[download pdf] Musical Scales and their Mathematics by Karlheinz Schüffler

Musical Scales and their Mathematics by Karlheinz Schüffler

• Musical Scales and their Mathematics
• Karlheinz Schüffler
• Page: 711
• Format: pdf, ePub, mobi, fb2
• ISBN: 9783662695401
• Publisher: Springer Berlin Heidelberg

Musical Scales and their Mathematics

Free book to download in pdf 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.

Musical Scales and their Mathematics. book by Karlheinz Schüffler
This book explores this question, revealing the complexity of creating ``harmony'' in tonal systems. Systematic nature of historical tunings and temperaments.
Musical Scales and their Mathematics - SpringerLink
This book offers a clear introduction to musical intervals and temperaments, requiring only basic school math for understanding.
Recommendations for books that explore the math behind music
Many styles of music do not emphasize harmony. A lot of atonal composers use mathematics to organize their music, and of course they can do so.
Musical Scales And Their Mathematics Book By Karlheinz Schuffler .
Buy the book Musical Scales and their Mathematics by karlheinz schuffler at Indigo.
Musical Scales and their Mathematics: Karlheinz Schuffler
Are musical scales just trivial? This book explores this question, revealing the complexity of creating "harmony" in tonal systems. Why 12 tones? Are there .

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