Research conducted at the State University of Maringá, Paraná, Brazil, from 2019 to 2024.

This research project intends to consolidate the investigations conducted during two former research projects, namely, "The formalization and abstraction of paradigmatic psychoacoustical properties of agglomerates of sounds of definite pitch as theoretical grounds for a new discipline of Harmony" (6182/2014-UEM) and "Formulation of a structural model for 19th-century Tonality from the critical revision of historical music theory bibliography" (1423/2010-UEM), continuing with the search for answers to the problematique of teaching music harmony in the context of the globalized world of the 21st century and after all the musical experimentation of the 20th century. Building from a theoretical framework developed during almost ten years of research, this research aims to prepare a comprehensive music harmony treatise book, which will include the dictionary of transpositional harmonic types developed during the earlier research projects, mediated and introduced by explanatory theoretical chapters. This treatise aims to develop a harmonic theory that tries to live up to a critical re-reading of two thousand years of music theory, consolidated for a contemporary practice in the 21st century, organized in three volumes written according to the methodology of a logic-deductive system “in geometrical order”, as in Baruch Spinoza's Ethics. This research is designed to be conducted in five stages, namely: a) a supplementation of the previous research projects, with the development of a taxonomy of transpositional subtypes; b) another supplementation to the earlier projects, with the composition of original musical works to demonstrate and exemplify the harmonic properties described in the theoretical framework developed by the research, to be incorporated as musical examples in the final treatise; c) consolidation of the text for the first volume of the harmony treatise: presentation of the theoretical grounds of music harmony; d) consolidation of the text for the second volume of the harmony treatise: reduction of the universe of harmonic constructs to 351 basic types and detailed study of their harmonic properties in the form of a Thesaurus; and e) consolidation of the text for the third volume of the harmony treatise: application of the concepts studied in the first two volumes in the conception of a functional triadic tonality, with the formulation and presentation of an analytic and constructive methodology for traditional tonal music composition. The research justifies itself by its goal to develop and formalize an appropriate theoretical framework for the learning of music harmony in a manner more attuned to the aesthetic concerns of the 21st century and its globalized world. Such a theoretical framework would be of great value and importance for the training of musicians, specially of composers, providing basic and generalized theoretical grounds to aid the search by contemporary composers of new harmonic languages.

1. Supplementation of the research project 6182/2014-UEM, with the development of a taxonomy of transpositional subtypes, which are tuning variations for each of the 351 transpositional types listed during that project, and the study of the impact of those variations in their harmonic properties;
2. Another supplementation of the research project 6182/2014-UEM, with the composition of musical works to demonstrate and exemplify the harmonic properties described in the theoretical framework developed by that project, to be added as musical examples in the final treatise;
3. The completion and consolidation of theoretical concepts on music harmony developed during two former research projects (1423/2010-UEM and 6182/2014-UEM) in the form of a Harmony Treatise, demonstrated in geometrical order and in three volumes: one for the presentation of the generalized theoretical grounds of musical harmony, a second one for the “Tn-Type Thesaurus”, accompanied by several theoretical explaining chapters, and a last volume for the description of a structural model for the traditional common-practice triadic tonality.

BARBOUR, J. M.. Tuning and Temperament: A Historical Survey. East Lansing: Michigan State College Press, 1951.
BLOOM, Harold. The Anxiety of Influence: a theory of poetry. New York: Oxford University Press, 1973.
BOSANQUET, R. H. M.. An Elementary Treatise on Musical Intervals and Temperament. London: Macmillan and Co., 1876.
BOETHIUS, Anicius Manlius Severinus. De institutione arithmetica libri duo, De institutione musica libri quinque. Lipsiae: in aedibus B. G. Teubneri, 1867 [ca. 510].
BREGMAN, Albert. Auditory Scene Analysis. Cambridge, MA: MIT Press, 1990.
BYRNE, David A. The Harmonic Theories of Sigfrid Karg-Elert: Acoustics, Function, Transformation, Perception. 2018. Dissertação (Doctor of Philosophy) – College-Conservatory of Music, University of Cincinnati, Cincinnati, Ohio, USA.
CHION, Michel. Guide des Objets Sonores. Paris: Buchet/Chastel, 1983.
COSTÈRE, Edmond. Lois et Styles des Harmonies Musicales. Paris: Presses Universitaires de France, 1954.
EULER, Leonhard. Du véritable caractère de la musique moderne. In: Histoire de l'Académie Royale des Sciences et des Belles-Lettres de Berlin anée 1764 (Memoires de l'academie des sciences de Berlin vol. 20). Berlin: Haude et Spener, 1766 [1764 a], pp. 174-199.
EULER, Leonhard. Conjecture sur la raison de quelques dissonances généralement reçues dans la musique. In: Histoire de l'Académie Royale des Sciences et des Belles-Lettres de Berlin anée 1764 (Memoires de l'academie des sciences de Berlin vol. 20). Berlin: Haude et Spener, 1766 [1764 b], pp. 165-173.
FORTE, Allen. The Structure of Atonal Music. New Haven: Yale University Press, 1973.
GAFFURIUS, Franchinus. Practica Musicae. Translation and transcription by Clement A. Miller (Musicological Studies and Documents, Vol. 20). Dallas: American Institute of Musicology, 1968 [1496].
HAUPTMANN, Moritz. The Nature of Harmony and Metre. London: Swan Sonnenschein & co., 1888.
HELMHOLTZ, Hermann L. F.. On the Sensations of Tone as a Physiological Basis for the Theory of Music (trad. Ellis, A. J., 3rd ed.). London: Longmans, Green and co., 1895.
LEVY, Ernst. A Theory of Harmony. Albany: State University of New York Press, 1985.
MOORE, B. C. J., PETERS, R. W. & GLASBERG, B. R.. Thresholds for the detection of inharmonicity in completones. Journal of The Acoustical Society of America. vol 77, pp. 1861-1867, 1985.
OETTINGEN, Arthur von. Harmoniesystem in Dualer Entwicklung. Leipzig: W. Glaser, 1866.
PARTCH, Harry. Genesis of a Music. New York: Da Capo Press, 1974.
PARNCUTT. R.. Harmony: A Psychoacoustical Approach. Springer-Verlag, 1989.
PROSDOCIMUS, de Beldemandis. Brevis Summula Proportionum Quantum Ad Musicam Pertinet. In: Herlinger, Jan (tradutor). Brief treatise on ratios that pertain to music; and, A little treatise on the method of dividing the monochord). Lincoln: University of Nebraska Press, 1987 [1409].
RAHN, J.. Basic Atonal Theory. New York: Schirmer Books, 1980.
REICHA, Antoine. Écrits inédits et oubliés, Volume 2,1: Theoretische Schriften und praktische Beispiele. Hildesheim: Georg Olms, 2015 [1803].
REINHARD, Johnny. Bach and Tuning (Sources and Studies in Music History from Antiquity to the Present, Volume 47). Frankfurt: PL Academic Research, 2016.
RIEMANN, Hugo. Harmony Simplified; or, The theory of the tonal functions of chords. London: Augener & Co., 1903.
ROEDERER, Juan. The Physics and Psychophysics of Music: an Introduction (4th ed.). New York: Springer Verlag, 2008.
SPINOZA, Baruch. Ethica Ordine Geometrico Demonstrata. In: Ethics & On the improvement of understanding. New York: Hafner Press, 1949 [1677].
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.
TERHARDT, Ernst. Pitch, Consonance, and Harmony. The Journal of the Acoustical Society of America, vol. 55, no. 5, p. 1061-1069, 1974.
THORESEN, Lasse. Spectromorphological Analysis of Sound Objects - An adaptation of Pierre Schaeffer's Typomorphology. In: Proceedings of the Electroacoustic Music Studies Network Conference EMS Beijing. 2006.
VITRUVIUS. Vitruvius on Architecture. Volume 1. Translated by Frank Granger. London: William Heinemann Ltd., 1931 [25 AC].
WERCKMEISTER, Andreas. Musicalische Temperatur. Translation by Elizabeth Hehr. In: Reinhard, Johnny. Bach and Tuning (Sources and Studies in Music History from Antiquity to the Present, Volume 47). Frankfurt: PL Academic Research, 2016 [1691].
ZARLINO, Gioseffo. Le Istitutioni Harmoniche (3rd ed.). Venetia: Francesco dei Franceschi Senese, 1573.
ZWICKER, Eberhard, & FASTL, Hugo. Psycho-Acoustics, Facts and Models (3rd ed.). Berlin: Springer-Verlag, 2007.