composer, pianist, music theorist

Formulation of a structural model for 19th-century Tonality from the critical revision of historical music theory bibliography

Research conducted at the State University of Maringá, Paraná, Brazil, from 2010 to 2014.

Being both a composer utterly curious about the secrets of the art of music and a teacher of all levels of composition and music theory, I have been dedicating myself for more than two decades to the research of an efficient way to localize, explain and graph, in a synthetic, clear and pedagogical manner, the constructive coherence of the tonal repertoires, specially those from the second half of the 19th century. To accomplish this, I have been preparing a large number of analyses of important works from the western repertoire, and I have been constantly performing studies and critical reviews of works from a 2000-year span of music theorists that range from Pythagoras, Boethius, Prosdocimus, Zarlino and Tartini, all the way to 19th and 20th-century theorists such as Gottfried Weber, Hugo Riemann, Schoenberg and Schenker. Given my main interest in the late Romantic repertoire, my most important sources are 19th-century texts, either in a direct form or mediated by current musicologists, of authors such as Gottfried Weber (1779-1839), Moritz Hauptmann (1792-1868), François-Joseph Fétis (1784-1871), Arthur von Oettingen (1836-1920), Carl Friedrich Weitzmann (1808-1880), Rudolf Louis (1870-1914), Ludwig Thuille (1861-1907), Sigfrid Karg-Elert (1877-1933), Arnold Schoenberg (1874-1951) and, specially, Hugo Riemann (1849-1919). With these as a starting point, the research intends to propose an alternative way of explaining the compositional procedures of 19th-century Extended Tonality (also called Chromatic Tonality), a way built from the critical revision of the body of ideas of 19th-century theorists, formalized in a Structural Model presented as a deductive logical system. This system is most likely to be prepared “Demonstrated in Geometric Order” (as in Spinoza's “Ethics”), in the most objective way possible, contrary to the subjectivity of most theoretical works in this field. With this research, I intend to retrieve for the 21st-century scholar part of the world of 19th-century Music Theory ideas and concepts. These concepts are reasonably unknown to contemporary traditional instructional methodologies and present an invaluable body of thought which is hugely important for the understanding of 19th-century repertoire. The archives of analyses of repertoire prepared by me will also be collected, critically revised and preserved, and will be refitted as illustrative exemplification materials for the proposed Structural Model.


  1. The proposition of an alternative way to explain the compositional procedures of the late 19th-century Extended Tonality(also known as Chromatic Tonality), built from the critical revision of the body of ideas of 19th-century theorists and formalized as a Structural Model presented in a deductive logical system;
  2. The retrieval of part of the body of ideas of 19th-century theorists, which is hugely important to the understanding of the repertoire of that era, and reasonably unknown to the contemporary traditional instructional methodologies;
  3. The collection, critical revision and preservation of the archives of analyses prepared by me of traditional repertoire, refitted as illustrative exemplification materials for the proposed Structural Model;
  4. The creation of instructional bibliographic materials for the teaching of the western canon of Music Theory.


BEETHOVEN, Ludwig Van. Studies in thorough-bass, counterpoint and the art of scientific composition. New York: Schuberth and comp, 1853.
BENSON, David J. Music: A Mathematical Offering. Cambridge: Cambridge University Press, 2006.
BRISOLLA, Cyro. Princípios de harmonia funcional. São Paulo: Annablume, 2006 [1979].
COHN, Richard. Introduction to Neo-Riemannian Theory: A Survey and a Historical Perspective. Journal of Music Theory, Duke University Press, Vol. 42, No. 2, Neo-Riemannian Theory, pp. 167-180, 1998.
COSTÈRE, Edmond. Lois et Styles des Harmonies Musicales. Paris: Presses Universitaires de France, 1954.
COSTÈRE, Edmond. Mort ou Transfigurations de l'Harmonie. Paris: Presses Universitaires de France, 1962.
EUCLIDES. The Thirteen Books of the Elements. New York: Dover, 1956 [circa 300 AC].
FÉTIS, F.-J. Traité complet de la théorie et de la pratique de l'Harmonie. Paris: G. Brandus et S. Dufour, 1861 [1844].
GALILEI, Vincenzo. Dialogo della musica antica et della moderna. New York:Broude Brothers, 1967 [1581].
HAAGMANS, Dirk. Scales, Intervals, Harmony, Book I. New York: J. Fischer and Bro, 1916.
HARRISON, Daniel. Harmonic Function in Chromatic Music. Chicago: University of Chicago Press, 1994.
HAUPTMANN, Moritz. The Nature of Harmony and Meter. London and New York: Novello, Ewer, 1888 [1853].
HELMHOLTZ, H. On The Sensations of Tone as a Physiological Basis for the Theory of Music. New York: Dover 1954 [1885].
HINDEMITH, Paul. Curso Condensado de Harmonia Tradicional: São Paulo: Vitale, 1949 [1943].
HURON, D. Tone and Voice: A Derivation of the Rules of Voice-Leading from Perceptual Principles. Music Perception Fall, Vol. 19, No. 1, 1–64, 2001.
JEPPESEN, K. Counterpoint: The Polyphonic Vocal Style of the Sixteenth Century. New York: Dover Publications, 1992 [1931].
KOELLREUTER, Hans Joachim. Harmonia Funcional – introdução à teoria das funções harmônicas. São Paulo: Ricordi Brasileira, 1980.
KRUMHANSL, C. L. Cognitive Foundations of Musical Pitch. New York: Oxford University Press, 1990.
LERDAHL, F., & Jackendoff, R. A Generative Theory of Tonal Music. Cambridge, Mass.: MIT Press, 1983.
LERDAHL, F. Tonal Pitch Space. Oxford: Oxford University Press, 2001.
LEWIN, David. A Formal Theory of Generalized Tonal Functions. Journal of Music Theory, Yale University, Vol. 26, No. 1, pg. 23-60, 1982.
LOUIS, R. & THUILLE, Ludwig. Harmonielehre. Sttutgart: Verlag von Carl Grüninger (Klett & Hartmann), 1907.
MENEZES, Flo. A acústica musical em palavras e sons. São Paulo: Ateliê Editorial, 2004.
MENEZES, Florivaldo, Apoteose de Schoenberg, 2a. edição, São Paulo: Ateliê Editorial, 2002.
MICKELSEN, William C. Hugo Riemann's Theory of Harmony: A Study. Lincoln: University of Nebraska Press, 1977.
MOONEY, Kevin. Hugo Riemann's Debut as a Music Theorist. Journal of Music Theory, Duke University Press, Vol. 44, No. 1, pp. 81-99, 2000.
MOTTE, Diether de la. Armonía. Barcelona: Idea Books, 1998 [1976].
OETTINGEN, Arthur von. Harmoniesystem in Dualer Entwicklung. Leipzig: W. Glaser, 1866.
OLIVEIRA, J. Zula de ; OLIVEIRA, Marilena de. Harmonia funcional. São Paulo: Cultura Musical, 1978.
PARNCUTT, Richard. Harmony: A Psychoacoustical Approach. Berlin: Springer-Verlag, 1989.
PISTON, W. Harmony. New York: Norton, 1962 [1941].
RAMEAU, J. P. Treatise on Harmony. New York: Dover, 1971 [1722].
REHDING, Alexander. Hugo Riemann and the birth of modern musical thought. Cambridge: Cambridge University Press, 2003.
RIEMANN, Hugo. Ideas for a Study On the Imagination of Tone, (translated by Robert Wason and Elizabeth West Marvin). Journal of Music Theory 36/1, pp. 81-117, 1992 [1915].
RIEMANN, Hugo. Harmony Simplified ; or, The theory of the tonal functions of chords. London: Augener & Co., 1903 [1893].
RIEMANN, Hugo. History of Music Theory, Book III. Translated by William C. Mickelsen. In Mickelsen, Hugo Riemann's Theory of Harmony: A Study. Lincoln: University of Nebraska Press, 1977 [1898].
RIMSKY-KORSAKOV, N. Tratado Prático de Armonia. Buenos Aires: Ricordi Americana, 1976 [1885].
RUDD, Rachel Eloise. Karl Friedrich Weitzmann's Harmonic Theory in Perspective. 1992. Dissertação (Doutorado) - Columbia University in the City of New York, New York, USA.
SCHENKER, Heinrich. Harmony. Chicago: University of Chicago Press, 1954 [1910].
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SCHENKER, Heinrich. Free composition. New York: Longman, 1979 [1935].
SCHOENBERG, Arnold. Funções Estruturais da Harmonia. São Paulo: Via Lettera, 2004 [1954].
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SCHOENBERG, A. Harmonia. São Paulo: Editora UNESP, 2001 [1911].
SEPE, J. Tratado de harmonia. São Paulo: Ricordi Brasileira, 1942.
SPINOZA, Baruch. Tractatus de Intellectus Emendatione. In: Ethics & On the improvement of understanding. New York: Hafner Press, 1949 [1662].
SPINOZA, Baruch. Ethica Ordine Geometrico Demonstrata. In: Ethics & On the improvement of understanding. New York: Hafner Press, 1949 [1677].
TCHAIKOVSKY, Peter Ilich. Guide to the Practical Study of Harmony. New York: Dover Books, 2005 [1872].
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