Division of music intervals by means of descriptive geometry and mechanical system methods in Gioseffo Zarlino’s treatises entitled Le Istitutioni Harmoniche and Sopplimenti Musicali
Journal Title: Notes Muzyczny - Year 2016, Vol 1, Issue 5
Abstract
The article presents the problem of interval division fundamental in the 16th-century theory and performance practice, which was presented in the treatises entitled Le institutioni harmoniche and Sopplimenti musicali by G. Zarlino (1517-1590). He based this essential problem on his observations and also on Euclid’s mathematics, Erastothenes’ mechanical mesolabium, the method of Philo of Byzantium and on the combination of mechanical descriptive methods. In the above mentioned treatises, Zarlino touches on, among others, the issue referring to determining tempered intervals. They are a result of dividing a selected consonance and, according to the author, they should be equal, i.e., diminished or augmented by the same value. In this perspective, the division of an interval into equal parts is, mathematically speaking, equal to determining a geometric mean. The segments we get using mathematical methods are then reflected in the length of strings of a monochord. The observations of the Italian theoretician gave rise to the study of instrument tuning, a compromise between the principles of harmony and aesthetics.<br/><br/>
Authors and Affiliations
Anna Wiśniewska
Keywords
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