## Section34.1Twelve-Tone Technique

In a twelve-tone composition, every note can be accounted for as being a member of the original series or one of its permutations, providing unity to the piece as a whole. Additionally, a twelve-tone series is a repository of intervals and can be seen as an outgrowth of atonal music with its emphasis on interval over chord or scale. The basic premises of twelve-tone music are as follows:

1. All twelve notes of the chromatic scale must occur

2. No note can be repeated in the series until the other 11 notes of the chromatic scale have occurred (exceptions include direct repetition of a note, trills, and tremolos)

3. The series can be inverted, retrograded, and the inversion can be retrograded

4. The order of notes in a series remains fixed, without reordering.

### Subsection34.1.1Row Forms

A twelve-tone series is also commonly called a twelve-tone “row,” and we will use the term “row” throughout this chapter.

The four types of row forms used in twelve-tone technique are prime (P), retrograde (R), inversion (I), and retrograde inversion (RI). The prime is the original row. The retrograde is the prime form backward. The inversion is the original row with all intervals in the row inverted (going in the opposite direction of the original). Finally, the retrograde inversion is the inversion retrograded (and therefore might have more appropriately been labeled “inversion retrograded” since “retrograde inversion” sounds like it refers to the backward form inverted instead of the inverted form backward).

### Subsection34.1.2Transposition Numbers

Each row form can be transposed to start on any note from the chromatic scale. We will use the same pitch integers as in set theory. For primes and inversions, we will use P and I accompanied by a pitch integer to specify the starting note. For example, P$\text{}_{0}$ is a twelve-tone row starting on C (pitch integer 0), P$\text{}_{3}$ is a twelve-tone row starting on E♭, and so forth. The same is the case for row forms like I$\text{}_{2}$ (starting on D), I$\text{}_{5}$ (starting on F), on so forth.

However, the retrograde (R) and retrograde inversion (RI) row forms use the pitch integer of the last note in the row to designate their transposition level. Therefore, R$\text{}_{1}$ ends on C♯, and RI$\text{}_{7}$ ends on G.