Twelve-Tone Music — Operations

Like pitch-class sets, twelve-tone rows can be transposed (Tn), inverted (I), or transposed and inverted (TnI). Like transposing a pitch-class set, transposing a row is accomplished by adding a constant value to all of the pitch-classes of the row while maintaining the order. In the example below, I have transposed P11 by T11 by adding 11 to each of the pitch classes of P11. The new row is called P10 because it begins with pitch class 10.

Inversion occurs when we subtract each pitch class of the row from a constant value. Again referring to the example below, when I do T10I of P11 is accomplished by subtracting every pitch class of P11 from 10.

Twelve-tone rows can be retrograded as well, symbolized as R. To retrograde a row we read it backwards. Reading P11 backwards results in the row form shown below P11 in the example: R11. (Remember that retrograde rows are labeld according to their final pitch class.) Reading I0 backwards results in RI0—just below it in the example.

It’s important that you know the difference between operations and row forms, because they are often labeled similarly. In these resources operations like transposition and inversion will always be italicized. Row forms will be bolded.

You need to memorize the effect of transposing, inverting, or retrograding any particular type of row. That is, you should know what kind of row form results when you perform any operation on it. For example, if you transpose a P-form, what kind of row form results? What about when you retrograde an RI-form? The flowchart below will be helpful: