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I've been looking into set theory and am trying to understand it, whilst also find applications of its use in my own composition.

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It can be used for that reason. The major scale, for instance, has an interval vector of <254361>, and we can expect that a collection with 6 instances of ic4 (the perfect fourth/fifth) and only one of ic6 (the tritone) will in some sense be more consonant than a collection without any instances of ic5 but several of ic1 (the minor second).

But there are other uses for the interval vector as well. I'll just share two briefly:

  1. As a means of relating interval content with the sets around them. (0137) and (0146), for instance, both have interval vectors of <111111> despite being two completely different sets. This way, a composer is using similar interval-class content while changing the sets articulated on the surface. (Conversely, composers can choose to use a set with a wildly different interval vector.)

  2. Keeping tones in common while transposing a set, as another means of relating to adjacent musical material. The interval vector actually tells you how many instances of each interval class will be held in common at that transposition level. For instance, let's return to the major scale, whose interval vector is <254361>. If we transpose that major scale by a major second (ic2), we can look at the interval vector to see that 5 pitch classes will be held in common between the two sets. Similar, three pitch classes will be the same if we transpose it by major third (ic4). The only caveat here is that we have to multiply the number in ic6 to see how many common tones are held there; if we transpose the major scale by a tritone, there will actually be two tones held in common, not just one.

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