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After briefly revising the concepts of consonance/dissonance, a respectivemathematic-computational model is described, based on Helmholtz's consonancetheory and also considering the partials intensity. It is then applied tocharacterize five scale temperaments, as well as some minor and major triadsand electronic amplification. In spite of the simplicity of the describedmodel, a surprising agreement is often observed between the obtainedconsonances/dissonances and the typically observed properties of scales andchords. The representation of temperaments as graphs where links correspond toconsonance (or dissonance) is presented and used to compare distincttemperaments, allowing the identification of two main groups of scales. Theinteresting issue of nonlinearities in electronic music amplification is alsoaddressed while considering quadratic distortions, and it is shown that suchnonlinearities can have drastic effect in changing the original patterns ofconsonance and dissonance.

Modeling Consonance and its Relationships with Temperament, Harmony, and Electronic Amplification