Article ID: CBB139505675

Arithmetic, Geometric and Harmonic Means in Music Theory (2014)


Some milestones in the development of music theory can be represented as a dialectical contrast between means. In Pythagorean harmony, arithmetic and harmonic means are generators of musical scales, while a specific theorem by Archytas precludes the geometric mean from this opportunity. The developments in Renaissance music theory are described by its protagonist, Zarlino, in terms of means. He identifies the overcoming of Pythagorean harmony with the intervention of the contrharmonic mean, the superiority of the major over the minor mode with the superiority of the harmonic mean over the arithmetic one, the contrast between natural and tempered tunings with the opposition between the arithmetic mean and the geometric one. Rameau, the major musical theorist of the Baroque era, also describes his "fundamental bass" using the three means (for the first time all together): the arithmetic and harmonic means applied to the vertical dimension of harmony, the geometric one to the horizontal dimension of melody.

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Authors & Contributors
Bellissima, Fabio
Boccadoro, Brenno
Berns, Jörg Jochen
Klotz, Sebastian
BaldisseraPacchetti, Marina
Creese, David
Bruniana & Campanelliana: Ricerche Filosofiche e Materiali Storico-testuali
Bollettino di Storia delle Scienze Matematiche
Berichte zur Wissenschaftsgeschichte
Journal of the Acoustical Society of America
Studies in History and Philosophy of Science
American Historical Review
Yale University
University of Chicago
University of Minnesota
Music theory
Harmony (music theory)
Zarlino, Gioseffo
Ptolemy, Claudius
Stumpf, Carl
Galilei, Vincenzo
Time Periods
17th century
Early modern
16th century
United States
Ancient Near and Middle East: Egypt, Sumer, Babylon, Assyria, Mesopotamia, Palestine, Persia
Jesuits (Society of Jesus)

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