Modeling Consonance and Its Relationships with Temperament and Harmony (CDT-10)

After revising the concepts of consonance/dissonance, a respective mathematic-computational model is described, based on Helmholtz's consonance theory and also considering the partials intensity. It is then applied to characterize five scale temperaments, as well as some minor and major triads. In spite of the simplicity of this model, a good agreement is often observed between the obtained consonances/dissonances and the typically observed properties of scales and chords. The representation of temperaments as graphs where links correspond to consonance (or dissonance) is also presented and used to compare distinct temperaments, allowing the identification of two main groups of approaches