Conference Agenda

Few twentieth-century pedagogical music theory texts have had the impact and enduring relevance of Arnold Schoenberg’s Fundamentals of Musical Composition (FMC). Although the 1967 posthumously published volume contains extensive analyses of works by Bach, Brahms, Mozart, and especially Beethoven, Schoenberg’s own music is minimally represented. Only three compositions are cited—“Traumleben,” the first of the Eight Songs, op. 6; String Quartet No. 2, op. 10; and String Quartet No. 1, 0p. 7—and these references appear without substantial analytical commentary.

The draft versions of FMC, however, reveal a different picture. Additional excerpts from Schoenberg’s music appear throughout the drafts but were omitted from the published text. These include Pelleas und Melisande, Verklärte Nacht, Gurre-Lieder, a passage from the first movement of String Quartet No. 2, and a detailed analysis of String Quartet No. 1. This paper focuses on these unpublished analytical materials and examines the chapters in which they were originally intended to appear. To my knowledge, these analyses survive only in the draft sources and are not replicated elsewhere in Schoenberg’s published theoretical or analytical writings. By presenting these materials for the first time, the paper offers new insight into how Schoenberg interpreted and heard his own works.

The presentation centers on Schoenberg’s analyses of Verklärte Nacht, Gurre-Lieder, and String Quartet No. 1, as preserved in the drafts. These examples employ brackets and braces to clarify rhythmic structure and formal articulation. Schoenberg’s annotations reveal a sustained concern with phrases of uneven length and with the construction of formal units through asymmetrical grouping.

The paper concludes by considering a brief reference in the final chapter, “Sonata-Allegro,” where Schoenberg cites a passage from String Quartet No. 2 as an example of a secondary theme that is not lyrical in character. Read alongside the unpublished drafts, this fleeting mention underscores the extent to which Schoenberg’s most direct reflections on his own music were excluded from the published book. More broadly, these self-analyses reveal how Schoenberg positioned his own music in continuity with the formal procedures of the tonal canon.

Within public music theory, visualizations typically eschew the staff notation and technical diagrams that characterize institutional music theory (Jenkins 2022). One such example is the visualization of frequency ratios by the harmonograph, which generated both public-facing scholarship and vernacular music theories (Rings 2013; Lucas 2021). Harmonographs are machines that create geometric drawings with swinging pendulums: one pendulum swings a pen across a writing surface mounted on the other. By the 1870s, middle-class British and American amateurs used harmonographs to reproduce Lissajous figures (Example 2), which graph the frequency relationship between two oscillations. These often accompanied explanations of musical interval, consonance, and dissonance in public demonstrations and contemporaneous textbooks on sound and music (Tyndall 1867; Taylor 1873; Zahm 1892; Turner 1997). For example, two pendulums whose oscillations form the frequency ratio 8:5 trace the figure of a “minor sixth.”

This paper examines the harmonograph as a tool of public music theory (O’Hara 2025), arguing that Victorian publics used it to theorize a physical basis for consonance. Through a case study of The Harmonograph (Whitty 1893), I show that the kinetic making of harmonograph visualizations contributes to their meaning. Extending scholarship on instruments of music theory (Rehding 2020), nineteenth-century studies of sound (Gillin 2021; Tkaczyk 2023), and music-theoretical visualizations (Hanninen 2015; Krämer 2017), I contend that harmonographs performed a slippage between acoustic motion and the musical experience of consonance and dissonance. Whitty and his interlocutors used this slippage to interpret harmonograms as a visual analogy for interval quantity and quality, correlating visual simplicity with consonance and visual complexity with dissonance. Yet because harmonograms relate intervals only by their degree of visual complexity, they destabilize the idea that consonance and dissonance are discrete ontological categories, anticipating Schoenberg’s ([1911] 1978) argument that consonance and dissonance differ in degree only. Ultimately, examining the harmonograph as a music-theoretical tool shows how music theorizing is shaped not only by images but also by their technical making. More broadly, by showing how the technical making of harmonograms contributed to the meaning of their visual content, this paper demonstrates how public-facing visualizations can offer insight into visualization’s epistemic functions.

What if the grades students earned in our courses were defined by successes in demonstrating their skill and knowledge as opposed to mistakes? This paper will present the “Stepping-Up Principle,” an approach to assessment that blends differentiated instruction with an alternative grading philosophy, allowing us to encourage tangible student progress while still holding fixed standards of achievement (Tomlinson and McTighe 2006, Nilson et al 2023). In this framework, students choose the difficulty level at which they feel confident demonstrating their skills or knowledge from a range of assessment options. Each level is tied to a specific grade (similar to point values for routines in gymnastics) and students earn that grade by successfully completing that level. In all cases, high standards are set for passing a given level, balancing the variability of difficulty for each tier of achievement. After an initial attempt, students have the opportunity to self-reflect and can then choose to reattempt the assessment at a different level. This design offers a pathway to both improve upon their initial achievement and show their highest level of competency.

By meeting students at their current ability level, we explicitly value and reward what a student can demonstrate positively, as opposed to focusing on perfection as a goal, and mistakes as diminishment of that goal. In short, we would prefer that our students succeed at an easier assessment than do fair or poorly on a harder assessment, since this provides us with more useful information on student mastery. This approach can also prompt a reconsideration of “failure” and the powerful negative impacts that it often carries for our most vulnerable students (Eskreis-Winkler and Fishbach 2022, Sharabi and Roth 2025, Feigenbaum 2021).

We will present example applications of this principle in both aural skills and written theory contexts, and discuss suggestions for implementation throughout the theory core. The flexibility of this principle allows it to be integrated into many diverse classroom contexts. We have found this to be an approach to assessment that foregrounds student agency, lowers stress, and values progress over (immediate) perfection, while still holding high benchmarks of student achievement.