Rethinking Modal Gender in the Context of the Universe of Tn-Types: Definitions and Mathematical Models for Tonicity and Phonicity

Marcus Alessi Bittencourt

Resumo


An indisputable cornerstone of the Western music tradition, the dialectic opposition between the major and minor grammatical modal genders has always been present in the imagination of musicians and music theorists for centuries. Such dialectics of opposition is especially important in the context of nineteenth-century harmonic dualism, with its ideas of tonicity and phonicity. These concepts serve as the main foundation for the way harmonic dualism conceives the major and minor worlds: two worlds with equivalent rights and properties, but with opposed polarities. This paper presents a redefinition of the terms tonicity and phonicity, translating those concepts to the context of post-tonal music theory. The terminologies of generatrix, tonicity, root, phonicity, vertex, and azimuth are explained in this paper, followed by propositions of mathematical models for those concepts, which spring from Richard Parncutt’s root-salience model for pitch-class sets. In order to demonstrate the possibilities of using modal gender as a criterion for the study and classification of the universe of Tn-types, we will present a taxonomy of the 351 transpositional set types, which comprises the categories of tonic (major), phonic (minor) and neutral (genderless). In addition, there will be a small discussion on the effect of set symmetries and set asymmetries on the tonic/phonic properties of a Tn-type.


Palavras-chave


Harmonic dualism; tonicity; phonicity; major/minor modal gender; post-tonal music theory.

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Referências


AZIMUTH. In: The Merriam-Webster Online Dictionary and Thesaurus, 2016. http://www.merriam-webster.com/dictionary/azimuth. Accessed October 5, 2016.

BARBOUR, James Murray. Tuning and Temperament – A Historical Survey. East Lansing: Michigan State College Press, 1951.

BENSON, Dave. Music: A Mathematical Offering. Cambridge: Cambridge University Press, 2006.

COSTÈRE, Edmond. Lois et styles des harmonies musicales. Paris: Presses Universitaires de France, 1954.

GAFFURIUS, Franchinus. Practica Musicae. Translated and transcripted by Clement A. Miller (Musicological Studies and Documents, v. 20). Dallas: American Institute of Musicology, 1968.

GENERATRIX. In: The Merriam-Webster Online Dictionary and Thesaurus, 2016. http://www.merriam-webster.com/dictionary/generatrix. Accessed October 5, 2016.

HARRISON, Daniel. Harmonic Function in Chromatic Music: A Renewed Dualist Theory and an Account of Its Precedents. Chicago: University of Chicago Press, 1994.

HAUPTMANN, Moritz. The Nature of Harmony and Metre. London: Swan Sonnenschein & co., 1888.

HAWKINS, John. A General History of the Science and Practice of Music. Re-print of the J. Alfred Novello edition of 1853. New York: Dover, 1963. 2 v.

HELMHOLTZ, Hermann von. On The Sensations of Tone as a Physiological Basis for the Theory of Music. London: Longmans, Green, and Co., 1875.

KLUMPENHOUWER, Henry. Dualist Tonal Space and Transformation in Nineteenth-Century Musical Thought. In: CHRISTENSEN, T. (Ed.). The Cambridge History of Western Music Theory. Cambridge: Cambridge University Press, 2002. 456-476.

LEVY, Ernst. A Theory of Harmony. Albany: State University of New York Press, 1985.

MICKELSEN, William. Hugo Riemann’s Theory of Harmony: A Study. Lincoln: University of Nebraska Press, 1977.

MOORE, B. C. J.; PETERS, R. W.; GLASBERG, B. R.. Thresholds for the Detection of Inharmonicity in Complex Tones. Journal of The Acoustical Society of America, USA, 77, 1861-1867, 1985.

OETTINGEN, Arthur von. Harmoniesystem in Dualer Entwicklung. Leipzig: W. Glaser, 1866.

PARNCUTT, Richard. Revision of Terhardt’s Psychoacoustical Model of the Root(s) of a Musical Chord. Music Perception, California, USA, v. 6-1, p. 65-93, Fall 1988.

_________. Harmony: A Psychoacoustical Approach. Berlin: Springer-Verlag, 1989.

_________. A Model of the Perceptual Root(S) of a Chord Accounting for Voicing and Prevailing Tonality. In: LEMAN, M. (Ed.). Music, Gestalt, and Computing - Studies in Cognitive and Systematic Musicology. Berlin: Springer-Verlag, 1997. p. 181-199.

_________. Tonal Implications of Harmonic and Melodic Tn-types. In: KLOUCHE, T.; NOLL, T. (Ed.). Mathematics and Computing in Music. Berlin: Springer-Verlag, 2009. p. 124-139.

PLACK, Christopher J.; OXENHAM, Andrew J.. The Psychophysics of Pitch. In: PLACK C. J.; OXENHAM, A. J.; FAY, R. R.; POPPER, A. N. (Ed.). Pitch: Neural Coding and Perception. New York: Springer, 2005. p. 7-55.

PLOMP, Reinier. Pitch of Complex Tones. The Journal of the Acoustical Society of America, USA, v. 41, n. 6, p. 1526-1533, 1967.

RAHN, John. Basic Atonal Theory. New York: Schirmer Books, 1980.

REHDING, Alexander. Hugo Riemann and the Birth of Modern Musical Thought. Cambridge: Cambridge University Press, 2003.

RIEMANN, Hugo. History of Music Theory, Book III. Translated and edited by C. William Mickelsen. Lincoln: University of Nebraska Press, 1977.

_________. Harmony Simplified; or, The Theory of the Tonal Functions of Chords. London: Augener & Co., 1903.

SCHUCK, O. H.; YOUNG, R.W.. Observations on the Vibrations of Piano Strings. Journal of The Acoustical Society of America, USA, v. 15-1, p. 1-11, 1943.

TARTINI, Giuseppe. Trattato di musica secondo la vera scienza dell'armonia. Padova: Stamperia del Seminario appresso Giovanni Manfrè, 1754.

TENNEY, James. A History of ‘Consonance’ and ‘Dissonance’. White Plains, NY: Excelsior, 1960.

WIENPAHL, Robert W.. Zarlino, the Senario and Tonality. Journal of the American Musicological Society, USA, v. 12-1, p. 27-41, 1959.

ZWICKER, Eberhard, & FASTL, Hugo. Psycho-Acoustics, Facts and Models. 3rd ed. Berlin: Springer-Verlag, 2007.




DOI: http://dx.doi.org/10.20504/opus2016b2215

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OPUS - Revista Eletrônica da Associação Nacional de Pesquisa e Pós-graduação em Música (ANPPOM)
ISSN 0103-7412 (versão impressa, 1989-2008), ISSN 1517-7017 (versão online, 2009- )