New Music as Generalizable Tonal Predictions: Toward an Anti-Racist Framework

i write this as a music psychology researcher who has spent much of her career thinking about how humans acquire tonality. I also write this as an immigrant and a child of colonial and postcolonial Hong Kong who has personally experienced openly racist remarks. And thus even before the #blacklivesmatter movement and as part of the Anti-Racism and Equity Committee of the Society for Music Perception and Cognition (Baker et al. 2020), I have continually been asking myself, Is this line of work anti-racist? And by extension, Am I being racist?Yust's thought-provoking essay couldn't have arrived at a better time. He treats tonality as bipartite: both as an institution (as in, tonal vs. post-tonal music theory), and as a set of organizing principles (such as major vs. minor) used to describe the pitch-related forms and functions of music. The former branch of this bipartite definition arose presumably as a result of the academic study of music in the heavily Western-influenced university system. As such, by 2023 it should no longer be surprising, to anyone who has paid attention to music theory in the last few years—and thus to Philip Ewell's influential work on the white racial frame of music theory (Ewell 2020) and the subsequent fallouts with Schenkerian analysis—that this definition of tonality is not immune to systemic racism and racist agendas. As such, I whole-heartedly agree that only an actively anti-racist agenda of music education that dares to make bold changes, such as jettisoning the term tonality altogether as Yust advocates, can counter the systemic racism of institutions as we are now able to see it.The other part of the definition of tonality, as a set of organizing principles, relates more directly to my work. Yust helpfully identifies six musical features under the concept of tonality: key, tonic/tonal center, scales and macroharmony, scale degree, triadic harmony/consonance, and functional harmony. It is worth noting that this already diverges from the National Institutes of Health's defined Strategies for Strengthening Evidence-Based Research for Music-Based Interventions (Chen et al. 2022): "Basic constituents of music include melody, harmony, and rhythm" (as a contributor, I fought to keep the word include in there. I would have preferred to add but are not limited to). The disciplinary boundaries of academic discourse are such that music theory has evolved to be predominantly pitch-based to the point that a contemporary education in academic music has come to be organized principally around harmony and tonality, even while the adjacent fields of music scientists and healthcare researchers are quick to bring in rhythm as a key organizational feature.The above claim by Chen et al. cites a comprehensive review on music cognition and cognitive neuroscience (Vuust et al. 2022a): "Music processing in the brain—namely, the perception of melody, harmony and rhythm—has traditionally been studied as an auditory phenomenon using passive listening paradigms." That review concluded that the brain continuously constructs predictions for what happens next given its experience with past exposure, and that this process, known as predictive coding, is a governing principle across multiple perceptual features of music. This view is indeed gaining traction in the music cognition world and should perhaps deserve further study in music theory as well.Writing in response to Vuust et al., Savage and Fujii (2022) note, "While melody and rhythm are indeed constituents traditionally found in almost all of the world's music, chord-based harmony is not, despite its recent expansion into popular music around the globe." Vuust et al. correctly note that "Whereas tonality is known in music from all cultures studied, neuroscientific studies have concentrated mainly on Western harmony," but then they continue to focus predictions from the PCM Predictive Coding of Music hypothesis on Western chordbased harmony, limiting the generality of this hypothesis. . . . We propose instead that a more general PCM framework could focus on tonality, rather than harmony. Western chordbased harmony could thus be seen as a special case of generalized tonal relationships between notes, which can take the form of chords, scales or nonchordbased simultaneous tones (for example, South Asian drone or Central Asian hocket)." (emphasis mine)This of course is a direct contrast against Yust's central claim in his essay that the story of tonality is problematic because "it's a story we tell about white music, and universalizing it is a simple act of holding up white music as a standard for all music."Is tonality racist or is harmony even worse? The relationship between harmony and tonality deserves more examination here. Yust includes triadic harmony and consonance as one of the most readily perceptible features of tonality, but neither a necessary nor a sufficient one: "Consonance is perhaps the most easily perceptible property of music that we call tonal. While it is certainly highly correlated with tonality, however, no theorists, to my knowledge, consider it either a necessary or sufficient property of tonal music." To clarify this relationship, and to situate it within music psychology, I continue to monitor the dialogue between Vuust et al. and Savage and Fujii. In response to Savage and Fujii's (2022) response to their own review, Vuust et al. (2022b) countered: We agree that Western-based harmony is a special case of the more general phenomenon of tonality. . . . We included a discussion of harmony as a well-researched example of how music perception may be subdued to a statistically learned musical grammar, for listeners from a Western culture. Furthermore, the statistical learning processes involved in harmony or tonality—and thereby the principles that underwrite predictive processing—have been generalized beyond musical cultures through behavioural and scanning studies using artificial tonal systems and grammars.This defends the use of prediction as an even more general property of music, one that encompasses harmony and tonality as well as rhythm. Of these, a reading of all the above authors would suggest that harmony is most readily researched, but perhaps most difficult to defend as a descriptor of all of music. Tonality is considered a little more inclusive in the features it encompasses, but due to external forces has become conflated with racist agendas all the same. Rhythm is perhaps least problematic of all here, partly due to its being underresearched and less developed within music theory specifically. In music cognition, in contrast to music theory, rhythm is easily one of the most established areas of contemporary study (Levitin, Grahn, and London 2018). Research agendas that focus their efforts toward a theory of musical rhythm (Large and Jones 1999; Toussaint 2019) may prove to lend themselves well toward building the "extension to the building" (to reuse Yust's metaphor) once the fence of tonality has been torn down.Moving beyond the unproductive study of tonality as a holistic organizing principle, I am interested in novel ways to study the key concepts of diverse musical systems. This novel approach should be able to account for multiple emergent properties of pitch-related relationships that unfold over time, such as the sense of a tonal center and the predictability of organized sets (such as scales) that afford forms and functions, as well as the generation of expectancy, tension, and resolution on the part of the listener. Importantly, an approach toward studying these pitch-related characteristics of music should accomplish the above goals without taking away the agency of the listener or the performer.Vuust et al. point toward artificial tonal systems and grammars, and the statistical learning thereof, as a logical extension toward a less problematic research agenda that investigates the principles underlying music perception, action, emotion, and learning as guided by the constraints of the brain's generative model. As artificial tonal systems can be designed to differ not only from Western tonal music but also from music of any established tradition, these systems may represent an important path forward for music theory. Much in the same way, studies in linguistics have moved past studies of European languages toward artificial languages (Hudson Kam and Newport 2005) and conlangs (Schreyer 2021) to show that the process of learning and creating new languages can elucidate the mechanisms of language learning while also creating real-world shifts in worldview among the learners themselves. Music in alternate scale systems, such as in the Bohlen-Pierce scale, lends itself to many of the same properties that tonal music affords. Heinz Bohlen and John Pierce independently conceived of the scale, which was then used for psychoacoustic studies as well as music-theoretical work by Max Mathews (e.g., in Mathews et al. 1988), who is widely credited as the founder of computer music.It is perhaps worth noting that neither Bohlen nor Pierce trained as a musician, but both trained as engineers with interests in music. Bohlen was a microwave engineer who described himself as "musically illiterate" but took on a side job when a friend who was a graduate student at the Hamburg Hochschule für Musik und Theater asked him to begin recording concerts at the school (Bohlen 2010). Being exposed to live performances of many different genres all at once, led Bohlen to ask the question of "With a universe of pitch steps available, why being sic so selective?" After reading works of Paul Hindemith, whose music was deemed "degenerate" by the Nazis and who fled Germany in 1938 (ORT n.d.), Bohlen (2010) concluded, If the axioms that were found are considered to have general validity, why not apply them to a theoretical system with only cubic-non-linear elements? . . . Sorting them according to their span and filling in all gaps following given examples produced a 13-step scale within the compass of 3/1. And lacking John Pierce's knack for inventing striking names, that is exactly what I called my discovery: the 13-step scale. Actually, I wasn't even certain at that time whether it was a discovery at all. After all, there was for quite a while no way to hear the scale or its intervals. All I knew was that there was a far-reaching duality to the traditional Western scale. That had to have a meaning.John Pierce was best known for his early ideas that led to the use of satellites for radio communications and was director of research at Bell Telephone Laboratories from 1951 to 1965. In a brief article published in the Journal of the Acoustical Society of America in 1966, Pierce wrote, "It appears that, by providing music with tones that have accurately specified but nonharmonic partial structures, the digital computer can release music from the tyranny of 12 tones without throwing consonance overboard" (Pierce 1966). Max Mathews wrote in Pierce's obituary, "He ended his career with undiminished creativity as a visiting professor of music, emeritus, at Stanford University, beginning in 1983. There he invented a new 13-tone music scale that spans not an octave but a tritave—an interval with a 1:3 frequency ratio" (Mathews 2003). However, Pierce credited Bohlen for finding the scale: "Unknown to Max Mathews and this author at the time, this question was pursued by Bohlen in a paper published in 1978 Bohlen 1978, and possibly earlier" (Pierce 1999).These men were undoubtedly trained in a Western context and therefore were sensitive to the same systemic forces that shaped a white-normative society that also shaped Western music. But the primary motivators behind the discovery of these music-theoretical tools seem to be curiosity, humility, and interdisciplinary collaboration, coupled with mathematical creativity, as opposed to the teleological thinking that links Western tonality to white-supremacist agendas. Thus, work in these scales may help break the coherence of tonality as a racist concept, by offering a logical extension to studying human perception, cognition, and learning of musical systems while not fitting into the evolutionary/teleological narrative. While it was conceptualized through mathematical exercises in divergent thinking by Western-trained thinkers to share many of the same features as Western tonal harmony, future work may compare this artificial scale with other theoretical or measured scales around the world (McBride, Passmore, and Tlusty 2021) without falling back on the teleological evolutionary narrative that Fétis and others adopted, as Yust shows, in pseudo-scientific defense of colonialism and white supremacy.William Sethares (2004) quips, in a fascinating nod to its complex historical context: "The octave is dead . . . long live the octave." Perhaps by investigating this otherworldly alternative tuning system that evades the octave, we can be learning simultaneously not only about the Western musical scale but also about the perceptual realities that can give rise to many musical systems (Loui 2012). Music in the Bohlen-Pierce scale has many perceptual and conceptual affordances (Krumhansl 1987; Mathews et al. 1988): the systematic relationships between pitches can give rise to consonance and dissonance, a tonal center, and leading tones. Tonal expectations for this scale can be rapidly acquired and generalized by Western listeners after only a short period of exposure to monophonic melodies (Loui et al. 2010), evincing similar neural responses for triadic harmony as Western chord progressions (Loui et al. 2009). Systematic manipulations of these expectations can, in turn, give rise to tension and resolution, result in call and response patterns, and invoke imagery and creativity while being realizable by acoustic as well as digital instruments (Hajdu 2015). And while it remains to be seen the extent to which individuals with non-Western musical experiences can quickly learn these relationships, results so far support that perceptual learnability of the Bohlen-Pierce scale is not limited to Western-trained listeners: In several hundred listeners recruited from China, we observed a similar pattern of learning and liking as US-based listeners for music written in Bohlen-Pierce scale (Kathios et al. 2023). Although the Chinese listeners primarily do have some experience with Western tunings, they also have more experience with the pentatonic scale than most US-based listeners do. While more work is needed to clarify the relationship between Chinese tuning systems and the Bohlen-Pierce scale, the results so far suggest that the acquisition of the same concepts that we group under tonality—for example, tonal center, scale, and harmony—can indeed be acquired under this new system.While the ability to learn from new musical sounds may be similar among cultures, the way music taps into imagination and creativity also underlies a set of questions of interest in music cognition. The imagined stories that listeners generate in response to Bohlen-Pierce-scale music are highly filtered through their own cultural lenses. Imagined stories that were prompted by Bohlen-Pierce-scale music show more similarity within cultures than among cultures even while both cultures found the music to be similarly unfamiliar and similarly engaging to listen to (Loui et al. 2023). Thus, artificial scales can afford the culture-bounded intersubjectivity that characterizes cognitive capacities of imagination and creativity (Margulis et al. 2022), as well as perceptual realities for listeners from more than one culture.To what degree can new music tap into the generative models of the mind, given the statistically learned predictive processes that guide how it has evolved to function? That strikes me as a productive research question, one that is informed but not tyrannized by the past, and one that returns agency to the contemporary listener. Part of the answer to this research question remains to be seen from studying what our minds can do, not what someone else's mind has already done. To the extent to which we believe that studying the brain can effectively answer questions about the mind, and to the extent to which predictive properties constrain how the brain works, we should be studying prediction at multiple levels. At a high level, this includes imagination and creativity—the act of generating musical ideas that have not yet been realized and yet are possible given one's background and culture.Looking to the future, I remain optimistic for music theory as a dynamic field of study, perhaps informed by ideas on predictive coding as described above (Clark 2013). With the knowledge that present perception is predicated on but not limited to past history, combining sensitive consideration of the past with more flexible, inclusive, and forward-thinking experiments may open up new possibilities for music studies (Margulis, Loui, and Loughridge 2023). While it behooves us to turn toward perceptual language, perception itself is a complex system that can be analyzed at multiple levels of description (Marr 1982). While mathematical models such as the geometry of musical spaces (Tymoczko 2010) offer a computational level of description, cognitive and neural studies offer the algorithmic and implementational levels of analysis of the more generalizable predictions and expectations that underlie musical creativity (Loui 2018, 2022).To conclude, I am sympathetic to Yust's sentiment: that the term tonality has become irreconcilably conflated with its problematic teleological evolutionary narrative, and that rejecting the use of tonality as a unified classifier is a major step in active pursuit of anti-racist research and pedagogical agendas against a white-normative current. I propose that turning to agent-centered perceptual predictions across multiple levels of analysis, such as for new music, offers a productively generalizable step moving forward.I thank Deirdre Loughridge, Elizabeth Margulis, and Aniruddh Patel for insightful comments on earlier versions. Preparation of this article was supported by National Science Foundation (NSF-CAREER 1945436, NSF-BCS 2240330), National Institutes of Health (R21AG075232, R43AG078012, and R01AG078376), and Northeastern University's College of Arts, Media and Design.