composer, pianist, music theorist

Tonicity-Phonicity Calculator


This project, developed in 2013 by Dr. Marcus Alessi Bittencourt, presents a computational model in PHP of psychoacoustic music theories by Richard Parncutt (Parncutt 1988, 1989, 1997 and 2009), with the addition of other theoretical components of his (Bittencourt 2011), combined to Set-Theory (Forte, 1973 and Rahn, 1980) and the theories by Edmond Costère (Costère, 1954). This model was implemented in the form of an analytical calculator available to the community via the internet as an HTML page. Such a tool allows the fast access to the analytical diagnostics generated by the computational model by means of an HTML page containing a concise form easily viewable and printable.

  • Read the complete article presented in 2011 at the II Encontro Internacional de Teoria e Análise Musical, São Paulo-SP, Brazil, which contains a basic introduction to the theories that are computationally modelled by this calculator.
  • Read the article containing the theoretical grounds and the formal explanation for the mathematical models used in this calculator.

The Project of the Analytical Calculator

The study of the properties of tonicity, phonicity and azimuth of pitch-class sets is an important task for compositional and analytical work. Nonetheless, such methodology requires a certain amount of calculations which are, although not too complex from the point of view of mathematicians, certainly boring and cumbersome from a musician's standpoint. It is with this realization in mind that this calculator was created: to provide quick and clear access to the interpretations and diagnostics done from the analysis of musical data submitted by a user. The project was implemented in PHP so that the calculator would be absolutely multi-platform and accessible online at the internet to all the music community, without the need to install special software, except for the usual web browser normally present in any modern computer.


BITTENCOURT, M.A. Sketches for the foundations of a contemporary experimental treatise on Harmony. In: II Encontro Internacional de Teoria e Análise Musical, 2011, São Paulo-SP, Brasil. Anais do II Encontro Internacional de Teoria e Análise Musical, São Paulo-SP, Brazil, 2011.
COSTÈRE, Edmond. Lois et Styles des Harmonies Musicales. Paris: Presses Universitaires de France, 1954.
FORTE, Allen. The Structure of Atonal Music. New Haven: Yale University Press, 1973.
PARNCUTT, Richard. Revision of Terhardt’s Psychoacoustical Model of the Root(s) of a Musical Chord. Music Perception. Vol. 6, No. 1 (Fall), pp. 65-93, 1988.
PARNCUTT, Richard. Harmony: A Psychoacoustical Approach. Berlin: Springer-Verlag, 1989.
PARNCUTT, Richard. 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, Germany: Springer-Verlag, 1997, p. 181-199.
PARNCUTT, Richard. Tonal implications of harmonic and melodic Tn-types. In KLOUCHE, T. & NOLL, T. (Eds.). Mathematics and computing in music. Berlin: Springer-Verlag, 2009, p. 124-139.
RAHN, John. Basic Atonal Theory. New York: Schirmer Books, 1980.
STRAUS, Joseph Nathan. Introduction to Post-Tonal Theory. New Jersey; Prentice Hall, 1990.

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