Introduction to Neo-Riemannian Theory: A Survey and a Historical Perspective

A Model of Triadic Post-Tonality for a Neoconservative Postmodern String Quartet by Sky Macklay

“…Finally, they say of their analysis that it "demonstrates that Bryars' harmonies are not to be dismissed simply as non-functional sonorities". Instead, "The parsimonious voice leading apparent in the music is a systematic, not arbitrary, consequence of the transformational system Bryars employs" (Roeder and Although Tymoczko (2008a) defines triadic transformations (e.g., neo-Riemannian transformations) as a strictly harmonic phenomenon that "does not specify any particular mapping between its notes" (p. 10), Richard Cohn (1998) explains that these transformations invert a triad, "mapping major and minor triads to each other", and that "because the inversional axis is defined in relation to the triad's component pitch classes, rather than as a fixed point in pitch-class space, this class of transformations is now referred by the term "contextual inversion" (p. 170). The present study asserts that Macklay's use of this class of triadic transformation is often equivalent to a contextually fluid voice mapping that can be described as a dual process of inversion.…”

Empirically testingTonnetz, voice-leading, and spectral models of perceived triadic distance

“…For example, in Figure 1 For many uses of a Tonnetz, this duplication can be ignored trivially by choosing a subset of the plane that contains just one member of each enharmonic equivalence class. 4 However, crucially, when measuring the Tonnetz distance between any two pitch classes 3 The two types of Tonnetz can also be characterized as geometrical duals (Cohn 1998;Tymoczko 2012). 4 In this paper, enharmonic equivalence refers to all Tonnetz locations with the same pitch in 12-tone equal temperament, which is the tuning of the experimental stimuli (in just intonation, their pitches would di↵er).…”

“…Hyer 1995;Cohn 1998;Tymoczko 2012) is somewhat di↵erent; here, the Tonnetz is often thought of as an approximate visualization of four important harmonic relationships -the parallel (e.g. C maj-C min), leittonwechsel (e.g.…”

GeneralizedTonnetze

“…This is discussed in many sources including [11], [14]. Throughout this section, we will be referring to the musical circle in Figure 3, with the {0, 3, 7} triad inscribed in it.…”