAAB
AAABA
AAABB
AAABC
AABAA
AABAB
AABAC
AABBA
AABBB
AABBC
AABCA
AABCB
AABCC
AABCD
ABAAA
ABAAB
ABAAC
ABABA
ABABB
ABABC
ABACA
ABACB
ABACC
ABACD
ABBAA
ABBAB
ABBAC
ABBBA
ABBBB
ABBBC
ABBCA
ABBCB
ABBCC
ABBCD
ABCAA
ABCAB
ABCAC
ABCAD
ABCBA
ABCBB
ABCBC
ABCBD
ABCCA
ABCCB
ABCCC
ABCCD
ABCDA
ABCDB
ABCDC
ABCDD
ABCDE