7.3: Twelve-Tone Theory - Intervallic Structure
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.