Academic literature on the topic 'Pitch-class set theory'

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Journal articles on the topic "Pitch-class set theory"

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Parks, Richard S. "Pitch-Class Set Genera: My Theory, Forte's Theory." Music Analysis 17, no. 2 (1998): 206. http://dx.doi.org/10.2307/854440.

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Heinemann, Stephen. "Pitch-Class Set Multiplication in Theory and Practice." Music Theory Spectrum 20, no. 1 (1998): 72–96. http://dx.doi.org/10.2307/746157.

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Heinemann, Stephen. "Pitch-Class Set Multiplication in Theory and Practice." Music Theory Spectrum 20, no. 1 (1998): 72–96. http://dx.doi.org/10.1525/mts.1998.20.1.02a00030.

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Buchler, Michael. "Analyzing atonal music: Pitch-class set theory and its contexts." Journal of Mathematics and Music 5, no. 2 (2011): 141–48. http://dx.doi.org/10.1080/17459737.2011.582814.

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Van Egmond, René, and David Butler. "Diatonic Connotations of Pitch-Class Sets." Music Perception 15, no. 1 (1997): 1–29. http://dx.doi.org/10.2307/40285737.

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This is a music-theoretical study of the relationship of two-, three-, four-, five-, and six-member subsets of the major (pure minor), harmonic minor, and melodic (ascending) minor reference collections, using pitchclass set analytic techniques. These three collections will be referred to as the diatonic sets. Several new terms are introduced to facilitate the application of pitch-class set theory to descriptions of tonal pitch relations and to retain characteristic intervallic relationships in tonal music typically not found in discussions of atonal pitch-class relations. The description comprises three parts. First, pitch sets are converted to pitchclass sets. Second, the pitch- class sets are categorized by transpositional types. Third, the relations of these transpositional types are described in terms of their key center and modal references to the three diatonic sets. Further, it is suggested that the probability of a specific key interpretation by a listener may depend on the scale-degree functions of the tones.
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Russ, M. "Analyzing Atonal Music: Pitch-Class Set Theory and Its Contexts. By Michiel Schuijer." Music and Letters 90, no. 4 (2009): 722–25. http://dx.doi.org/10.1093/ml/gcp075.

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Scheideler, Ullrich. "Michiel Schuijer, Pitch-Class Set Theory and The Construction of Musical Competence, Dissertation, Utrecht 2005." Zeitschrift der Gesellschaft für Musiktheorie [Journal of the German-Speaking Society of Music Theory] 5, no. 1 (2008): 181–88. http://dx.doi.org/10.31751/279.

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Salles, Paulo. "Voice Leading Among Pitch-Class Sets: Revisiting Allen Forte’s Genera." MusMat: Brazilian Journal of Music and Mathematics IV, no. 2 (2020): 66–79. http://dx.doi.org/10.46926/musmat.2020v4n2.66-79.

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The theory of PC-set class genera by Allen Forte was an important contribution to the understanding of similarity relations among PC sets within the tempered system. The growing interaction between the universes of PC-sets and transformational theories has been explored the space between sets of the same or distinct cardinality, by means of voice-leading procedures. This paper intends to demonstrate Forte’s method along with proposals by other authors like Morris, Parks, Straus, Cohn, and Coelho de Souza. Some analysis demonstrates such operations in passages picked from Heitor Villa-Lobos’s works, like the Seventh String Quartet and the First Symphony.
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Brown, Helen. "The Interplay of Set Content and Temporal Context in a Functional Theory of Tonality Perception." Music Perception 5, no. 3 (1988): 219–49. http://dx.doi.org/10.2307/40285398.

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The purpose of this study was to provide evidence for the perceptual component of an analysis of pitch relationships in tonal music that includes consideration of both formal analytic systems and musical listeners' responses to tonal relationships in musical contexts. It was hypothesized (1) that perception of tonal centers in music develops from listeners' interpretations of time-dependent contextual (functional) relationships among pitches, rather than primarily through knowledge of psychoacoustical or structural characteristics of the pitch content of sets or scales and (2) that critical perceptual cues to functional relationships among pitches are provided by the manner in which particular intervallic relationships are expressed in musical time. Excerpts of tonal music were chosen to represent familiar harmonic relationships across a spectrum of tonal ambiguity/specificity. The pitch-class sets derived from these excerpts were ordered: (1) to evoke the same tonic response as the corresponding musical excerpt, 2) to evoke another tonal center, and (3) to be tonally ambiguous. The effect of the intervallic contents of musical excerpts and strings of pitches in determining listeners' choices of tonic and the effect of contextual manipulations of tones in the strings in directing subjects' responses were measured and compared. Results showed that the musically trained listeners in the study were very sensitive to tonal implications of temporal orderings of pitches in determining tonal centers. Temporal manipulations of intervallic relationships in stimuli had significant effects on concurrences of tonic responses and on tonal clarity ratings reported by listeners. The interval rarest in the diatonic set, the tritone, was the interval most effective in guiding tonal choices. These data indicate that perception of tonality is too complex a phenomenon to be explained in the time-independent terms of psychoacoustics or pitch- class collections, that perceived tonal relationships are too flexible to be forced into static structural representations, and that a functional interpretation of rare intervals in optimal temporal orderings in musical contexts is a critical feature of tonal listening strategy.
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Frederick, Leah. "Generic (Mod-7) Voice-Leading Spaces." Journal of Music Theory 63, no. 2 (2019): 167–207. http://dx.doi.org/10.1215/00222909-7795257.

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This article constructs generic voice-leading spaces by combining geometric approaches to voice leading with diatonic set theory. Unlike the continuous mod-12 spaces developed by Callender, Quinn, and Tymoczko, these mod-7 spaces are fundamentally discrete. The mathematical properties of these spaces derive from the properties of diatonic pitch-class sets and generic pitch spaces developed by Clough and Hook. After presenting the construction of these voice-leading spaces and defining the OPTIC relations in mod-7 space, this article presents the mod-7 OPTIC-, OPTI-, OPT-, and OP-spaces of two- and three-note chords. The final section of the study shows that, although the discrete mod-7 versions of these lattices appear quite different from their continuous mod-12 counterparts, the topological space underlying each of these graphs depends solely on the number of notes in the chords and the particular OPTIC relations applied.
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Dissertations / Theses on the topic "Pitch-class set theory"

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McNeilis, Michael James. "Portfolio of compositions : pitch-class set theory in music and mathematics." Thesis, University of Liverpool, 2017. http://livrepository.liverpool.ac.uk/3009792/.

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This portfolio contains six scores of contemporary works, one electroacoustic piece submitted in concrete audio format and a critical commentary. Three additional scores are included as appendices, which present alternative arrangements of the acoustic works. An accompanying data DVD includes stereo recordings of a concert performance and four workshop performances, as well as stereo and 5.1 versions of the electroacoustic piece. With existing literature primarily focussing on pitch-class set theory as an analytical tool, this study aims to answer the question: Can set theory be used as the basis of a compositional framework to advance the creative process within the interdisciplinary field of music and mathematics? The pieces in the portfolio consider how set theory can be applied alongside mathematical principles like mutation, symmetry and proportion to inform musical networks and topologies based on material such as the octatonic scale, whole-tone scale and the all-interval tetrachords. A particular emphasis is placed on relationships between pitch-class sets in order to produce coherent compositional designs which link micro-level material to macro-level form and structure. Postcompositional evaluation of each work helps to create subsequent designs in the portfolio, and culminates in the piece Aggregation, which assesses the mathematical principles and compositional techniques developed earlier in the portfolio to encapsulate the research within a unified design and large-scale work. The results of the research establish set theory as a viable mathematical language for both the precompositional and compositional stages of the creative process, and demonstrate refinement of my own compositional methodology and musical style.
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Fernandez, Ibarz Erik. "Peter Schat's Tone Clock: The Steering Function and Pitch-Class Set Transformation in Genen." Thesis, Université d'Ottawa / University of Ottawa, 2015. http://hdl.handle.net/10393/32397.

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Dutch composer Peter Schat’s (1935-2003) pursuit of a compositional system that could generate and preserve intervallic relationships, while allowing the composer as much flexibility as possible to manipulate musical material, led him to develop the tone-clock system. Fundamentally comprised of the twelve possible trichords, the tone clock permits each to generate a complete twelve-tone series through the “steering” principle, a concept traced to Boulez’s technique of pitch-class set multiplication. This study serves as an overview of Schat’s tone-clock system and focuses primarily on the effects of the steering function in “Genen” (2000). Furthermore, I expand on the tone-clock system by combining transformational theory with Julian Hook’s uniform triadic transformations and my proposed STEER and STEERS functions, which express the procedures of the steering principle as a mathematical formula. Using a series of transformational networks, I illustrate the unifying effect steering has on different structural levels in “Genen,” a post-tonal composition.
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du, Plessis Janine. "Transformation Groups and Duality in the Analysis of Musical Structure." Digital Archive @ GSU, 2008. http://digitalarchive.gsu.edu/math_theses/66.

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One goal of music theory is to describe the resources of a pitch system. Traditionally, the study of pitch intervals was done using frequency ratios of the powers of small integers. Modern mathematical music theory offers an independent way of understanding the pitch system by considering intervals as transformations. This thesis takes advantage of the historical emergence of algebraic structures in musicology and, in the spirit of transformational theory, treats operations that form mathematical groups. Aspects of Neo-Riemannian theory are explored and developed, in particular the T/I and PLR groups as dual. Pitch class spaces, such as 12, can also be defined as torsors. In addition to surveying the group theoretical tools for music analysis, this thesis provides detailed proofs of many claims that are proposed but seldom supported.
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Ripley, Angela N. "Surviving Set Theory: A Pedagogical Game and Cooperative Learning Approach to Undergraduate Post-Tonal Music Theory." The Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1437583773.

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McGowan, James (James John). "Harmonic Organization in Aaron Copland's Piano Quartet." Thesis, University of North Texas, 1995. https://digital.library.unt.edu/ark:/67531/metadc278850/.

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Soares, Guilherme Rafael. "Luteria composicional de algoritmos pós-tonais." Universidade Federal de Juiz de Fora, 2015. https://repositorio.ufjf.br/jspui/handle/ufjf/112.

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Submitted by Renata Lopes (renatasil82@gmail.com) on 2015-12-07T16:46:12Z No. of bitstreams: 1 guilhermerafaelsoares.pdf: 5619162 bytes, checksum: 75fa907e315795bd1f893ed8c941e9bd (MD5)<br>Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2015-12-07T21:41:38Z (GMT) No. of bitstreams: 1 guilhermerafaelsoares.pdf: 5619162 bytes, checksum: 75fa907e315795bd1f893ed8c941e9bd (MD5)<br>Made available in DSpace on 2015-12-07T21:41:38Z (GMT). No. of bitstreams: 1 guilhermerafaelsoares.pdf: 5619162 bytes, checksum: 75fa907e315795bd1f893ed8c941e9bd (MD5) Previous issue date: 2015-03-30<br>FAPEMIG - Fundação de Amparo à Pesquisa do Estado de Minas Gerais<br>Esta pesquisa sistematiza um catálogo de experimentos constituído de estudos musicais e seus algoritmos geradores, organizando procedimentos para composição assistida por computador orientados por regras derivadas de análises musicais de contexto pós-tonal. Os procedimentos são inspirados em apontamentos de estudos sobre pós-tonalidade no compositor Béla Bartók, encontrados nas obras de Lendvai (1971), Antokoletz (1984), Cohn (1991) e Suchoff (2004). Problematizam-se aqui os conceitos de ciclos intervalares, eixos de simetria, polimodalismo e peculiaridades de coleções referenciais de classes de altura - conforme sugestões de Forte (1973), Straus (2004) e Susanni e Antokoletz (2012). São detalhadas questões computacionais para esta implementação, utilizando como base as ferramentas OpenMusic e biblioteca Python Music21. Um legado em código aberto fica disponível para continuidades possíveis deste trabalho.<br>This research produces a catalog of experiments in musical studies and its related generative algorithms, organizing procedures for computer aided composition oriented by constraints extracted from post-tonal musical analyses. The procedures are inspired by post-tonality studies of Béla Bartók’s music, found in the works of Lendvai (1971), Antokoletz (1984), Cohn (1991) and Suchoff (2004). Main focus on problematization of interval cycles, symmetry axis, polymodalism and peculiarity of referencial collections from pitch-class set theory - as sugested by Forte (1973), Straus (2004) and Susanni e Antokoletz (2012). Details of computational issues for the implementation, using the open source tools OpenMusic and Music21 (python library) as base.
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Books on the topic "Pitch-class set theory"

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Analyzing atonal music: Pitch-class set theory and its contexts. University of Rochester Press, 2008.

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Book chapters on the topic "Pitch-class set theory"

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Roig-Francolí, Miguel A. "Introduction to Pitch-Class Set Theory." In Understanding Post-Tonal Music, 2nd ed. Routledge, 2021. http://dx.doi.org/10.4324/9780429340123-4.

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Auerbach, Brent. "Exemplars of Basic Motivic Analysis." In Musical Motives. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780197526026.003.0007.

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Chapter 6 demonstrates the BMA method from start to finish by applying it to two complete sonata movements by Beethoven. The first section presents a pitch/pitch-class motivic analysis, and the second a rhythm motive analysis. The results of investigation across these two pieces shed light on a remarkable, shared trait. Both works pose a prime motive at the start and telegraph a set of expectations of how that motive will combine with itself. Paired fifth pitch-class motives chase each other over the course of Beethoven’s First Piano Sonata in F minor, Op. 2, no. 1 (I). Paired six-note rhythmic motives do the same over the course of his Fifth Piano Sonata in C minor, Op. 10, No. 1 (III). The pairs are always in flux, redefining their interrelations across their respective movements.
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"Writing Well About Science: Techniques From Teachers of Science Writing." In A Field Guide for Science Writers, edited by Deborah Blum, Mary Knudson, and Robin Marantz Henig. Oxford University Press, 2005. http://dx.doi.org/10.1093/oso/9780195174991.003.0008.

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1. Read your work out loud. You will be able to hear rhythm and flow of language this way, and you really cannot hear it when reading silently. 2. Don't be shy. Ask other writers to read a draft for you. Everyone gets too close to the story to see the glitches, and a dispassionate reader is a writer's best friend. Good writers gather readers around them for everything from newspaper stories to whole books (which require really good friends). 3. Think of your lead as seduction. How are you going to get this wary, perhaps uninterested reader, upstairs to see your etchings? You need to begin your story in a way that pulls the reader in. My favorite basic approach goes seductive lead, so-what section (why am I reading this), map section (here are the main points that will follow in this story). That approach leads me to my next tip, which is 4. Have a dear sense of your story and its structure before you begin writing. If you think of a story as an arc, in the shape of a rainbow, then it's helpful to know where it will begin and where it will end so that you know in advance how to build that arc. 5. Use transitions. A story has to flow. Leaping from place to place like a waterstrider on a pond will not make your prose easy to follow. 6. Use analogies. They are a beautiful way to make science vivid and real—as long as you don't overuse them. 7. In fact, don't overwrite at all. And never, never, never use clichés. If you want to write in your voice, generic language will not do. In my class, there are no silver linings, no cats let out of bags, no nights as black as pitch. A student who uses three clichés in a story gets an automatic C from me. 8. Write in English. This applies not only to science writing but to all beats in which a good story can easily sink in a sea of jargon.
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