IX. Twelve-Tone Music
Naming Conventions for Rows
Mark Gotham
Key Takeaways
- This chapter goes through the different ways of representing twelve-tone material:
- pitches by pitch name or pitch class;
- rows and transformations with P0 starts on C (fixed zero) or P0 starts wherever we chose (moveable zero)
- matrices, setting out these different row conventions.
- When reading other writing on twelve-tone music, be prepared for any of these conventions to be used. But in your own work, simply choose one you feel comfortable with and use it consistently.
In analyzing twelve-tone music, there are different conventions for labeling rows, transformations, and even pitches and intervals. This chapter compares the main approaches that you’re most likely to encounter in analytical writings. The focus is on rows and matrices, but before we get to that, let’s deal first with the pitches themselves.
Pitch
As we’ve seen earlier in the book, it is useful in some analytical contexts to use pitch-class notation (integers from 0 for C to 11 for B) as an alternative to spelling out those pitches (e.g., C♯ vs D♭). This convention is mostly associated with non-tonal music (including most twelve-tone music), where it can be handy for performing the kinds of mathematical operations we’ve seen (in both pitch-class set analysis and twelve-tone music) and for sidestepping questions of pitch spelling. There’s often still a logic to the pitch spellings used in a twelve-tone piece, but that logic is often of a different and perhaps less generalizable kind. For instance, using specific pitch spellings in a row-form representation usually doesn’t reflect a hierarchy or tonality in the same way that the pitches of a scale do in tonal music.
Rows
For rows, the main difference in notation and labeling centers on a single choice about which pitch to organize our rows around:
- the same pitch in all contexts (conventionally, that pitch is C)
- a pitch that’s important to the musical context in question
For instance, in the Basics of Twelve-Tone Theory chapter, we set out the row of Elisabeth Lutyens’s Motet starting on C, which gave us the twelve-tone row 0–11–3–7–8–4–2–6–5–1–9–10. Alternatively, we could set out the P0 starting on D, as the first voice to enter (alto) starts on D4 and proceeds to sing the first hexachord of this prime-form row on that pitch level.[1] That would give us a P0 of 2–1–5–9–10–6–4–8–7–3–11–0.
Option 1: P0 starts on C (fixed zero)
In this convention, whatever you decide the prime form to be, the transposition of that form starting on C is P0. This is probably the most common convention today, and sometimes called “zero-centered” or “fixed-zero” (by analogy to tonal solfège systems).
As we have set P0 to begin on C, I0 also begins on C, and R0 and RI0 will end on C. This separation of P0 and I0 from R0 and RI0 makes sense because we prefer P0 and R0 to be exact retrogrades of one other (and likewise I0 and RI0). We could theoretically have an even more