The structure of RI-invariant tweleve-tone rows

Abstract

This paper presents an efficient method for generating the class of all twelvetone rows which are transpositions of their own retrograde-inversions. It is shown here that the members of this class can be obtained from a subclass of those rows whose first six notes are ascending and whose first note is C. The number of twelve-tone rows in this subclass is 192, and a complete listing is given in an appendix to this paper. The theory as developed here can be applied to tone rows having any even number of notes. 402[2]Rl-invariant twelve-tone rows 403

Invariance properties of Schoenberg's tone row system

“…In a further paper (see [7]) the authors present an efficient method for generating all twelve-tone rows which are transpositions of their own retrograde-inversions. This is an alternative procedure to that outlined in the proof of Theorem 4.2.…”

“…(Note also that for this example the sequence of 11 intervals between the 12 notes, namely (1,3,1,3,1,5,1,3,1,3,1), is symmetric. Similar relationships between intervals and notes are explored in detail in [7]. )…”