Research conducted at the State University of Maringá, Paraná, Brazil, from 2014 to 2019.

This research project, which was conducted from 2014 to 2019 at the State University of Maringá, Paraná, Brazil, with funding from a two-year fellowship grant (2014-2016) given by the Araucaria Foundation for the Scientific and Technological Development of the State of Paraná, aimed to construct the theoretical grounds for a new discipline of Harmony by means of the theoretical formalization and abstraction of paradigmatic psychoacoustical properties of agglomerates of sounds of definite pitch. The research investigated and defined paradigmatic psychoacoustical concepts for this type of sounds, their qualification and mathematical quantification, as well as the enumeration and a qualitative and taxonomical study of a Harmonic Universe defined by these studies. The research included the computational implementation of the quantitative mathematical modellings developed, creating Computer-Assisted Composition software components that aim at the fast taxonomical identification of a harmonic combination and the survey of its properties and comparative interrelationships with other combinations. Among the expected direct results of this research are: a) the development and formalization of a more appropriate theoretical body for the learning of Music Harmony in a way which is prepared and atuned to the musical and aesthetic directives of the 21st century and of a globalized world; and b) to make viable the creation of software components to aid contemporary composers in their task of researching new harmonic languages, serving them as basic theoretical grounds. The methodology for this research included three stages: 1) definition and quantitative mathematical formalization of archetypal psychoacoustical concepts, which includes a bibliographical revision of previous modern and historical theoretical works on the subject, as well as modern psychoacoustical research; 2) definition of a Harmonic Universe and its taxonomical study; and 3) the final formalization of the research, including the programming of software components and scientific papers.

1. The investigation and definition of archetypal psychoacoustical concepts capable of being used as grounds for the design of horizontal and vertical mixtures of sounds of definite pitch;
2. The qualification of these archetypal psychoacoustical concepts, and the research, choice and formalization of a quantification method for these concepts, according to mathematical modelling methods;
3. The enumeration as well as the qualitative and taxonomical study of several paradigmatic harmonic combinations, grounded by the formalization of the basic psychoacoustical concepts studied;
4. The computational implementation of the mathematical methods developed for the modelling of the paradigmatic musical concepts studied, creating possible software components of the “Computer-Assisted Composition” type that aim at the fast taxonomical identification of a harmonic combination and the survey of its properties and comparative interrelationships with other combinations.

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