Dibben, Nicola. “The Perception of Structural Stability in Atonal Music: The Influence of Salience, Stability, Horizontal Motion, Pitch Commonality, and Dissonance.” Music Perception 16.3 (Spring 1999): 265-294.

In this article, two psychological studies are conducted in order to examine the influence of various pitch-related phenomena on the listener’s ability to perceive structural stability in atonal music.  The results suggest that it is possible to perceive prolongational structures in atonal music, and that phenomenal accents, voice-leading, and dissonance are important factors in such perception.

Lerdahl, Fred. “Atonal Prolongational Structure.” Contemporary Music Review 4 (1989): 65-87.

Lerdahl addresses the problems inherent in both traditional Schenkerian and set theoretical methods of analyzing atonal music.  In particular, Lerdahl responds to Straus’s 1987 criticism of attempts to use Schenker’s methods to identify prolongational structures in post-tonal music.  Lerdahl suggests that certain parts of Schenker’s methods may be useful, although not as theorists have tried to use them in the past.  Lerdahl develops a method for analyzing prolongation in atonal music that hinges on the identification of contextual salience in atonal music as functionally similar to stability in tonal music.  This method is presented as a logical extension of Lerdahl and Jackendoff’s theories in A Generative Theory of Tonal Music (1983).

Lerdahl, Fred. “Spatial and Psychoacoustic Factors in Atonal Prolongation.” Current Musicology 63 (Fall 1997): 7-26.

In this article, Lerdahl continues the trend of his earlier article and adds some psychological consideration for the applicability of prolongational analytical methods in atonal music.  Examples from 20^th century music are given.  This article may turn out to be tangential to the critical summary, but it may also be useful as an elaboration of Lerdahl’s ideas regarding atonal analysis.

Straus, Joseph N. “The Problem of Prolongation in Post-Tonal Music.” Journal of Music Theory 31.1 (Spring 1987): 1-21.

With this article, Straus is responding to what he sees as the fundamental problems with using Schenkerian methods (especially with regards to prolongation) to analyze atonal music.  In particular, he argues that post-tonal music is “incapable of sustaining a prolongational middle ground or of being meaningfully described in terms of prolongation” (p. 2).  In the course of his argument, Straus highlights some false assumptions that previous analysts have made, with particular reference to problems in Travis’s 1966 article.

Travis, Roy. “Directed Motion in Schoenberg and Webern.” Perspectives of New Music 4.2 (Spring-Summer 1966): 85-89.

Travis uses a general form of Schenkerian methods to analyze portions of Schoenberg’s op. 19, no. 2 and Webern’s op. 27.  This article is an example of an earlier attempt to apply Schenker’s theories to atonal music, and provides a starting point for understanding Straus’s and Lerdahl’s criticisms of these attempts.  Straus, in particular, responds directly to Travis’s analysis.

The section "Analysis of 20th-Century Atonal Music" was prepared by Elizabeth Medina-Gray