This paper will provide insights into Shostakovich’s tonal language by showing how his use of the SLIDE relation is a harmonic outgrowth of the “lowered” modality that has long been associated with his melodic style. The SLIDE relation (known since the 1950s by Russian theorists as the “common-third” relation) is perhaps as characteristic of Shostakovich’s tonal language as his lowered modality. This paper will combine perspectives from both Russian and American music theory to attempt an integration of SLIDE and lowered diatonic modality—and thereby the harmonic and melodic dimensions—in Shostakovich’s music. Particular emphasis will be given to how the lowered degrees of Shostakovich’s modes afford numerous opportunities for SLIDE to emerge in tonal-functional contexts (e.g., as an altered Tonic, Dominant, or Subdominant function), and how SLIDE and lowered modality mutually contribute to the expressive dynamics of Shostakovich’s music.

Although George Russell’s Lydian Chromatic Concept of Tonal Organization (1953, 4th ed. 2001) is well-known among jazz musicians and pedagogues, it has made relatively little impact in academic music theory circles. Only recently has Marc Hannaford advocated for wider study of Russell’s seventy-year-old text, highlighting Russell’s groundbreaking analyses of jazz and impressionist music. This paper has a different focus. I aim to use LCCOTO as an analytical methodology in a genre for which it at first appears entirely unsuited: twelve-tone music of the early twentieth century. This idea is not entirely out of left field, as Russell himself writes that LCCOTO can apply to “even the most radical twelve-tone (atonal) music” (2001: 39). By verifying Russell’s claim, I demonstrate that LCCOTO can and should be considered a foundational music theoretical system, of comparable power and scope to theories like Schenkerism, set theory, transformational theory, etc.

As a case study, I consider Anton Webern’s Piano Variations, op. 27/1, which engages LCCOTO’s more chromatic constructs (Outgoing Modal Tonics, African-American Blues Scales, and Lydian Chromatic Scales) in a thoroughgoing manner. I use a Monte Carlo simulation to consider hypothetical revoicings of the pitch classes in Webern’s twelve-tone row, demonstrating that Webern’s degree of adherence to Tonal Gravity is only reproduced by the computer 0.31% of the time. This yields to a discussion of Tonal Gravity and twelve-tone music more generally, in which I use other computational methodologies to evaluate LCCOTO’s compatibility across all hypothetical tone rows and within a digital corpus of tone rows in the repertoire.

Finally, drawing from Philip Ewell’s pointed critiques of music theory’s white racial frame, I reflect on our field’s longtime rejection of LCCOTO. I contend that academic music theorists have not neglected Russell’s work for formalist reasons, but rather because woven into LCCOTO’s formalist innovations is a revolutionary philosophy that challenges dominant ideas about what music theory itself is and can be. To conclude, I provide a handful of personal meditations on how LCCOTO has transformed my relationship with my discipline.

Joseph Schillinger’s (1895-1943) pioneering work, The Schillinger System of Musical Composition, introduces an innovative approach to composing with the Fibonacci sequence (i.e., 1, 2, 3, 5, 8, etc.). Schillinger directly derives melodic material from Fibonacci numbers by converting them into pitch and pitch class intervals measured in semitones between consecutive notes, a departure from the sequence’s more common role in structuring proportions (see Howat, Madden, Powell, among others). Over the last century, Schillinger’s methodology has been modelled—knowingly and unknowingly—by music theorists and composers (Haek, Bourgeois, Krenek, Staniland, Walker, among others). This talk aims to explore these Fibonacci applications, analyze their commonalities, and propose other possibilities of incorporating the Fibonacci series into music composition.

The presentation will begin by outlining Schillinger’s approaches to linking Fibonacci numbers to pitch and pitch class space. This includes two significant mappings: unilateral symmetry and bilateral symmetry. The unilateral series maps the Fibonacci numbers in a unidirectional ascending order in both pitch and pitch class space. Schillinger also proposes forming melodies through bilateral symmetry—mimicking the 90° rotations of a golden spiral. In this approach, the Fibonacci-derived intervals alternate between ascending and descending intervallic motion from a fixed pitch. As will be demonstrated, extensions and minor modifications to Schillinger’s bilateral and unilateral symmetry represent the primary ways composers integrate the Fibonacci sequence—as a generator of pitch—into their compositions. These, along with other modifications to Schillinger’s approach, will showcase the remarkable possibilities of composing with bilateral and unilateral symmetry.