7.3: Twelve-Tone Theory - Intervallic Structure

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Page ID: 61904

Robin Wharton and Kris Shaffer eds.
Open Music Theory via Hybrid Pedagogy Publishing

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Pitch-class orderings are not the only things ordered by twelve-tone rows. Because pitch classes are always in relationships with one another, a twelve-tone row is also an ordered collection of intervals. Understanding the intervallic structure of a row class is the best way to get a sense of what it will sound like.

Below, you’ll see the figure from resource on operations. Below each of the row forms in that example, I have shown the series of ordered pitch-class intervals.

Rows that are transpositionally-related (as P11 and P10 are) have the same series of ordered pitch-class intervals.

Rows that are inversionally-related (as P10 and I0 are) have complementary ordered pitch-class intervals. That is, intervals in corresponding locations in the row forms “sum to 12.”

Rows that are retrograde-related have ordered pitch-class intervals that are reverse complements. Compare P10 and R10. Reading R10 backwards, the final three intervals (for example) are 4 1 8. Those are the complements of P10′s first three intervals: 8 11 4.

Rows that are retrograde-inversion related have ordered pitch-class intervals that are reverses of one another. Compare P10 and RI0. Reading RI0′s intervals backwards, you’ll notice that they are the same as P10′s read forwards.