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Crystals of Sound: Applying the Physics of Phase Transitions to Musical Intonation
No full textWe explore a physics-based model describing systems of musical intonation. Under the assumption that tuning systems seek to balance minimization of dissonance with maximization of compositional variety, we can use the same methods that are used to describe how transitions between the phases of matter are governed by a balance between minimizing energy and maximizing entropy. In both cases, a parameter – temperature – controls the balance between these factors. We show that as the temperature is raised from low to high, our model generates tuning systems that closely resemble those used throughout the history of Western music, from just intonation, to meantone temperaments, to equal temperament. We demonstrate how our model reflects the way in which tuning systems evolved along with trends in composition by comparing the results of our model vs. temperature to a corpus of 9620 pieces vs. year of composition from 1568-1968. By changing parameters in the model, we also find that other tuning systems, such as 31-tone temperaments, emerge. These results provide a new lens for understanding tuning systems, and a new approach for generating novel systems of intonation
Aesthetics, Modalities, Evolution, and Creativity: Commentary on Friedman et al. (2024)
No full textThis commentary situates Friedman et al. (2024) – and by extension, Clemente et al. (2021) – within a broader research context. Both papers raise important issues, but neither study’s result can be considered definitive. The operationalization and assessment of aesthetic constructs across many investigations should reflect the inherent diversity of human artmaking, yielding a structured sense of the conditions under which modality-specific versus modality-general representations predominate in aesthetic or evaluative cognition. Additionally, I note that this research enterprise touches on two sets of issues, which are simultaneously central to an understanding of the nature of human artistry, yet which remain under-represented in contemporary research. One concerns the murky evolutionary origin of our human artistic capacity, including the role of cross-modal processing and its role in aesthetic cognition. The second involves the first-person deployment of this capacity in creative problem solving, rather than in a merely receptive mode. Both speak to the importance of understanding inherent structure and constraints on human aesthetics and creativity
Sources of Gene Tree Discordance and Their Implications for Systematics and Evolution of a Megadiverse Australian Plant Radiation (Subtribe Hakeinae, Proteaceae)
No full textResolving phylogenetic relationships in the presence of conflicting signal across genes is one of the major challenges of the phylogenomic era. Conflicting signal can emerge from biological processes, such as incomplete lineage sorting or introgression, or have technical origins, such as from misaligned sequences. Decisions made in the process of estimating species trees may therefore result in alternative tree topologies and large variation in branch support values with important taxonomic consequences. To explore how these methodological choices affect the estimation of relationships, we compare alternative strategies for alignment cleaning, loci filtering, and phylogenetic estimation for 551 taxa in the Proteaceae subtribe Hakeinae. We found that node support values across gene trees were generally low and gene discordance was high in the Hakeinae, and that the degree of discordance varied across the phylogeny, as well as geographically across Australia. Higher stringency of alignment cleaning tended to decrease node support, while removing undesirable loci tended to increase gene concordance. Cleaning, filtering, and phylogenetic estimation method (short-cut coalescent vs. concatenation) have significant effects on tree topologies with distinct clusters of similar topologies detected in tree space. In some cases, this has important systematic consequences for two of Australia’s largest and best-known plant genera, with concatenated approaches resolving Hakea and Grevillea as reciprocally monophyletic, but coalescent approaches showing that Hakea is nested within Grevillea. Our results suggest that widespread gene discordance may be the result of rapid radiation and incomplete lineage sorting, demonstrating the importance of assessing the drivers of discordance to understand phylogenetic relationships
Going to Therapy With John Bunyan
No full textReaders have long recognized that Grace Abounding (first edition 1666) might suggest that John Bunyan (b. 1628 – d. 1688) suffered from mental illness. Some critics have posited that Bunyan suffered from obsessive-compulsive disorder, but others argue that what may appear to be OCD symptoms in Bunyan's narrative are in fact processes of spiritual examination fostered by early modern Protestant devotion. Drawing on my own experience as an OCD sufferer, I argue that far from encouraging religious scrupulosity (a type of OCD), early modern Protestant devotional practice contains strategies that anticipate modern OCD therapy and therefore may well have helped Bunyan manage his OCD symptoms. Bunyan had access to these strategies by way of the commentary on Galatians (first edition 1535) by the German Reformation theologian Martin Luther (b. 1483 – d. 1546). Luther directs his readers to understand their spiritual anxieties and troubling thoughts as trials visited upon them by Satan, and he encourages them not to respond to these anxieties and thoughts by performing works but instead to wait faithfully upon divine aid. Similarly, in OCD therapy, patients are taught that intrusive thoughts are outside of our conscious control, and we are instructed not to respond to these thoughts by performing actions (compulsions), which only validate and intensify the anxiety, but rather to "sit with" the anxiety and wait for it to pass. Bunyan's spiritual autobiography therefore suggests that he used devotional practice to make sense of his own experience and to manage his mental and spiritual affliction
Texture and Sonata Form in Classical String Quartets: A Corpus Study
No full textHow does musical texture relate to large-scale form in classical string quartets? Are certain textural strategies associated with sections or formal functions in a sonata movement? Some music theorists have argued that contrapuntal textures are more common in developments and transitions. In their view, these medial sections would use polyphony to foster a sense of looseness, instability, and momentum. Our study tested these claims by examining a pre-existing corpus of string quartet movements in sonata form by Joseph Haydn, Wolfgang Amadeus Mozart, and Ludwig van Beethoven. We measured texture in terms of average onset synchrony, where lower onset synchrony represents greater rhythmic and textural independence among parts. Although average onset synchrony was lower in developments, compared to expositions, for most pieces in the corpus (65.22%), there was a significant interaction between section and composer, and post hoc analysis indicated that this difference in onset synchrony was significant only for Beethoven. Within expositions, transitions did not tend to have lower onset synchrony, and there was no significant effect for subsection. However, there was a significant main effect for composer here. Overall, these results imply that textural strategies in classical sonata form are complex and may vary from piece to piece and from composer to composer
Reexamining the Association between Aesthetic Sensitivity to Musical and Visual Complexity
No full textIn a provocative recent study, Clemente et al. (2021) found that individual differences in aesthetic sensitivity to stimulus complexity in the musical domain were uncorrelated with those in the visual domain. This ostensibly contradicts existing theory and research pointing to a link between idiographic preferences for musical and visual complexity. However, a review of their methodology reveals that Clemente et al. (2021) inadvertently introduced confounds in the temporal dynamics of their experimental stimuli as well as in their operational definitions of complexity in each domain. To address these confounds, we conceptually replicated part of their procedure using musical and visual stimuli that were either very closely matched in their temporal dynamics and/or for which complexity was operationalized more similarly. With these modifications, reliable positive correlations indeed emerged between aesthetic sensitivities to complexity across domains, providing renewed evidence for cross-modal correspondence in evaluative responses to musical sounds and visual images
Commentary on Buechele et al. (2023): Communicating Across the Divide – a Place for Physics in Music?
No full textThe theory of Jesse Berezovsky (2019) is a rare foray of a physicist into the territory of music science. In their follow-up article in Empirical Musicology Review, Ryan Buechele, Alex Cooke, and Jesse Berezovsky (2024) show how the evolution of Western tuning systems and compositions can be rationalized by a theoretical model that describes a trade-off between minimizing sensory dissonance and maximizing compositional variety. From the Renaissance period onwards there was a trend towards more dissonance, and more compositional variety in both tuning systems and compositions. While this historical progression has perhaps been described qualitatively elsewhere, this model provides a more precise quantitative description of the phenomenon. The validity and scope of this model ought to be tested further by comparing its predictions with empirical measurements of tuning systems in both Western and non-Western cultures, alongside predictions of other theories of scale evolution. In the hope of encouraging and facilitating more of these interdisciplinary endeavors, I discuss some of my anecdotal experiences as a physical scientist embedded in the music science community, and offer advice on how to achieve better understanding and communication across disciplines
An Alternative Proof that the Real Numbers are Uncountable
No full textMany students as well as educators find it difficult to accept Cantor’s Diagonalization argument that the real numbers are uncountable. In this paper, we provide an alternative proof that may be easier for students to accept. The proof could provide further insight into the reason that the real numbers are uncountable. That is, any statement that leads to anything being possible includes the fact that the statement is impossible