Transposition (music) - Twelve-tone Transposition

Twelve-tone Transposition

Milton Babbitt defined the "transformation" of transposition within the twelve-tone technique as follows: By applying the transposition operator (T) to a set we will mean that every p of the set P is mapped homomophically (with regard to order) into a T(p) of the set T(P) according to the following operation:

where T_o is any integer 0-11 inclusive, where, of course, the T_o remains fixed for a given transposition. The + sign indicates ordinary transposition.

Allen Forte defines transposition so as to apply to unordered sets of other than twelve pitches:

the addition mod 12 of any integer k in S to every integer p of P.

thus giving, "12 transposed forms of P".