Bass, Richard.  “Prokofiev’s Technique of Chromatic Displacement,” Music Analysis 7, no. 2 (1988): 197-214.

Bass notes two authors’ observations (William Austin and Malcolm Brown) on the chromaticism in Prokofiev’s music and builds on them to make a larger argument about Prokofiev’s “concept of expanded tonality,” as Brown terms it.  Bass contends that a fundamental component of Prokofiev’s expanded tonality is one that “permits a relationship approaching equivalency between any two key systems separated by a semitone” (199).  Moreover, it is the “displacement of individual notes within the system that is fundamental to the technique” (199).  For Bass, a displaced note (a “so-called ‘wrong’ note,” 199) also acts as a type of substitution, whereby the note is not “altered” but rather “represents a diatonic one; the diatonic note it represents is present as a ‘shadow’ cast by the displacement itself, and the result is a musical ‘synesis’ in which function is clear but terms in the diatonic syntax are not in strict agreement” (199).  Thus, Bass argues that our ambiguous perception of these notes allows a composer to use them motivically, to “draw parallel relationships between it and other events in the voice-leading structure” (200).  Bass then fleshes out this idea, showing that a larger theoretical system, based on a Schenkerian model, can “explain not only the fundamental diatonic structure of a piece, but also how the seemingly foreign elements assume both a tonal and a motivic role” (200).

Travis, Roy.  “Towards a New Concept of Tonality?,’” Journal of Music Theory 3, no. 2 (1959): 257-284.

In his article, Travis is concerned with defining tonality in music as such: “Music is tonal when its motion unfolds through time a particular tone, interval, or chord” (261).  Furthermore, Travis argues that this is carried out by musical motion, “through means of its structure and prolongations” (263).  This has important ramifications for music that operates outside of the most traditional sense of tonality.  Travis contends that a broader conception of tonality, still adherent to his earlier definition, can fruitfully contribute to our understanding of 20^th-century music.  In other words, he is interested in how “techniques of tonal coherence...[can] be applied to certain sonorities and melodic procedures characteristic of the newest music” (257).  In light of this, Travis makes a strong claim: “There is no reason why... any other conceivable combination of tones appropriate to the composer’s artistic purpose cannot become the tonic sonority of a tonal music.  It is only necessary that the combination be capable of definition in terms of structure which is susceptible to vital and expressive prolongation” (263).  In order to support that claim, he asserts that “it is almost a general principle of musical coherence that those chords which mark the beginning or end of a given procedure of motion tend to serve in a structurally more important capacity than the chords in the midst of that motion” (266).  He then attempts to demonstrate this through examples from Stravinky’s Le Sacre du Printemps and Bartok’s Mikrokosmos.

The section "Analysis of 20th-Century Neo-Tonal Works" was prepared by James Park