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Daily Overview |
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GM: General Mathematics Location: G530 Session Chair: Markus Kunze | |
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A mathematical coordinate system for music naturtoene, Switzerland A mathematical coordinate system for music by Rolphe F. FEHLMANN Abstract Mathematical music theory is most often based on the two historical milestones: on the one hand it is the system of the ‘sectio canonis’ of the Greek EUCLID [300 B.C.], i.e. the division of a string on the monochord leading to the mathematical proportions of musical tones. And on the other hand it is the 12-tone tempering system introduced by the Dutch mathematician Simon STEVIN [NL, 1548–1620] in his treatise ‘Van de spiegeling der singconst’ (published posthum in 1884). In this presentation the starting point is the sequence of the natural resonance modes [NRMs], aka the harmonic sequence. The reflection of this sequence is usually called the subharmonics and has evoked lots of discussions around its existence. In this alternative approach the numbering of the NRMs as it is done within the ethnic music in Switzerland, (alphorn, buechel, tiba and natural yodel) serves as the basis for a one-to-one mapping to the mathematical number line of the common coordinate system of DESCARTES [F, 1596-1650] Generally speaking it will not only facilitate the correspondence between mathematics and music, but also more specifically, basic mathematical operations can easily be applied to music. It turns out that chords can be interpreted as vectors and progressions as matrices. | |
