Musical Scales and their Mathematics

Häftad, Engelska, 2026

Del i serien Mathematics Study Resources

742 kr

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Beskrivning

Are musical scales just trivial? This book explores this question, revealing the complexity of creating "harmony" in tonal systems.Why 12 tones? Are there alternatives? Are 12 fifths equal 7 octaves? What is "consonance"? When are intervals "perfect" or "imperfect"? What is meant by "tonal characteristics", "whole tone" and "semitone"? "Ancient tuning" vs potentially new?Answers need thoughtful explanations, revealing interconnectedness. In this context, mathematics is pivotal, explaining scale generation, temperament systems, etc.Divided into three parts, this book covers:Modern interval arithmetic driven by prime numbers.Architectural principles of scales, with examples.Systematic nature of historical tunings and temperaments.Understanding only requires school knowledge, developed into algebraic tools applied musically.

Produktinformation

Utgivningsdatum:2026-09-11
Mått:155 x 235 x undefined mm
Format:Häftad
Språk:Engelska
Serie:Mathematics Study Resources
Antal sidor:711
Förlag:Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN:9783662695401
Originaltitel:Die Tonleiter und ihre Mathematik

Utforska kategorier

Musikvetenskap inom Kultur
Tillämpad matematik inom Naturvetenskap och teknik
Musikhistoria inom Kultur

Mer om författaren

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.

Innehållsförteckning

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.