Musical Scales and their Mathematics

Explains musical temperaments clearly and vividly, solely using basic school mathematics The new edition has been completely redesigned and features an entirely fresh approach to musical intervals Suitable for enthusiasts of both mathematics and music

Auteur

Prof. Dr. Karlheinz Schüffler is a mathematician, organist, and choir conductor. As a mathematician, he teaches at the University of Düsseldorf and previously at the Niederrhein University of Applied Sciences (Krefeld). As a musician, he has been dedicated to church music since his youth, with both organ and mathematical music theory being his areas of expertise.

Contenu

Part I: Mathematical Theory of Intervals. Musical intervals and tones.- The commensurability of musical intervals.- Harmonic-rational and classical-antique intervals. - Iterations and their music-mathematical laws.- Part II: Mathematical Theory of Scales. Scales and their models.- Combinatorial games surrounding characteristics.- Diatonic and chromatic aspects of the circle of fifths.- Part III: Mathematical Temperament Theory. The Pythagorean interval system.- Meantone temperament.- The natural-harmonic system and enharmonics.- Equal temperament and its intriguing context.- Epilogue Postlude.- Indexes.