Musical Scales and their Mathematics: Mathematics Study Resources, cartea 14
Autor Karlheinz Schüffleren Limba Engleză Paperback – 31 oct 2024
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.
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Specificații
ISBN-13: 9783662695401
ISBN-10: 3662695405
Pagini: 730
Ilustrații: Approx. 730 p.
Dimensiuni: 155 x 235 mm
Ediția:2024
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Mathematics Study Resources
Locul publicării:Berlin, Heidelberg, Germany
ISBN-10: 3662695405
Pagini: 730
Ilustrații: Approx. 730 p.
Dimensiuni: 155 x 235 mm
Ediția:2024
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Mathematics Study Resources
Locul publicării:Berlin, Heidelberg, Germany
Cuprins
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.
Notă biografică
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.
Textul de pe ultima copertă
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:
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 Hochschule Niederrhein (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.
The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content.
This book is a translation of an original German edition. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation.
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.
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 Hochschule Niederrhein (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.
The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content.
This book is a translation of an original German edition. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation.
Caracteristici
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