Hearing the Tonality in Microtonality

In the late 1970s and 1980s, composer-pianist Easley Blackwood wrote a series of microtonal compositions exploring the tonal and modal behavior of a dozen non–twelve-tone equal temperaments, ranging from 13 to 24 tones per octave. This dissertation investigates a central paradox of Blackwood’s microtonal music: that despite being full of intervals most Western listeners have never heard before, it still seems to “make sense” in nontrivial ways. Much of this has to do with the music’s idiosyncratic approach to tonality, which I define as a regime of culturally conditioned expectations that guides one’s attentional processing of music’s gravitational qualities over time. More specifically, Blackwood configures each tuning’s unfamiliar elements in ways that correspond to certain schematic expectations Western listeners tend to have about how tonal music “works.” This is why it is still possible to hear the forest of tonality in this music, so to speak, despite the odd-sounding trees that comprise it. Because of its paradoxical blend of expectational conformance and expectational noncompliance, Blackwood’s microtonal music makes for a useful tool to snap most Western-enculturated listeners out of their ingrained modes of musical processing and reveal certain things about tonality that are often taken for granted. Accordingly, just as Blackwood writes conventional-sounding music in unconventional tunings, this dissertation rethinks several familiar music-theoretic terms and concepts through the defamiliarizing lens of microtonality. I use Blackwood’s microtonal music as a prism to shine a light on traditional theories of tonality, scale degrees, consonance and dissonance, and harmonic function, arguing that many of these theories rely on assumptions that are tacitly tied to twelve-tone equal temperament and common-practice major/minor music. By unhooking these terms and concepts from any one specific tuning or historical period, I build up a set of analytical tools that can allow one to engage more productively with the many modalities of tonality typically heard on a daily basis today. This dissertation proceeds in six chapters. The four interior chapters each center on one of the terms and concepts mentioned above: scale degrees (Chapter 2), consonance and dissonance (Chapter 3), harmonic function (Chapter 4), and tonality (Chapter 5). In Chapter 2, I propose a system for labeling scale degrees that can provide more nuance and flexibility when reckoning with music in any diatonic mode (and in any tuning). In Chapter 3, I advance an account of consonance and dissonance as expectational phenomena (rather than purely psychoacoustic ones), and I consider the ways that non-pitched elements such as meter and notation can act as “consonating” and/or “dissonating” forces. In Chapter 4, I characterize harmonic function as arising from the interaction of generic scalar position and metrical position, and I devise a system for labeling harmonic functions that is better attuned to affective differences across the diatonic modes. In Chapter 5, I synthesize these building blocks into a conception of fuzzy heptatonic diatonic tonality that links together not only all of Blackwood’s microtonal compositions but also more familiar musics that use a twelve-tone octave, from Euroclassical to popular styles. The outer chapters are less explicitly music-analytical in focus. Chapter 1 introduces readers to Blackwood’s compositional approach and notational system, considers the question of his intended audience, and discusses the ways that enculturation mediates the cognition of microtonality (and of unfamiliar music more generally). Chapter 6 draws upon archival documents to paint a more detailed picture of who Blackwood was as a person and how his idiosyncratic worldview colors his approach to composition, scholarship, and interpersonal interaction. While my nominal focus in these six chapters is Blackwood’s microtonal music, the repertorial purview of my project is far broader. One of my guiding claims throughout is that attending more closely to the paradoxes and contradictions of Blackwood’s microtonality can help one better understand the musics they are accustomed to hearing. For this reason, I frequently compare moments in Blackwood’s microtonal music to ones in more familiar styles to highlight unexpected analogies and point up common concerns. Sharing space with Blackwood in the pages that follow are Anita Baker, Ornette Coleman, Claude Debussy, and Richard Rodgers, among others—not to mention music from Curb Your Enthusiasm, Fortnite, Sesame Street, and Star Wars. Ultimately, this project is a testament to the value of stepping outside of one’s musical comfort zone. For not only can this reveal certain things about that comfort zone that would not be apparent otherwise, but it can also help one think with greater nuance, precision, and (self-)awareness when “stepping back in” to reflect upon the music they know and love

Towards music perception by redundancy reduction and unsupervised learning in probabilistic models

PhDThe study of music perception lies at the intersection of several disciplines: perceptual psychology and cognitive science, musicology, psychoacoustics, and acoustical signal processing amongst others. Developments in perceptual theory over the last fifty years have emphasised an approach based on Shannon’s information theory and its basis in probabilistic systems, and in particular, the idea that perceptual systems in animals develop through a process of unsupervised learning in response to natural sensory stimulation, whereby the emerging computational structures are well adapted to the statistical structure of natural scenes. In turn, these ideas are being applied to problems in music perception. This thesis is an investigation of the principle of redundancy reduction through unsupervised learning, as applied to representations of sound and music. In the first part, previous work is reviewed, drawing on literature from some of the fields mentioned above, and an argument presented in support of the idea that perception in general and music perception in particular can indeed be accommodated within a framework of unsupervised learning in probabilistic models. In the second part, two related methods are applied to two different low-level representations. Firstly, linear redundancy reduction (Independent Component Analysis) is applied to acoustic waveforms of speech and music. Secondly, the related method of sparse coding is applied to a spectral representation of polyphonic music, which proves to be enough both to recognise that the individual notes are the important structural elements, and to recover a rough transcription of the music. Finally, the concepts of distance and similarity are considered, drawing in ideas about noise, phase invariance, and topological maps. Some ecologically and information theoretically motivated distance measures are suggested, and put in to practice in a novel method, using multidimensional scaling (MDS), for visualising geometrically the dependency structure in a distributed representation.Engineering and Physical Science Research Counci

Music Listening as Therapy

Music is a universal phenomenon and is a real, physical thing. It is processed in neural circuits that overlap with language circuits, and it exerts cognitive, emotional, and physiological effects on humans. Many of those effects are therapeutic, such as reduced symptoms of physical and mental ailments. Music is the result of the elements rhythm, melody, harmony, timbre, dynamics, and form. Rhythm is the focus of pop music, and melody is the focus of classical music. The mind perceives and organizes music in learned, consistent ways in order to generate predictions and extract meaning. There are perceptual laws and information processing limitations to this process. Predictions are based in schematic and veridical approaches, which give rise to expectations. Frustrated expectations result in an effective response. Music only has meaning unto itself and the music listener ascribes any extra-musical meaning. This includes any emotional meaning. The unfolding of a song is much like how Gestalt Therapy theory conceptualizes human experience. Mindfulness offers a clear definition of how one can frame and approach experience to support health and well-being. MinMuList (said “min-mew-list”) is an evidenced-based workshop that offers a concise discussion and straightforward methods for implementation of these aspects of music and psychology

A Derivation of the Tonal Hierarchy from Basic Perceptual Processes

In recent decades music psychologists have explained the functioning of tonal music in terms of the tonal hierarchy, a stable schema of relative structural importance that helps us interpret the events in a passage of tonal music. This idea has been most influentially disseminated by Carol Krumhansl in her 1990 monograph Cognitive Foundations of Musical Pitch. Krumhansl hypothesized that this sense of the importance or centrality of certain tones of a key is learned through exposure to tonal music, in particular by learning the relative frequency of appearance of the various pitch classes in tonal passages. The correlation of pitch-class quantity and structural status has been the subject of a number of successful studies, leading to the general acceptance of the pitch-distributional account of tonal hierarchy in the field of music psychology. This study argues that the correlation of pitch-class quantity with structural status is a byproduct of other, more fundamental perceptual properties, all of which are derived from aspects of everyday listening. Individual chapters consider the phenomena of consonance and dissonance, intervallic rootedness, the short-term memory for pitch collection, and the interaction of temporal ordering and voice-leading that Jamshed Bharucha calls melodic anchoring. The study concludes with an elaborate self-experiment that observes the interaction of these properties in a pool of 275 stimuli, each of which is constructed from a single dyad plus one subsequent tone

The Choreography of the Soul: A Psychedelic Philosophy of Consciousness

This is a 2020 revision of my 1988 dissertation "The Choreography of the Soul" with a new Foreword, a new Conclusion, a substantially revised Preface and Introduction, and many improvements to the body of the work. However, the thesis remains the same. A theory of consciousness and trance states--including psychedelic experience--is developed. Consciousness can be analyzed into two distinct but generally interrelated systems, which I call System X and System Y. System X is the emotional-visceral-kinaesthetic body. System X is a harmonic system of "endokinetic" (internal bodily) and "ectokinetic" (emotionally expressive) movement. System Y is a "teleokinetic" (goal directed) system that includes language, cognition, perception, voluntary motor control, manipulation of the environment, etc. Contrary to theories of consciousness prevalent in the Western philosophical traditions that begin with Plato, I argue that System Y is secondary to and dependent upon System X, not the reverse. In building my thesis I draw upon the work of Friedrich Nietzsche, psychoanalysis, Jungian depth psychology, political anthropology, modern neuroscience, Pythagorean music theory, and the mathematical theory of harmonic systems

Harmonic duality : from interval ratios and pitch distance to spectra and sensory dissonance

Dissonance curves are the starting point for an investigation into a psychoacoustically informed harmony. Its main hypothesis is that harmony consists of two independent but intertwined aspects operating simultaneously, namely proportionality and linear pitch distance. The former aspect is related to intervallic characters, the latter to ‘high’, ‘low’, ‘bright’ and ‘dark’, therefore to timbre. This research derives from the development of tools for algorithmic composition which extract pitch materials from sound signals, analyzing them according to their timbral and harmonic properties, putting them into motion through diverse rhythmic and textural procedures. The tools and the reflections derived from their use offer fertile ideas for the generation of instrumental scores, electroacoustic soundscapes and interactive live-electronic systems.LEI Universiteit LeidenResearch in and through artistic practic