Musical Scales and Their Mathematics

By Karlheinz Schüffler

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.

• Format: Paperback
• Language: English
• ISBN: 3662695405
• ISBN13: 9783662695401
• Release Date: September 2026
• Publisher: Springer
• Length: 711 Pages