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Musical Scales and their Mathematics

Nyhet

Häftad, Engelska, 2026

AvKarlheinz Schüffler,Karlheinz Schuffler

929 kr

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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

Utgivningsdatum2026-09-11
Mått155 x 235 x undefined mm
FormatHäftad
SpråkEngelska
SerieMathematics Study Resources
Antal sidor711
FörlagSpringer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN9783662695401
OriginaltitelDie Tonleiter und ihre Mathematik

Tillhör följande kategorier

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

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.