Applications of system dynamics modelling to computer music

Based on a composer's psycho-acoustic imagination or response to music, system dynamics modelling and simulation tools can be used as a scoring device to map the structural dynamic shape of interest of computer music compositions. The tools can also be used as a generator of compositional ideas reflecting thematic juxtaposition and emotional flux in musical narratives. These techniques allow the modelling of everyday narratives to provide a structural/metaphorical means of music composition based on archetypes that are shared with wider audiences. The methods are outlined using two examples

Linear Verticalities: Structural symbiosis among chromatic and microtonal aggregations in Georges Aperghis' Contretemps AND les instances (2019) for diffused, synthesized sounds and large ensemble

This dissertation aims to shed light on aspects of harmonic construction in Georges Aperghis' Contretemps, a twenty-minute composition for soprano and large ensemble. The foundation of this analysis is the hypothesis that the piece is governed by emblematic intervallic aggregations while their linear and vertical hypostases are inextricably intertwined with each other, formulating global axioms for the harmonic construction of the piece. Through a series of reductions and prolongational analyses, the research explores the role of the linear pitch aggregations articulated in various instrumental combinations. This analysis uses Allen Forte's pitch-class set theory for the representation of the intervallic structures, while 24-tone equal temperament (24-TET) serves as a point of reference in organizing the chromatic and microtonal pitch aggregations. The continual fusion of chromatic and microtonal entities forges a saturated soundscape with, sometimes, indiscernible chordal constructions. Multiple overlapping perspectives are possible concerning the global intervallic axioms that underline and determine distinct archetypes of chordal structures in the work

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

Organicism in Live Experimental Electroacoustic Music

This paper explores the potential for an organicist or relational holistic approach to experimental electroacoustic music composition that is indeterminate with respect to performance. It follows a phenomenological interpretation of the musical work as the product of dynamic, temporal or relational processes involving the performers, their instruments, the sounds themselves, the whole acoustic space and the audience. An analysis of an electroacoustic composition and Decibel ensemble performance is offered for which organic indeterminacy is described in terms of a performative openness towards the creation of experimental music

From novel to familiar : the learning of pitch intervals and event frequencies in microtonal music systems

This PhD project aims to investigate the learning of novel music systems during brief exposures (up to 20 minutes). Specifically, it examined the learning of microtonal pitch systems, including the learning of their pitch interval structure and the frequency of occurrence of each pitch member of the systems. Five experiments have been conducted and the findings are separately submitted to peer-reviewed journals for publication. The submitted manuscripts are provided as individual chapters in this thesis. Experiment 1 and 2 are presented in manuscript (MS) 1, 3 is presented in MS 2, while 4 and 5 are presented in MS 3. Experiments in MS 1 explored the influence of structural similarity on the learning of novel tuning systems. Non-musicians were exposed to microtonal tuning systems that are different from the western tonal system (12-tone equal temperament or 12TET) in terms of temperament (equal or unequal) and pitch intervals (based on frequency ratio(s) or frequency difference). It was hypothesized that systems that are structurally similar to 12TET in terms of temperament and pitch interval definitions (such as 11TET) would be learned more rapidly than those that are dissimilar (such as the 81 primes scale). This hypothesis was supported in part by earlier evidence on the influence of prior musical knowledge on the learnng of unfamiliar music (such as Oram & Cuddy (1995) and Rohrmeier & Widdess (2012)). Participants were tested on their memory of the relative pitches of each tuning system as well as their knowledge of which relative pitches correspond to which tuning system (pitch membership). Results indicate better pitch memory for the tuning system with two frequency ratios (Tuning system: WF) while learning of pitch membership was not found after a brief exposure. Given the findings in MS 1, MS 2 targeted the incidental learning of a microtonal scale that follows a pitch interval structure similar to WF in MS 1, which is unequal tempered with two frequency ratios. This MS extends the data-driven interpretation of MS1 in terms of my overall hypothesis. Thus, a new paradigm is developed and learning of the scale is implied by the level of sensitivity to the incongruent pitch intervals. This paradigm utilises a timbre shift detection task where participants are required to detect a timbre shift in one of the pitches of a microtonal melody. The pitch before the shift is manipulated to be either a member of the scale (congruent), just like the rest of the pitches in the melody, or a pitch from a different musical scale (incongruent). The melodies are arranged such that an incongruent pitch is a statistical cue to an upcoming timbre shift, so that when participants hear an incongruent pitch, they would have high expectation of the imminent shift and therefore respond faster when it comes. However, faster reaction times would only be observed if participants have sufficiently learnt the pitch intervals of the microtonal scale and the relationship between the incongruent pitch and the timbre shift. In other words, a faster reaction time is expected in the condition where an incongruent tone was placed before the timbre shift, than in the condition where the incongruent tone was absent. Non-musicians in MS 2 showed successful learning of both, and this experiment was extended in MS 3 where musicians were tested. Surprisingly, the same results were not observed in musicians who are professionally trained in 12TET only (general musicians) and those who are microtonal music experts (trained in 12TET and also had extensive experience in multiple microtonal tunings). While similar results with those from the non-musicians might be obtained by having a comparative sample of general musicians, the unexpected results among microtonal musicians, ironically, might still be due to their musical experience and practice. MS 3 also interrogated our overall hypothesis further by examining the learning of the frequency of occurrence of pitches of the same microtonal scale (the relative event-frequencies) in non-musicians: a similar approach was previously taken by Loui & Schlaug (2012), who examined the learning of event frequencies of the Bohlen-Pierce scale. The effect of structural similarity was once again investigated by the manipulation of event-frequency of the microtonal scale so as to be similar or dissimilar to the functional hierarchy (difference in usage) of pitches in diatonic music. Participants were exposed to melodies generated based on the similar or dissimilar pattern of event-frequency and goodness-of-fit ratings of pitches of the scale were obtained at random points in the melodies. Results delineate an insignificant effect of structural similarity, since learning was found in both patterns of event-frequency, implied by the positive correlation between the goodness-of-fit rating and the frequency of occurrence of the corresponding pitches, and demonstrated by an analytical model of the results showing the influence of the pitch-class probabilities. This result illustrates the ability to learn event frequencies in a novel musical scale among musically untrained participants. Altogether, the findings in all the experiments indicate that non-musicians can learn aspects of the pitch intervals and event-frequency of an unfamiliar microtonal scale rapidly, and learning is faster when the scale is well-formed and octave-based with two frequency ratios. Inconsistent with predictions, general and microtonal musicians did not show such rapid learning, and how this might relate to the paradigm used is discussed. This project provides informative understanding of how listeners with different musical background and experiences approach and learn a novel music system, which has implications for research in music cognition and perception, traditional and computer music composition, music production, and music performance including improvisation

Criação de música baseada na proporção áurea: abordagem teórica e prática à escala de 34 tons de igual temperamento

The sensory phenomena of music perception are considered to be highly non-linear. The golden ratio plays a key role in nonlinear dynamic systems and has been recognized as an aesthetic element in many places over time. This research develops the 34-note equal tempered scale (34-TET). A microtonal model based on the golden ratio, containing the harmonic musical intervals, and permitting a consistent approach that embraces the different temperaments throughout history, as well as other music cultures. These theoretical properties are practically exposed in two portfolios, including compositional samples of art music with European roots (from the Renaissance to the twentieth century), popular music (bossa nova, tango, swing), maqãm, and Indian music. The second portfolio, created within the scope of this thesis, contains the artistic work “The Asian Garden” combining the equal tempered scales of 34 and 12 notes (12-TET), and provides additional cultural references from China and Japan. The 34-TET scale offers an overall approach to just intonation scale more than twice as good as that of 12-TET, with all consonant intervals well below the differential threshold. If a maximum impurity value was accepted, not appreciably different from that agreed upon when the equal-tempered 12- tone scale was standardized (17.65 cents vs. 15.67 cents), then the 34-TET scale would become, additionally, a useful tool for approaching different cultures.Os fenómenos sensoriais de perceção musical são considerados substancialmente não lineares. A proporção áurea desempenha um papel fundamental em sistemas dinâmicos não lineares e tem sido reconhecida como um elemento estético em vários contextos ao longo do tempo. Esta investigação desenvolve a escala de 34 notas de temperamento igual (34- TET). Trata-se de um modelo microtonal baseado na proporção áurea, contendo os intervalos harmónicos musicais, e permitindo uma abordagem consistente que abrange os distintos temperamentos ao longo da história, assim como outras culturas musicais. Estas propriedades teóricas estão praticamente expostas em dois portefólios, incluindo exemplos de composição erudita com raízes europeias (desde o Renascimento ao século XX), música popular (bossa nova, tango, swing), maqãm e música indiana. O segundo portefólio contém o trabalho artístico “The Asian Garden,” criado no âmbito desta tese, que combina escalas de temperamento igual de 34 e de 12 notas (12-TET), e fornece referências culturais adicionais da China e Japão. A escala 34-TET oferece uma abordagem global à escala de entonação justa que é mais de duas vezes melhor do que a da escala 12-TET, com todos os intervalos consonantes consideravelmente abaixo do limiar diferencial. Se fosse aceite um valor máximo de impureza não muito diferente do valor acordado quando a escala de 12 tons igualmente temperados foi padronizada (17,65 cents em vez de 15,67 cents), a escala 34-TET tornar-se-ia, adicionalmente, uma ferramenta útil para a aproximação de culturas diferentes.Programa Doutoral em Músic

Teaching rule‐based algorithmic composition: the PWGL library cluster rules

This paper presents software suitable for undergraduate students to implement computer programs that compose music. The software offers a low floor (students easily get started) but also a high ceiling (complex compositional theories can be modelled). Our students are particularly interested in tonal music: such aesthetic preferences are supported, without stylistically restricting users of the software. We use a rule‐based approach (constraint programming) to allow for great flexibility. Our software Cluster Rules implements a collection of compositional rules on rhythm, harmony, melody, and counterpoint for the new music constraint system Cluster Engine by Örjan Sandred. The software offers a low floor by observing several guidelines. The programming environment uses visual programming (Cluster Rules and Cluster Engine extend the algorithmic composition system PWGL). Further, music theory definitions follow a template, so students can learn from examples how to create their own definitions. Finally, students are offered a collection of predefined rules, which they can freely combine in their own definitions. Music Technology students, including students without any prior computer programming experience, have successfully used the software. Students used the musical results of their computer programs to create original compositions. The software is also interesting for postgraduate students, composers and researchers. Complex polyphonic constraint problems are supported (high ceiling). Users can freely define their own rules and combine them with predefined rules. Also, Cluster Engine’s efficient search algorithm makes advanced problems solvable in practice

Classification of Triadic Chord Inversions Using Kohonen Self-organizing Maps

In this paper we discuss the application of the Kohonen Selforganizing Maps to the classification of triadic chords in inversions and root positions. Our motivation started in the validation of Schönberg´s hypotheses of the harmonic features of each chord inversion. We employed the Kohonen network, which has been generally known as an optimum pattern classification tool in several areas, including music, to verify that hypothesis. The outcomes of our experiment refuse the Schönberg´s assumption in two aspects: structural and perceptual/functional

HARMONIC INTONATION AND IMPLICATION (ANALYSES AND COMPOSITIONS): Harmonic perception and intonation in the reception and performance of alternative tuning systems in contemporary composition

Most composers and theorists will acknowledge that some compromise is necessary when dealing with the limitations of human performance, perception, and the realities of acoustic theory. Identifying the thresholds for pitch discrimination and execution is an important point of departure for defining workable tuning schemes, and for training musicians to realise compositions in just intonation and other alternative tuning systems. The submitted paper 'HARMONIC INTONATION AND IMPLICATION (ANALYSES AND COMPOSITIONS): Harmonic perception and intonation in the reception and performance of alternative tuning systems in contemporary composition' is a phenomenological study of harmonic perception and intonation through the analysis of recordings, scores, theoretical papers, and discussion with practicing musicians. The examined repertoire covers western 'art' music of the late nineteenth to early twenty-first centuries. I approach my research from the composer's point of view though filtered through the ears and eyes of the performer, who is here considered 'expert listener'. lt is considered that intonation is a dynamic experience subject to influences beyond just intonation or equal temperament (the two poles for intonational reference)-the performance is assumed 'correct', rather than the idealised version of the composer. My goal is to relate the performance to the intentions of the composer and raise questions regarding the choice of notation, resolution of the tuning systems, the complexity of the harmonic concept, etc. and perhaps to suggest how to extend a general theory of harmony that embraces both musical practice and psychoacoustics. lt is with the understanding that harmonic implication affects intonation, but that intonation is subject to several other forces making intonation a complex system (and therefore not fully predictable)