The Musical Scale - a Triviality or a Problem?
This book examines this provocative question. It soon becomes clear that combining tones into "harmonious" tonal systems represents a challenge of unexpected complexity, encompassing a remarkably large number of interconnected problems.
and many similar ones quickly show that their answers not only require well-considered justifications but are also closely interconnected. In this examination, "mathematics" plays a key role. Starting with "simple proportions and numerical relationships", a veritable network emerges, in which both the methods of scale generation with their circle of wolf fifths an Euler grid selection procedures, as well as the models of temperament systems, can be scientifically explained. In three parts,
are presented and equipped with numerous examples. The music-mathematical calculations and explanations require only basic school-level knowledge, which are then developed and applied to musical themes. A small peculiarity: stories from the fairytale world of musical mythical creatures accompany the text and explain it in an amusing way.
This book is a translation of the original German edition Die Tonleiter und ihre Mathematik, 4th edition, by Karlheinz Schüffler, published by Springer-Verlag GmbH, DE in 2026. The translation was done with the help of an artificial intelligence machine translation tool. A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation.
| ISBN: | 9783662695401 |
| Publication date: | 24th August 2025 |
| Author: | Karlheinz Schüffler |
| Publisher: | Springer an imprint of Springer Berlin Heidelberg |
| Format: | Paperback |
| Pagination: | 711 pages |
| Series: | Mathematics Study Resources |
| Genres: |
Applied mathematics Theory of music and musicology History of music Mathematics |
The Musical Scale - a Triviality or a Problem?
This book examines this provocative question. It soon becomes clear that combining tones into "harmonious" tonal systems represents a challenge of unexpected complexity, encompassing a remarkably large number of interconnected problems.
and many similar ones quickly show that their answers not only require well-considered justifications but are also closely interconnected. In this examination, "mathematics" plays a key role. Starting with "simple proportions and numerical relationships", a veritable network emerges, in which both the methods of scale generation with their circle of wolf fifths an Euler grid selection procedures, as well as the models of temperament systems, can be scientifically explained. In three parts,
are presented and equipped with numerous examples. The music-mathematical calculations and explanations require only basic school-level knowledge, which are then developed and applied to musical themes. A small peculiarity: stories from the fairytale world of musical mythical creatures accompany the text and explain it in an amusing way.
This book is a translation of the original German edition Die Tonleiter und ihre Mathematik, 4th edition, by Karlheinz Schüffler, published by Springer-Verlag GmbH, DE in 2026. The translation was done with the help of an artificial intelligence machine translation tool. A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation.
Musical Scales and Their Mathematics features in the following genres: Applied mathematics, Theory of music and musicology, History of music, Mathematics
Musical Scales and Their Mathematics is available in Paperback
Musical Scales and Their Mathematics was written by Karlheinz Schüffler and published by Springer an imprint of Springer Berlin Heidelberg
Musical Scales and Their Mathematics has 711 pages
Yes it is part of Mathematics Study Resources series
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