Quantification of the degree of chromatic dissonance as a music compositional planning tool: a pedagogical proposal
DOI:
https://doi.org/10.5965/2525530409022024e0104Keywords:
degree of dissonance, compositional planning in music, harmony, musical compositionAbstract
The study of the vertical or harmonic dimension of music involves two fundamental perspectives: the lexical and the syntactic. In the lexical context, we deal with chords, while in the syntactic perspective, we focus on the relationships between these chords. When we approach the harmonic lexicon, we encounter two fundamental dimensions, one of a quantitative nature and the other qualitative. The quantitative dimension concerns the counting of the notes that compose the chords, i.e., their cardinality. Meanwhile, in the qualitative realm, we adopt the expression 'degree of dissonance' to describe this characteristic. In the first part of this study, we will explore the construction of a harmonic lexicon with chords containing three notes, using combinations of intervals between the different notes of the chromatic scale. In the second part, we will analyze various factors of a syntactic nature, including tonality, parsimony, degree of dissonance, stochastic aspects, and the concept of intertextuality in music.
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References
ALDWELL, Edward e Carl Schachter. Harmony and Voice Leading. 2ª Ed. New York: Harcourt Brace Jovanovich, Publishers, 1989.
BACH, J. S. 371 Vierstimmige Choräle. Partitura (redução para piano). Alfred Dörffel, Ed. Leipzig: Breitkopf und Härtel, s.d.[1871]. Disponível em: https://ks15.imslp.org/files/imglnks/usimg/7/7b/IMSLP318117-SIBLEY1802.26185.dcca-39087032500649score.pdf. Acesso em 06.07.24.
BARTÓK, Béla. 44 Duos for 2 Violins, Sz.98. Partitura. Vienna: Universal Edition, 1933. Disponível em https://imslp.eu/files/imglnks/euimg/7/77/IMSLP631964-PMLP47288-44_Violin_Duos.pdf. Acesso em 07.07.24.
BILBAO, Stefan; DESVAGES, Charlotte; DUCCESHI, Michele; HAMILTON, Brian; HARRISON-HARSLEY, Reginald; TORIN, Alberto; WEBB, Craig. Physical Modeling, Algorithms, and Sound Synthesis: The NESS Project. Computer Music Journal, v.43, n.2/3, p. 15-30, 2019.
BLOOM, Harold. A Angustia da influência. Rio de Janeiro: Imago, 2002.
BOULEZ, Pierre. Relevés d’apprenti. Paris : Seuil, 1966.
BOULEZ, P. Apontamentos de aprendiz. São Paulo: Perspectiva, 1995.
COHN, Richard. Audacious Euphony: Chromaticism and the Triad’s Second Nature. Oxford: Oxford University Press, 2011.
COHN, Richard. Introduction to Neo Riemannian Theory: A Survey and a Historical
Perspective. Journal of Music Theory, 1998, v. 42, n. 2, p. 167-180.
FINEBERG, Joshua. Spectral music. Contemporary Music Review, 2000a, v.19, n.2, p.1-5.
FINEBERG, Joshua. Guide to the basic concepts and techniques of spectral music. Contemporary Music Review, 2000b, v.19, n.2, p. 81-113.
FINEBERG, Joshua. Musical examples, Contemporary Music Review. 2000c, v.19, n.2, p.115-134.
FINEBERG, Joshua. Bibliography, Contemporary Music Review. 2000d, v.19, n.2, p.135-143.
GAULDIN, Robert. Harmonic Practice in Tonal Music. New York: W. W. Norton & Company, 1997.
HELMHOLTZ, Hermann. On the Sensations of Tone. New York: Dover, 1954.
HINDEMITH, P. The Craft of Musical Composition. New York: Associated Music Publishers, 1945.
HINDEMITH, Paul. Curso condensado de harmonia tradicional, com predomínio de exercícios e um mínimo de regras. Tradução de Souza Lima. São Paulo: Irmãos Vitale, s/d [1949].
HURON, David. Interval-Class Content in Equally Tempered Pitch-Class Sets: Common Scales Exhibit Optimum Tonal Consonance. Music Perception, v. 11, n. 3, 1994, p. 289-305.
HUTCHINSON, William; KNOPOFF, Leon Knopoff. The Acoustic Component of Western Consonance. Interface, v.7, n.1, 1978, p. 1-29.
KLEIN, Michael L. Intertextuality in Western Art Music. Bloomington and Indianapolis: Indiana University Press, 2005.
KOELLREUTTER, Hans Joachim. Harmonia Funcional: introdução à teoria das funções harmônicas. 3ª Ed. São Paulo: Ricordi, 1986.
KORSIN, Kevin. Toward a New Poetics of Musical Influence. Music and Analysis, v. 10, n. 1/2, p. 3-72, 1991.
KOSTKA, Stefan; PAYNE, Dorothy. Tonal Harmony: with an Introduction to Twentieth-Century Music. 3ª Ed. New York: McGraw-Hill, Inc.,1995.
KOSTKA, Stefan. Materials and Techniques of Twentieth-Century Music. Upper Saddle River, NJ: Prentice Hall, 1999.
KRISTEVA, Julia. Introdução à semanálise. Tradução: Lúcia Helena França Ferraz. 2ª ed. São Paulo: Perspectiva, 2005.
McHOSE, Allen Irvine. The Contrapuntal Harmonic Technique of the Eighteenth Century. New York: F.S.Crofts & Company, 1947.
MENEZES, Flo. Apoteose de Schoenberg. São Paulo: Ateliê Editorial, 2002.
PACHELBEL, Johann. Canon and Gigue in D major, P.37. Partitura (3 violinos e baixo contínuo). Leipzig: Kistner & Siegel, n.d.[1929]. Disponível em https://vmirror.imslp.org/files/imglnks/usimg/e/e1/IMSLP44549-PMLP04611-Pachelbel-KanonundGigueFS.pdf. Acesso em 07.07.24.
PARNCUTT, Richard; REISINGER, Daniel; FUCHS, Andreas; KAISER, Fabio. Consonance and Prevalence of Sonorities in Western Polyphony: Roughness, Harmonicity, Familiarity, Evenness, Diatomicity. Journal of New Music Research, v.48, n.1, 2019, p.1-20.
PERSICHETTI, Vincent. Twentieth-Century Harmony: Creative Aspects and Practice. New York: W.W. Norton, 1961.
PISTON, W.; DEVOTO, M. Harmony. 5th ed. New York: Norton, 1987.
PITOMBEIRA, Liduino. Formal Design, Textural Profile, and Degree of Harmonic Endogeny as modeling factors. Anais do II Congresso da TeMA. Florianópolis: UDESC, 2017, p.42-51.
PITOMBEIRA, Liduino. Um exercício de paráfrase estrutural a partir da análise do Quarteto Op. 22 de Anton Webern. Claves, v. 5, 2008, p. 88-100
PLOMP, R.; LEVELT, W. J. M. Tonal consonance and critical bandwidth. The Journal of the Acoustical Society of America, 38, 1965, p. 548–560.
ROADS, Curtis; WIENEKE, Paul. Grammar as Representations for Music. Computer Music Journal, v.3, n.1, 1979, p.48-55.
SCHNEIDER, A. (1997). ‘Verschmelzung’, tonal fusion, and consonance: Carl Stumpf revisited. In: Marc Leman (Ed.), Music, Gestalt, and computing. Berlin: SpringerVerlag, 1997, p.115–143.
STRAUS, Joseph N. Remaking the Past: Musical Modernism and the Influence of the Tonal Tradition. London: Harvard University Press, 1990.
STRAUS, Joseph N. Introdução à Teoria Pós-tonal. Ricardo Bordini, Trad. Salvador: EDUFBA, 2013.
TCHAIKOVSKY, Peter. Guide to the Practical Study of Harmony. Leipzig: P. Jurgenson, 1900.
TELESCO, Paula. Enharmonicism and Omnibus Progression in Classical-era Music. Music Theory Spectrum, v.20, n.2, 1998, p. 242-279.
TEMPERLEY, David. A Statistical Analysis of Tonal Harmony. Disponível em: http://davidtemperley.com/kp-stats/ Acesso em: 26 de junho de 2021.
TYMOCZKO, Dmitri. A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice. Oxford: Oxford University Press, 2011.
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