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Gjerdingen, Robert O. "Music Theory Pedagogy: What Paul Taught Nadia." Music Theory and Analysis (MTA) 6, no. 2 (October 30, 2019): 230–54. http://dx.doi.org/10.11116/mta.6.2.4.
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The teaching of harmony in the United States, if judged objectively, has been a massive failure, even though a dedicated corps of fine musician-scholars labors to impart the curriculum to eager if not always adequately prepared students. These students are taught "about" harmony, as if the topic were really about tonality or the imaginary desires of chords. The only students who can perform and create harmony at a professional level are those who learned such skills outside the academy. The situation was not always so bleak. Nadia Boulanger, for example, learned the art of harmony from her teacher at the Paris Conservatory, Paul Vidal. Even though she was not taught roman numerals or chord functions, she learned harmony as a performative art, as something to express what was implicit in a given melody or bass. The article describes what Paul taught Nadia, and how the incredibly high standards for crafting harmonic-contrapuntal musical fabrics at the Paris Conservatory could be mastered by students willing to memorize the intricacies of a centuries-old art.
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Harrison, Daniel, Ernst Levy, and Siegmund Levarie. "A Theory of Harmony." Journal of Music Theory 31, no. 2 (1987): 353. http://dx.doi.org/10.2307/843718.
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Krims, Adam. "Music Theory as Productivity." Canadian University Music Review 20, no. 2 (March 4, 2013): 16–30. http://dx.doi.org/10.7202/1014455ar.
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The author here proposes Julia Kristeva's notion of "productivity" as a way of conceiving of the relations between different theories of music. By such a notion, rather than confirming, disconfirming, or exemplifying a theory, a particular musical work (or works) may redistribute the theory. The redistribution, in fact, might not only modify the initial theory—something certainly not original to productivity—but may also bring it into articulation with fundamentally opposed models of musical function, without which, nevertheless, the original theory remains incomplete. An extended example is adduced from Schubert's Schubert's Impromptu in G-flat Major, D. 899, in connection with, first, Schenker's Free Composition (Der freie Satz), and second, Schoenberg's Theory of Harmony (Harmonielehre); Schenker's inconsistent practice with respect to first-order neighbours, along with certain issues in the Impromptu, become the occasion for examining a case of productivity.
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Rahn, Jay. ""Chinese Harmony" and Contemporary Non-Tonal Music Theory." Canadian University Music Review 19, no. 2 (March 1, 2013): 115–24. http://dx.doi.org/10.7202/1014452ar.
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Twentieth-century Chinese theorists and composers have developed a distinctively indigenous approach to harmony, based in part on earlier pentatonic traditions. Mixed as it is with conventions of diatonic and chromatic harmony imported from Europe and North America, the resulting "Chinese harmony" poses music-theoretical problems of coordinating diatonic and pentatonic scales, and tertial and quartal chords. A survey of Chinese harmony as expounded by Kang Ou shows these difficulties to be theoretically intractable within solely Chinese or Euro-American frameworks, but soluble through recent formulations in atonal—or more appropriately, non-tonal-theory, as advanced by such writers as John Clough.
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Alcorta, Candace S., Richard Sosis, and Daniel Finkel. "Ritual harmony: Toward an evolutionary theory of music." Behavioral and Brain Sciences 31, no. 5 (October 2008): 576–77. http://dx.doi.org/10.1017/s0140525x08005311.
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AbstractJuslin & Västfjäll (J&V) advance our understanding of the proximate mechanisms underlying emotional responses to music, but fail to integrate their findings into a comprehensive evolutionary model that addresses the adaptive functions of these responses. Here we offer such a model by examining the ontogenetic relationship between music, ritual, and symbolic abstraction and their role in facilitating social coordination and cooperation.
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Walden, Daniel K. S. "Frozen Music: Music and Architecture in Vitruvius’ De Architectura." Greek and Roman Musical Studies 2, no. 1 (January 28, 2014): 124–45. http://dx.doi.org/10.1163/22129758-12341255.
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AbstractThis paper explores the convergence of musical and architectural theory in Vitruvius’De Architectura.Section 1 describes Vitruvius’ architectural lexicon, borrowed from Aristoxenus (I.2), and explores his description of the laws of harmony, modeled onElementa Harmonica(V.4). Section 2 explores how Vitruvius proposes using music theory in practical architectural design, including construction of columns using architectural orders analogous to Aristoxeniangenera(I.2.6; IV.1); acoustical designs for theatres (V.5); and the development of machines, including siege engines ‘tuned’ like musical instruments (X.12) and water-organs [hydrauli] constructed to execute all the different varieties of tuning (X.8). Section 3 reflects on Vitruvius’ use of analogies with a musical instrument, thesambuca, to explain his understanding of cosmic harmony and architectural form, and his possible sources (VI.1). Finally, Section 4 discusses Vitruvius’ ideas about the importance of a liberal arts education that includes study of music theory. The best architects, Vitruvius explains, can discover in music the secrets to forms they both encounter in nature and create themselves.
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Feitosa, Marco. "Partitional Harmony: The Partitioning of Pitch Spaces." MusMat: Brazilian Journal of Music and Mathematics IV, no. 2 (December 28, 2020): 01–27. http://dx.doi.org/10.46926/musmat.2020v4n2.01-27.
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In this preliminary work, we seek to present a brief historical review of the use of partitions in music, to provide a concise introduction to the theory of partitions, and lastly, through an extensive bibliographic revision and a thoughtful theoretical reflection, to lay the foundations of what we call partitional harmony - a comprehensive harmonic conception which relates the theory of partitions to several fields of post-tonal music theory. At the end, some basic operations (pitch, transposition, inversion, and multiplication) are defined and an illustrative musical application is provided, followed by our research prospects.
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Han, Siuebin. "Sang Tong’s contribution to the development of the national theory of harmony." Problems of Interaction Between Arts, Pedagogy and the Theory and Practice of Education 50, no. 50 (October 3, 2018): 61–76. http://dx.doi.org/10.34064/khnum1-50.05.
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Background. The article is devoted to the study of the scientific works of Sang Tong in the field of the national theory of harmony. His studies has a leading role in the development theoretical thought in the area of Chinese musicology and composition. Sang Tong’s contribution to national music education is determined by clarity of presentation of his teaching materials supported by numerous examples that is motivation for students to comprehend the science of composition. Being an outstanding composer, Sang Tong talentedly integrated the dissonant and pentatonic writing, emphasizing in his writings the national specifics due to atonal organization of music. The works of Sang Tong sounds abroad, they are performed on a concert stage, occupies a worthy place in the educational process of students of conservatories from different countries. In this connection, seems to be relevant the purpose of this article is to identify the main provisions of the theoretical works of the outstanding Chinese composer in the field of the national science of harmony and their role in the development of Chinese musical art in the second half of the 20th century. The mastering of this information is extremely necessary for the performers of San Tong music, as well as for teachers who are studying this musical repertoire in a class with students. Finally, the information presented will provide an opportunity to comprehend the artistic value of the musical heritage of Sang Tong, as well as allow attract more wide circles of professional musicians and audiences to his works. The results of the study. The first theoretical work of Sang Tong was the article “Theory of chord application and their subordination” (1957), where the musician analyzes the views of various authors on the problem of harmonization in composer’s work, systematizes them, giving a personal assessment. He gives many examples of the use of one or another composition tool. The composer considers methods of textural complexity in the study “Parallels to historical evolution and its application in Chinese and foreign musical works combined with pentatonic melody” (1963). In searching for his own composer’s writing, Sang Tong wanted to find the perfect textural balance: on the one hand, not reaching the difficult to perceive linear polyphony, on the other – not simplifying the texture into primitive forms of contrasting polyphony (as a variation of heterophony). The research experience of the 1960s and the 70s Sang Tong summarized in the monograph “Discussion on the horizontal and acoustic structure of pentatonic” (1980), which became a quality-teaching tool in the field of secondary music education. University vocalists also study at lectures on harmony, which helps them to expand the horizons of knowledge about national music. In 1982, Sang Tong published the first comprehensive study of contemporary music in China entitled “Introduction to harmonic processing techniques” in the journal Musical Art. Since 1994, Sang Tong planned to write a fundamental work that sums up his research – the ontology of Chinese music, but from year to year, because of illness, postponed it. Finally, in 2004, the Shanghai Music Publishing House published a series of Sang Tong articles in the form of a monograph “The Historical Evolution of Semitones”. This work is a fundamental study of the history of the development of harmony in China, which provides answers to the questions of the evolution of Chinese semantics and, related to it, the theory of the acoustics of Chinese instruments. Thinking about the quality of secondary music education, Sang Tong decided to prepare a textbook for an initial five-year program of study. In 2001, he published the Harmony Course, submitting it to the state commission for consideration as a school textbook. The San Tong’s Course of Harmony has become a basic national textbook in China. To date, the level of this theoretical work is considered unsurpassed and attributed to masterpieces in the field of music education. It is distinguished by a solid theoretical foundation that allows the students to find any answers to questions concerning the principles of voce-leading, transport, rules of resolution of various intervals. Conclusions. The composer and theorist Sang Tong entered the history of Chinese music of the twentieth century as the founder in the field of the modern national theory of harmony. For more than fifty years of academic research, Sang Tong has made an outstanding contribution to the development of theory of harmony in China, was creating a number of musicological studies of harmony that demonstrate the highest theoretical level. He laid a solid foundation for the future development of the national school of harmony theory, bringing the younger generation of Chinese composers to a high professional level.
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Braun, Yehezkel. "Traditional Harmony Reconsidered." British Journal of Music Education 3, no. 1 (March 1986): 49–61. http://dx.doi.org/10.1017/s026505170000512x.
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The author questions conventional attitudes to harmony teaching and describes his own approach based upon a careful observation of harmonic usage in masterworks. In particular he seeks to establish a view of chords as musical entities in their own right, not ‘group-related’ by principles such as ‘inversion’ but possessing a variety of possible functions arising from musical context rather than from established and immutable harmonic theory.
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Ashton-Bell, Robert Linton Tavis. "On the Geometric Realisation of Equal Tempered Music." Mapana Journal of Sciences 18, no. 3 (July 1, 2019): 53–75. http://dx.doi.org/10.12723/mjs.50.5.
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Since the time of Pythagoras (c.550BC), mathematicians interested in music have asked, “What governs the whole number ratios that emerge from derivations of the harmonic series?” Simon Stevin (1548-1620) devised a mathematical underlay (where a semitone equals 21/12) that gave rise to the equal temperament tuning system we still use today. Beyond this, the structure of formalised musical orderings have eluded many of us. Music theorists use the tools and techniques of their trade to peer into the higher-order musical structures that underpin musical harmony. These methods of investigating music theory and harmony are difficult to learn (and teach), as complex abstract thought is required to imagine the components of a phenomenon that cannot be seen. This paper outlines a method to understanding the mathematical underpinnings of the equal tempered tuning system. Using this method, musical structure can be quantitatively modelled as a series of harmonic elements at each pulse of musical time.
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Antonelli, Francesca. "Lavoisier and Music." Nuncius 33, no. 3 (November 26, 2018): 585–630. http://dx.doi.org/10.1163/18253911-03303008.
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Abstract Notes sur la Musique are a set of notes devoted by the French chemist Antoine Laurent Lavoisier (1743–1794) to music theory and in particular to the rules for correct composition. Given its subject matter, Notes constitutes a unicum in Lavoisier’s corpus that has been little studied and never published. This essay will present the initial results of an in-depth analysis of this manuscript, followed by a transcription of the text. It will be argued that a large part of the Notes were derived from the writings of Alexandre Théophile Vandermonde (1735–1796), a mathematician who collaborated with Lavoisier on his scientific experiments, but who also developed his own system of harmony. After a brief examination of Vandermonde’s contributions to music theory, various passages from Lavoisier’s Notes will be evaluated in order to show the link between the two scientists’ perspectives on music. Some of Vandermonde’s unpublished papers will also be taken into consideration. On the basis of this analysis, hypotheses will be advanced regarding the circumstances that could have led Lavoisier to take an interest in music theory. Overall, this paper will shed light on a little-known side of Lavoisier’s cultural interests and activities and provide elements that could contribute to a better understanding of his Notes sur la Musique.
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Honisch, Erika Supria. "Of Music, Morals, and Salads." Common Knowledge 27, no. 2 (May 1, 2021): 280–308. http://dx.doi.org/10.1215/0961754x-8906173.
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Abstract This article uses music and the discourse about music to understand the practice of tolerance in Prague during the period immediately preceding the outbreak of the Thirty Years’ War. Drawing on Las ensaladas (Prague, 1581), a collection of vernacular polyphony compiled by the Spanish composer Mateo Flecha the Younger, and Harmoniae morales (Prague, 1589–90), comprising musical settings of Latin texts by the Slovenian composer Jacobus Handl, the article argues that such music offered Prague's diverse citizens a medium for reflecting on how to live morally and peaceably. Ultimately, this article challenges the commonplace that musical harmony offered an effective model for social harmony, arguing that the practice of singing together exposed the limits of tolerance even as it illuminated how difference might be accommodated.
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Bagci, Hakan. "Examining the relationship between the attitudes towards harmony courses and piano playing habits." Cypriot Journal of Educational Sciences 15, no. 1 (February 29, 2020): 112–26. http://dx.doi.org/10.18844/cjes.v15i1.4613.
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The primary problem of this study is to determine whether there is a significant relationship between the attitudes towards harmony courses and the piano playing habits of the students. In this study, a correlational survey model was employed. The population of this study consisted of students who are studying at music departments in Turkey during the academic year of 2019–2020 and the sample included 248 students from nine different universities and four different departments related to music (Music Education, Performance, Musicology and Turkish Music). For data collection purposes, the scale of attitudes towards harmony courses developed, the scale of piano playing habits developed and a questionnaire to determine the variables affecting students’ habits and attitudes developed by the researcher were used. There is no significant difference found between the students’ departments and their piano playing habits. The study revealed that students’ piano playing habits varied according to their personal instruments.
Keywords: Attitudes, harmony education, music education, music theory, piano education.
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Rosner, Burton S., and Eugene Narmour. "Harmonic Closure: Music Theory and Perception." Music Perception 9, no. 4 (1992): 383–411. http://dx.doi.org/10.2307/40285561.
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Music theorists have often disagreed about the material variables that determine the perception of harmonic closure. To investigate this controversial topic, we presented subjects with pairs of selected two-chord progressions. The subjects judged which member of each pair seemed more closed. Preferences varied across pairs of cadences and generally obeyed transitivity. Quantitative reformulation of theoretical harmonic variables permitted correlational analysis of the results. Three or four variables, including one or two that reflect learned stylistic structures, best explained our findings. Conventional harmonic factors of scale step, soprano position, and root position demonstrated surprisingly little explanatory power.
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Smid, Deanna. "Spoken song and imagined music in Cymbeline." Cahiers Élisabéthains: A Journal of English Renaissance Studies 102, no. 1 (April 13, 2020): 87–102. http://dx.doi.org/10.1177/0184767820914539.
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Believing her to be dead, Arviragus and Guiderius perform the funerary rite for Innogen in William Shakespeare’s Cymbeline, but the men speak the words of the dirge listed as ‘Song’ in the first folio. Readers and spectators familiar with Shakespeare’s other late plays would expect musical solace here, yet the spoken song fails to comfort the brothers, and it may rattle the audience because it conjures the ending of Romeo and Juliet in their imaginations. The audience’s imagination is again invoked by the ‘harmony’ at the end of the play – a harmony they do not witness and thus must imagine.
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TRAMO, MARK JUDE, PETER A. CARIANI, BERTRAND DELGUTTE, and LOUIS D. BRAIDA. "Neurobiological Foundations for the Theory of Harmony in Western Tonal Music." Annals of the New York Academy of Sciences 930, no. 1 (June 2001): 92–116. http://dx.doi.org/10.1111/j.1749-6632.2001.tb05727.x.
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Garnett, Liz. "Ethics and aesthetics: the social theory of barbershop harmony." Popular Music 18, no. 1 (January 1999): 41–61. http://dx.doi.org/10.1017/s0261143000008722.
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Until recently, the world of the British barbershop singer was a self-enclosed community whose existence went largely unrecognised both by musicians involved in other genres and by the public at large. In the last few years this has started to change, chiefly due to the participation of barbershop choruses in the televised competition ‘Sainsbury's Choir of the Year’. Encouraged by the success of Shannon Express in 1994, many other choruses entered the 1996 competition, four of them reaching the televised semi-finals, and two the finals. During this increased exposure, it became apparent that television commentators had little idea of what to make of barbershoppers, indeed regarded them as a peculiar, and perhaps rather trivial, breed of performer. This bafflement is not surprising given the genre's relative paucity of exposure either in the mass media or in the musical and musicological press; the plentiful articles written by barbershoppers about their activity and its meanings are almost exclusively addressed to each other, to sustain the community rather than integrate it into wider musical life. The purpose of this paper, however, is not to follow the theme of these intra-community articles in arguing that barbershop harmony should actually be regarded as a serious and worthy art, or to explain to a bewildered world what this genre is actually about; rather, it aims to explore the way that barbershop singers theorise themselves and their activity to provide a case study in the relationship between social and musical values. That is, I am not writing as an apologist for a hitherto distinctly insular practice, but exploiting that very insularity as a means to pursue a potentially very broad question within a self-limited field of enquiry.
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Schneider, Albrecht. "Book Review: The Theory of Harmony as a Grammar of Music: Propositional Schemata in Music and Language." International Journal of Music Education os-17, no. 1 (May 1991): 96. http://dx.doi.org/10.1177/025576149101700128.
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ITZKOVITZ, SHALEV, RON MILO, NADAV KASHTAN, REUVEN LEVITT, AMIR LAHAV, and URI ALON. "RECURRING HARMONIC WALKS AND NETWORK MOTIFS IN WESTERN MUSIC." Advances in Complex Systems 09, no. 01n02 (March 2006): 121–32. http://dx.doi.org/10.1142/s021952590600063x.
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Western harmony is comprised of sequences of chords, which obey grammatical rules. It is of interest to develop a compact representation of the harmonic movement of chord sequences. Here, we apply an approach from analysis of complex networks, known as "network motifs" to define repeating dynamical patterns in musical harmony. We describe each piece as a graph, where the nodes are chords and the directed edges connect chords which occur consecutively in the piece. We detect several patterns, each of which is a walk on this graph, which recur in diverse musical pieces from the Baroque to modern-day popular music. These patterns include cycles of three or four nodes, with up to two mutual edges (edges that point in both directions). Cliques and patterns with more than two mutual edges are rare. Some of these universal patterns of harmony are well known and correspond to basic principles of music theory such as hierarchy and directionality. This approach can be extended to search for recurring patterns in other musical components and to study other dynamical systems that can be represented as walks on graphs.
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Berezovsky, Jesse. "The structure of musical harmony as an ordered phase of sound: A statistical mechanics approach to music theory." Science Advances 5, no. 5 (May 2019): eaav8490. http://dx.doi.org/10.1126/sciadv.aav8490.
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Music, while allowing nearly unlimited creative expression, almost always conforms to a set of rigid rules at a fundamental level. The description and study of these rules, and the ordered structures that arise from them, is the basis of the field of music theory. Here, I present a theoretical formalism that aims to explain why basic ordered patterns emerge in music, using the same statistical mechanics framework that describes emergent order across phase transitions in physical systems. I first apply the mean field approximation to demonstrate that phase transitions occur in this model from disordered sound to discrete sets of pitches, including the 12-fold octave division used in Western music. Beyond the mean field model, I use numerical simulation to uncover emergent structures of musical harmony. These results provide a new lens through which to view the fundamental structures of music and to discover new musical ideas to explore.
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Rohrmeier, Martin. "The Syntax of Jazz Harmony: Diatonic Tonality, Phrase Structure, and Form." Music Theory and Analysis (MTA) 7, no. 1 (April 30, 2020): 1–63. http://dx.doi.org/10.11116/mta.7.1.1.
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The regularities underlying the structure building of chord sequences, harmonic phrases, and combinations of phrases constitute a central research problem in music theory. This article proposes a formalization of Jazz harmony with a generative framework based on formal grammars, in which syntactic structure tightly corresponds with the functional interpretation of the sequence. It assumes that chords establish nested hierarchical dependencies that are characterized by two core types: preparation and prolongation. The approach expresses diatonic harmony, embedded modulation, borrowing, and substitution within a single grammatical framework. It is argued in the second part that the proposed framework models not only core phrase structure, but also relations between phrases and the syntactic structures underlying the main forms of Jazz standards. As a special case, the Blues form relies heavily on the plagal derivation from the tonic and is analyzed in comparison with other analytical approaches to the Blues. The proposed theory is specified to a sufficient level of detail that it lends itself to computational implementation and empirical exploration, and this way it makes a step towards music theory building that embraces the close links between formal, mathematical, and computational methods.
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Smirnov, V. A. "Music theory and the harmony method in J. Kepler's work the harmony of the Universe." Astronomical & Astrophysical Transactions 18, no. 3 (December 1999): 521–32. http://dx.doi.org/10.1080/10556799908203010.
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Neidhöfer, Christoph. "A Theory of Harmony and Voice Leading for the Music of Olivier Messiaen." Music Theory Spectrum 27, no. 1 (April 2005): 1–34. http://dx.doi.org/10.1525/mts.2005.27.1.1.
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Adam, Nathaniel. "Hearing Harmony: Toward a Tonal Theory for the Rock Era by Christopher Doll." Journal of Music Theory 63, no. 2 (October 1, 2019): 261–67. http://dx.doi.org/10.1215/00222909-7795200.
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Biamonte, Nicole. "Hearing Harmony: Toward a Tonal Theory for the Rock Era. By Christopher Doll." Music Theory Spectrum 42, no. 1 (2020): 154–57. http://dx.doi.org/10.1093/mts/mtz025.
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Aghnini, Aghnini, Sunarto Sunarto, and Triyanto Triyanto. "The Form and Function of Antan Delapan Music in Muara Lawai Village, Muara Enim District." Catharsis 9, no. 1 (May 31, 2020): 1–9. http://dx.doi.org/10.15294/catharsis.v9i1.38242.
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Antan Delapan music is one of the arts found in the district of Muara Enim, South Sumatra. Antan Delapan art is currently displaced by the development of western music, therefore the form and function of music plays an important role in maintaining the Antan Delapan music among the people of Muara Enim Regency. The purpose is to study the form and function of Antan Delapan music. The method in this study uses descriptive qualitative with an interdisciplinary approach, while the data collection technique uses observation, interviews, and document studies. The data validity technique uses source triangulation. Data analysis techniques use the concepts of Strauss and Corbic. The results of this study are the form of Antan Delapan music which is dissected through the elements of time, melody, harmony, while the function of Antan Delapan music in the community as, entertainment, aesthetic appreciation, means of communication, cultural harmony, and as an integration. And it is hoped that this research can be useful for the people of Muara Enim Regency, especially the Muare Lawai Village Community in order to know the function and form of Antan Delapan music and can maintain the Antan Delapan music among the Muare Lawai villagers, and is useful for readers who will use music theory about the form and music function.
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Lerdahl, Fred. "Calculating Tonal Tension." Music Perception 13, no. 3 (1996): 319–63. http://dx.doi.org/10.2307/40286174.
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The prolongational component in A Generative Theory of Tonal Music assigns tensing and relaxing patterns to tonal sequences but does not adequately describe degrees of harmonic and melodic tension. This paper offers solutions to the problem, first by adapting the distance algorithm from the theory of tonal pitch space for the purpose of quantifying sequential and hierarchical harmonic tension. The method is illustrated for the beginning of the Mozart Sonata, K. 282, with emphasis on the hierarchical approach. The paper then turns to melodic tension in the context of the anchoring of dissonance. Interrelated attraction algorithms are proposed that incorporate the factors of stability, proximity, and directed motion. A distinction is developed between the tension of distance and the tension of attraction. The attraction and distance algorithms are combined in a view of harmony as voice leading, leading to a second analysis of the opening phrase of the Mozart in terms of voiceleading motion. Connections with recent theoretical and psychological work are discussed.
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Fieldman, Hali. ":Harmony in Context;The Complete Musician: An Integrated Approach to Tonal Theory, Analysis, and Listening;The Musician's Guide to Theory and Analysis." Music Theory Spectrum 30, no. 2 (October 2008): 366–82. http://dx.doi.org/10.1525/mts.2008.30.2.366.
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De Haas, W. Bas, José Pedro Magalhães, Frans Wiering, and Remco C. Veltkamp. "Automatic Functional Harmonic Analysis." Computer Music Journal 37, no. 4 (December 2013): 37–53. http://dx.doi.org/10.1162/comj_a_00209.
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Music scholars have been studying tonal harmony intensively for centuries, yielding numerous theories and models. Unfortunately, a large number of these theories are formulated in a rather informal fashion and lack mathematical precision. In this article we present HarmTrace, a functional model of Western tonal harmony that builds on well-known theories of tonal harmony. In contrast to other approaches that remain purely theoretical, we present an implemented system that is evaluated empirically. Given a sequence of symbolic chord labels, HarmTrace automatically derives the harmonic relations between chords. For this, we use advanced functional programming techniques that are uniquely available in the Haskell programming language. We show that our system is fast, easy to modify and maintain, robust against noisy data, and that its harmonic analyses comply with Western tonal harmony theory.
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Keren-Sagee, Alona. "JOSEPH SCHILLINGER – A DISCIPLE'S REMINISCENCES OF THE MAN AND HIS THEORIES: AN INTERVIEW WITH PROF. ZVI KEREN." Tempo 64, no. 251 (January 2010): 17–27. http://dx.doi.org/10.1017/s0040298210000033.
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Joseph Schillinger (1895–1943), the eminent Russian-American music theorist, teacher and composer, emigrated to the United States in 1928, after having served in high positions in some of the major music institutions in the Ukraine, Khar'kov, Moscow, and Leningrad. He settled in New York, where he taught music, mathematics, art history, and his theory of rhythmic design at the New School for Social Research, New York University, and the Teachers College of Columbia University. He formulated a philosophical and practical system of music theory based on mathematics, and became a celebrated teacher of prominent composers and radio musicians. Schillinger's writings include: Kaleidophone: New Resources of Melody and Harmony (New York: M. Witmark, 1940; New York: Charles Colin, 1976); Schillinger System of Musical Composition, 2 vols. (New York: Carl Fischer, 1946; New York: Da Capo Press, 1977); Mathematical Basis of the Arts (New York: Philosophical Library, 1948; New York: Da Capo Press, 1976); Encyclopedia of Rhythms (New York: Charles Colin, 1966; New York: Da Capo Press, 1976).
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Rehding, Alexander. "Music Theory's Other Nature: Reflections on Gaia, Humans, and Music in the Anthropocene." 19th-Century Music 45, no. 1 (2021): 7–22. http://dx.doi.org/10.1525/ncm.2021.45.1.7.
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The new historical paradigm ushered in by the Anthropocene offers a timely and urgent opportunity to rethink the relationship of humans and nature. Bruno Latour's take on the Gaia hypothesis, which rejects the traditional subject/object divide, shows how the human can be inscribed into the work of music theory. This turn toward Latour's Actor-Network Theory, which erases the categorical difference between human and nonhuman agents, now dressed up in cosmic garb under the banner of the Gaia hypothesis, appears to be distant from traditional music-theoretical concerns, but the connection is in fact less far-fetched than it seems. J. G. Kastner's music theory, taking its cue from the sound of the Aeolian harp, serves as a test case here: the Aeolian harp, played by wind directly, had long served as a Romantic image of the superhuman forces of nature, but Kastner argues that the Aeolian network only becomes complete in human ears. By unraveling the various instances and agencies of Kastner's theory, this article charts a novel approach to music and sound that sidesteps the conceptual problems in which the nineteenth-century mainstream habitually gets entangled. Kastner's work is based on a fundamental crisis in the conception of sound, after the invention of the mechanical siren (1819) tore down any certainties about the categorical distinction between noise and musical sound. Seeking to rebuild the understanding of sound from the ground up, Kastner leaves no stone unturned, from the obsolete Pythagorean tradition of musica mundana to travelers’ reports about curious sonic environmental phenomena from distant parts of the world. Where the old mechanistic paradigm was built on a “physical music” (and a static “sound of nature” based on the harmonic series), Kastner proposes a new “chemical music” that is based on the dynamic, ever-changing sonority of the Aeolian harp. This chemical music does not (yet) exist, but Kastner gives us some clues about its features, especially in his transcription/simulation of the sound of the Aeolian harp scored for double symphony orchestra. Kastner's “chemical music” finally closes the music-theoretical network that he builds around his new conception of the supernatural sound of the Aeolian harp and its human and nonhuman agents.
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Baker, Nancy K. "'Der Urstoff der Musik': Implications for Harmony and Melody in the Theory of Heinrich Koch." Music Analysis 7, no. 1 (March 1988): 3. http://dx.doi.org/10.2307/939244.
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Chan, Paul Yaozhu, Minghui Dong, and Haizhou Li. "The Science of Harmony: A Psychophysical Basis for Perceptual Tensions and Resolutions in Music." Research 2019 (September 29, 2019): 1–22. http://dx.doi.org/10.34133/2019/2369041.
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This paper attempts to establish a psychophysical basis for both stationary (tension in chord sonorities) and transitional (resolution in chord progressions) harmony. Harmony studies the phenomenon of combining notes in music to produce a pleasing effect greater than the sum of its parts. Being both aesthetic and mathematical in nature, it has baffled some of the brightest minds in physics and mathematics for centuries. With stationary harmony acoustics, traditional theories explaining consonances and dissonances that have been widely accepted are centred around two schools: rational relationships (commonly credited to Pythagoras) and Helmholtz’s beating frequencies. The first is more of an attribution than a psychoacoustic explanation while electrophysiological (amongst other) discrepancies with the second still remain disputed. Transitional harmony, on the other hand, is a more complex problem that has remained largely elusive to acoustic science even today. In order to address both stationary and transitional harmony, we first propose the notion of interharmonic and subharmonic modulations to address the summation of adjacent and distant sinusoids in a chord. Based on this, earlier parts of this paper then bridges the two schools and shows how they stem from a single equation. Later parts of the paper focuses on subharmonic modulations to explain aspects of harmony that interharmonic modulations cannot. Introducing the concept of stationary and transitional subharmonic tensions, we show how it can explain perceptual concepts such as tension in stationary harmony and resolution in transitional harmony, by which we also address the five fundamental questions of psychoacoustic harmony such as why the pleasing effect of harmony is greater than that of the sum of its parts. Finally, strong correlations with traditional music theory and perception statistics affirm our theory with stationary and transitional harmony.
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Huron, David. "Tone and Voice: A Derivation of the Rules of Voice-Leading from Perceptual Principles." Music Perception 19, no. 1 (2001): 1–64. http://dx.doi.org/10.1525/mp.2001.19.1.1.
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The traditional rules of voice-leading in Western music are explicated using experimentally established perceptual principles. Six core principles are shown to account for the majority of voice-leading rules given in historical and contemporary music theory tracts. These principles are treated in a manner akin to axioms in a formal system from which the traditional rules of voice-leading are derived. Nontraditional rules arising from the derivation are shown to predict formerly unnoticed aspects of voice-leading practice. In addition to the core perceptual principles, several auxiliary principles are described. These auxiliary principles are occasionally linked to voice-leading practice and may be regarded as compositional "options" that shape the music-making in perceptually unique ways. It is suggested that these auxiliary principles distinguish different types of part writing, such as polyphony, homophony, and close harmony. A theory is proposed to account for the aesthetic origin of voice-leading practices.
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Graybill, Roger. "Reviews of Recent Textbooks in Theory and Musicianship. 4. Harmony: Harmony and Voice Leading . Edward Aldwell, Carl Schachter. ; Music in Theory and Practice . Bruce Benward, Gary White. ; Tonal Harmony, with an Introduction to Twentieth-Century Music . Stefan Kostka, Dorothy Payne. ; Harmony . Walter Piston. ; The Shaping of Musical Elements . Armand Russell, Allen Trubitt. ; Harmony: Patterns and Principles . Allen Winold." Music Theory Spectrum 15, no. 2 (October 1993): 257–66. http://dx.doi.org/10.1525/mts.1993.15.2.02a00080.
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Marianto, Adi, and Esy Maestro. "ANALISIS KOMPOSISI ADELITA KARYA FRANCISCO TARREGA." Jurnal Sendratasik 10, no. 1 (December 5, 2020): 315. http://dx.doi.org/10.24036/jsu.v9i2.110564.
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This study aims to describe the results of an analysis of Adelita's music composition in terms of melody, rhythm, and harmony analyzed based on motives, themes, phrases, and periods. It aims to find out the creation concept made by the composer. This research belongs to a qualitative descriptive analysis research. The main instrument in this study was the researcher itself. The researcher processed the data by doing some steps such as reading scores from Adelita's material, then classifying the data from understanding music theory, from the structural aspect, as well as the melody, rhythm, and harmony, so that the researcher can make a summary of the data found in the form of writings which describe an understanding of music theory. Then, the researcher conducted a feasibility test on the song with the aim that the song analyzed can be used as a learning material for students studying classical guitar material and as an eligibility to be taken as musical knowledge. The results show that Adelita's work is unique in terms of playing techniques and ornamentation. By using simple melody, rhythm, and harmony, Adelita can be accepted as a reference for learning classical guitar. The assessment was obtained from simple melody, rhythm, and harmony analysis. Thus, it can be used as a reference for learning classical guitar for students who take the course of classical guitar major instrument.Keywords: Structure Analysis, Adelita Composition, Francisco Tarrega
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Zacharakis, Asterios, Maximos Kaliakatsos-Papakostas, Costas Tsougras, and Emilios Cambouropoulos. "Musical blending and creativity: An empirical evaluation of the CHAMELEON melodic harmonisation assistant." Musicae Scientiae 22, no. 1 (February 21, 2018): 119–44. http://dx.doi.org/10.1177/1029864917712580.
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This article presents the CHAMELEON melodic harmonisation assistant that utilises the principles of conceptual blending theory as a means for the invention of hybrid or novel harmonic idioms and an empirical evaluation of a number of computer-generated melodic harmonisation blends. Melodies originating from various idioms were harmonised either according to the harmonic rules of the original idiom, according to the rules of a different idiom (melody–harmony blends), or by blending idioms, modes and transported versions of the same idiom (harmony–harmony blends). In two similar experimental set ups, the task of the listeners was to i) perform idiom, mode or type of chromaticism classification, ii) report their preference, and iii) rate the degree of expectancy characterising each harmonisation. The results show that harmonic blending (either melody–harmony or harmony–harmony) influences the identification of idiom, mode and type of chromaticism. This suggests that the harmonic blending system has indeed succeeded in producing perceivable blends under various conditions that were unexpected and also equally preferred compared to non-blends.
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Yoon, Jin Hee, and Zong Woo Geem. "Empirical Convergence Theory of Harmony Search Algorithm for Box-Constrained Discrete Optimization of Convex Function." Mathematics 9, no. 5 (March 4, 2021): 545. http://dx.doi.org/10.3390/math9050545.
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The harmony search (HS) algorithm is an evolutionary computation technique, which was inspired by music improvisation. So far, it has been applied to various scientific and engineering optimization problems including project scheduling, structural design, energy system operation, car lane detection, ecological conservation, model parameter calibration, portfolio management, banking fraud detection, law enforcement, disease spread modeling, cancer detection, astronomical observation, music composition, fine art appreciation, and sudoku puzzle solving. While there are many application-oriented papers, only few papers exist on how HS performs for finding optimal solutions. Thus, this preliminary study proposes a new approach to show how HS converges on an optimal solution under specific conditions. Here, we introduce a distance concept and prove the convergence based on the empirical probability. Moreover, a numerical example is provided to easily explain the theorem.
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Mazlan, Chamil Arkhasa Nikko. "Utilizing Pragmatism Approach in Learning Jazz Guitar Reharmonization Technique using Malay Asli Song." JURNAL SENI MUSIK 9, no. 1 (June 18, 2020): 50–57. http://dx.doi.org/10.15294/jsm.v9i1.37376.
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Details of developing jazz guitar reharmonization learning book using Malay Asli song will not discuss here, however, this article divulges pragmatism approach that can be transcending in explaining logic between learning jazz guitar reharmonization techniques using Malay Asli Song. Although music is a universal language, traditional music and western music educators do not come to an agreement diffusing learning western music elements such in traditional music or vice versa. As a result, reharmonization technique only become known on western music repertoires. While traditional music practitioners presenting the same old repertoires, with deep-rooted dogmatic excuses to maintain what they called traditional authentic values. To conduct this study, relevant data on pragmatism was done through document analysis. The result show pragmatism approach can help music educators to reconceptualize teaching and learning traditional music using jazz reharmonization technique to recreate and innovate a new sound and contextual of learning jazz harmony, not just using on jazz standards repertoires, in making music theory beneficial to both traditional and modern music educators and students.
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DRABKIN, WILLIAM. "SCHUBERT, SCHENKER AND THE ART OF SETTING GERMAN POETRY." Eighteenth Century Music 5, no. 2 (September 2008): 209–36. http://dx.doi.org/10.1017/s1478570608001498.
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Nearly half a century after gaining a solid footing in the academic world, the achievements of Heinrich Schenker remain associated more with tonal structure and coherence than with musical expression. The focus of his published work, exemplified largely by instrumental music from the eighteenth and early nineteenth centuries, supports this view. There are just five short writings about music for voices: two essays on Bach’s St Matthew Passion, one on the opening number from Haydn’s Creation, and two on Schubert songs. To be sure, romantic lieder appear as music examples for the larger theory books, but there they serve as illustrations of harmony, voice leading and form, rather than the relationship of word to tone.
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Blackburn, Bonnie J. "On Compositional Process in the Fifteenth Century." Journal of the American Musicological Society 40, no. 2 (1987): 210–84. http://dx.doi.org/10.2307/831517.
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The change from "successive composition" to "simultaneous conception" is one of the great turning points in the history of music. The latter term, derived from Pietro Aaron's allusion to the method of composition used by modern composers, does not correctly convey Aaron's meaning. He said that modern composers "take all the parts into consideration at once," disposing them in different ranges and thus allowing the avoidance of awkward clashes between the inner voices. This more harmonic orientation finds confirmation in the writings of Giovanni Spataro, whose theory of harmony, later developed by Zarlino, contradicts a current view of fifteenth-century music as purely intervallic counterpoint founded on a superius-tenor framework in which the bass is nonstructural and nonessential. The theory is grounded in the functional role of dissonance, adumbrated a century earlier in the treatise by Goscalcus. Discussion of the new compositional process can already be found fifty years earlier in the writings of Johannes Tinctoris. That this has not been recognized is due to persistent confusion over the term res facta. The key to comprehending this term lies in a correct understanding of what Tinctoris meant by counterpoint: it is not what we today call counterpoint but successive composition. Res facta differs from counterpoint in that each voice must be related to every other voice so that no improper dissonances appear between them. This method, "harmonic composition," could be quasi-simultaneous or successive; the criterion is the ultimate result-the finished work of art. Res facta is both a method of composition and a term that denotes a work composed in this manner, analogous to Listenius's opus perfectum et absolutum. The musica poetica of the sixteenth century is the legacy of res facta, and the two terms are indirectly connected. The new process of composition is the foundation for Tinctoris's delineation of an ars nova beginning about 1437, a date that may have been chosen in recognition of its first great representation in Dufay's Nuper rosarum flores.
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LANZELLOTTI, FEDERICO. "IN SEARCH OF PERFECT HARMONY: GIUSEPPE TARTINI'S MUSIC AND MUSIC THEORY IN LOCAL AND EUROPEAN CONTEXTS LJUBLJANA, 16–17 NOVEMBER 2020." Eighteenth Century Music 18, no. 2 (August 17, 2021): 329–31. http://dx.doi.org/10.1017/s1478570621000038.
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Oshanova, N. T. "MATHEMATICAL FOUNDATIONS OF MUSIC BY AL-FARABI." BULLETIN Series of Physics & Mathematical Sciences 71, no. 3 (September 30, 2020): 24–30. http://dx.doi.org/10.51889/2020-3.1728-7901.03.
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This article discusses the mathematical foundations of al - Farabi music, and suggests the main actions of arithmetic operations with Farabi relations to obtain musical intervals. Farabi drew attention to some problems for the study of musical art. This article provides an extensive understanding of how the three main problems are needed to get the ratio. Musical intervals have different values. You can divide them, multiply them, and listen to them. In music theory, you need to be familiar with the mathematical foundations for working with ratios, as well as arithmetic operations like multiplication, division, and addition. Farabi not only gives a scientific idea of the ratio of sounds, but also reveals the mathematical foundations of the emergence of harmony and musical melodies.
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Murphy, Paul, and Cristóbal García Gallardo. "Jean-Philippe Rameau’s Influence on Harmonic Theory in Spain." Music Theory Spectrum 42, no. 1 (December 16, 2019): 81–104. http://dx.doi.org/10.1093/mts/mtz024.
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Abstract It is well known that the music-theoretical ideas of Jean-Philippe Rameau (1683–1764) were disseminated throughout much of Europe in large part by the summary editions issued by the mathematician and philosopher Jean Le Rond d’Alembert (1717–83) and certain German, English, and Italian translations that followed. Little is known, however, about how Rameau’s revolutionary and controversial theories appeared in Spain, and even less about how they were received and interpreted. In response, we offer a contextual analysis of the effects that these ideas had on both forward-looking intellectuals as well as on conservative professional musicians grounded in music of the past.
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Agmon, Eytan. "The Webern in Mozart: Systems of Chromatic Harmony and Their Twelve-Tone Content." Music Theory Spectrum 42, no. 2 (2020): 173–92. http://dx.doi.org/10.1093/mts/mtaa010.
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Abstract Toward the end of his 2012 book, Audacious Euphony, Richard Cohn asks, “how does music that is heard to be organized by diatonic tonality [as in the age of Mozart] become music that is heard to be organized in some other way [as in the age of Webern]”? In the present article, a theory different from Cohn’s is offered as answer. The theory’s three sub-theories, harmonic hierarchy, within-key chromaticism, and “solar” key distance, lead to a distinction between four types of harmonic systems: the strictly diatonic, the first- and second-order chromatic, and the restricted twelve-tone system. As its name implies, the latter harmonic system allows for twelve-tone levels, though under a restriction (termed Principle of Diatonic Fusion) that holds “the Webern in Mozart” in check.
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Carterette, Edward C., Kathryn Vaughn, and Nazir A. Jairazbhoy. "Perceptual, Acoustical, and Musical Aspects of the Tambūrā Drone." Music Perception 7, no. 2 (1989): 75–108. http://dx.doi.org/10.2307/40285453.
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The basso continuo principle, as embodied in Rameau's theory of functional harmony, was paralleled by the introduction of drone instruments in the classical music of India. In order to understand how these two systems are tied together in human music perception, we studied the role of tambūrā interactions with North Indian rags played on the sitār. Raman (1914-1922) had applied his theory of discontinuous wave motion to mechanical and musical properties of the strings of the violin. He noted the remarkable, powerful harmonic series that arose from the nonlinear interaction of the tambürã string and grazing contact with its curved bridge. We analyzed the waveforms of the most common drone tunings. Each of the four strings was played with and without juari ("life-giving" threads). The upward transfer and spread of energy into higher partials imparts richness to tambūrā tones and underlies the use of different drone tunings for different rags. Specific notes of rāg scales are selectively and dynamically enhanced by different drone tunings. Based on coincident features of spectral and musical scale degrees, we computed an index of spectral complexity of the interactions of tambūrā tunings with rãg scales. We speculate that the use of juari contributes to stable pitch centers, implied scale modulation, and an improvisational flexibility.
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Narmour, Eugene. "Analyzing Form and Measuring Perceptual Content in Mozart's Sonata K. 282: A New Theory of Parametric Analogues." Music Perception 13, no. 3 (1996): 265–318. http://dx.doi.org/10.2307/40286173.
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Hierarchic analysis in music necessarily separates form from content. However, in active listening, the two are indivisible. To illustrate this, I first analyze in Part 1 the opening movement in Mozart's Sonata K. 282 from the top down, using traditional methods in music theory. Arriving at the manifest level, I then dissect the music from the bottom up, relying on the implication-realization model (Narmour, 1977,1989,1990,1991a, 1992). The contrasting perspectives reveal in great detail some of the movement's richly complex structuring. More generally, they confirm the inextricable feedback between parametric content and the meaning of form, specifically with respect to the contrary functions of closure and nonclosure. Following these analyses, Part 2 forges a synthesis by developing an implicative theory of analogical structures for melody, harmony, duration, and meter. Because, in terms of bottom-up processing, the analytical symbology for tracking structures is commensurable, we can, in all four primary parameters, weight similarity (aa), difference (ab), closure (stability), and nonclosure (implication) with comparable numbers. Further, by adding in some essential stylistic properties from the top down (scale step, diatonic pitch set, tonal cadential closure), we are able to represent the overall rhythmic shape of the first phrase in a single twodimensional graph. Thereby, we recapture from hierarchic analysis the perceptual sense that, in on-line listening, form and content are synthetically one.
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Adamer, Lorenz. "Plutarch’s Platonic Question IX: The Trichonomy of the Soul from the Perspective of Music Theory (Politeia 443d-e)." Ploutarchos 17 (November 9, 2020): 9–24. http://dx.doi.org/10.14195/0258-655x_17_1.
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In the IXth question of his Platonicae Quaestiones, Plutarch takes up the musical analogy of Politeia 443d-e, which applies the trichonomy of the soul to the concept of harmony by means of the three horoi. The concrete question of whether Plato assigned the place of mese to spirit or to reason is left open by Plutarch according to his zétema concept, but offers meaningful opportunities for the understanding of Platonic soul trichonomy: both the peculiarity of the horoi and the ambiguity of harmonia must be diligently assessed from a musictheoretical perspective in order to comprehensively understand the analogy of soul trichonomy.
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Bernstein, David W., and Georg Capellen. "Georg Capellen's Theory of Reduction: Radical Harmonic Theory at the Turn of the Twentieth Century." Journal of Music Theory 37, no. 1 (1993): 85. http://dx.doi.org/10.2307/843945.
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John J. Sheinbaum. "Theory and Analysis of Classic Heavy Metal Harmony (review)." Notes 67, no. 1 (2010): 94–96. http://dx.doi.org/10.1353/not.2010.0025.
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