# Neo-Riemannian Transformations and Wyschnegradsky's DC-scale

This chapter starts by looking at Richard Cohn's *generalized parsimonious
trichord* and the generalized neo-Riemannian transformations that derive
from it. Cohn himself includes some quarter-tone examples in his article
"Neo-Riemannian Operations, Parsimonious Trichords, and Their *Tonnetz *
Representations" (*JMT *1997) so it was natural to cite Cohn's work in
this dissertation. There was one problem, though, and that is that the
quarter-tone version of Cohn's generalized trichord does not appear to have
much significance in the music I have studied. Indeed, quarter-tone composers
seem to be more interested in tetrachords than trichords. I wanted to find
a chord from an actual composer's music that I could subject to various
transformations.

It turns out that if we assume that Wyschnegradsky's *diatonicized
chromatic* scale is analogous to the major scale, and that the tonic
tetrachord I found in Chapter 5 is analogous
to the major triad, then we can come up with quarter-tone equivalents for the
canonic neo-Riemannian transformations, P, L, and R, and that these
transformations can even participate in transformation cycles such as those
found in Cohn.

## Contents of Chapter 6

- Chapter 6: Neo-Riemannian Transformations and Wyschnegradsky's DC-scale
- The current version of this chapter, available as a PDF.
- Example 6.1
- The conventional neo-Riemannian transformations: P, L, and R.
- Example 6.3
- Musical realizations of Cohn's generanlized transformations in c=12 and c=24.
- Example 6.14
- My diatonicized chromatic neo-Riemannian transformations: DCP, DCL, and DCR.