René Descartes’i heksahordide akustilisest ehitusest

Abstract

As we know, the medieval system of solmization is based on hexachords which correspond to the first six degrees of the modern major key. Its tones have been designated as solmization syllables ut–re–mi–fa–sol–la. According to the theory outlined in the treatise Compendium musicae (1618) by the French philosopher and mathematician René Descartes (1596–1650), the interval ut to re must always be a minor whole-tone (9:10), re to mi a major whole-tone (8:9), mi to fa a major semitone (15:16), fa to sol a major whole-tone, and finally sol to la a minor whole-tone. Among the notes of the English physicist and mathematician Isaac Newton dated 1665, there is a diagram, which, probably following one of Descartes’s examples, represents five hexachords. In these, Descartes’s figures marking string lengths are replaced by figures marking units of the 53-division of the octave, having the size of 22.6 cents. In this study, all the Descartes hexachords possible in the 53-division are discussed and compared with those of John Hothby (?–1487) and Gioseffo Zarlino (1517–1590).