ideas for new chapters

Intervallic Structure in Twelve-Tone Rows

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.

License

Intervallic Structure in Twelve-Tone Rows Copyright © 2021 by Mark Gotham; Kyle Gullings; Chelsey Hamm; Bryn Hughes; Brian Jarvis; Megan Lavengood; and John Peterson. All Rights Reserved.

Share This Book