Music: A Mathematical Offering by David J. Benson

About this book :-
"Music: A Mathematical Offering" by David J. Benson explores how mathematics helps us understand music, sound, and harmony. The book shows that musical ideas such as pitch, rhythm, and harmony are deeply connected to mathematical structures. Benson begins with the basics of sound and vibration, explaining how waves create musical tones and how the human ear perceives them. This foundation makes the subject approachable even for readers without advanced mathematical training. The book then moves into how "mathematics and music" interact through concepts like ratios, symmetry, and patterns. It explains musical scales, tuning systems, and temperaments using clear mathematical reasoning, helping readers see why certain sounds feel consonant or dissonant. Topics such as "Fourier analysis", resonance, and overtones are introduced to show how complex sounds can be broken down into simpler components. Benson also discusses historical developments, connecting ancient musical theory with modern scientific understanding. In later chapters, the book explores modern applications, including digital sound, signal processing, and the design of musical instruments. Written for musicians, mathematicians, teachers, and curious readers, it successfully bridges art and science. Overall, the book demonstrates how "sound and harmony" can be explained through "mathematical structures", offering a rich and insightful perspective on music.

Book Detail :-
Title: Music: A Mathematical Offering by David J. Benson
Publisher: Cambridge University Press (CUP)
Year: 2008
Pages: 531
Type: PDF
Language: English
ISBN-10 #: 0521619998
ISBN-13 #: 978-0521619998
License: University Educational Resource
Amazon: Amazon

About Author :-
The author David J. Benson is a mathematician and educator known for clearly explaining complex ideas and connecting mathematics with real-world subjects. His academic background includes "abstract algebra" and mathematics education, and he has a strong interest in showing how mathematical thinking applies beyond traditional theory. In "Music: A Mathematical Offering", Benson combines his expertise in "mathematics and music" to explain sound, harmony, and musical structure. His writing makes advanced ideas like "Fourier analysis" and "sound and vibration" accessible to a wide audience, including students, teachers, and curious readers.

Book Contents :-
1. Waves and harmonics 2. Fourier theory 3. A mathematician’s guide to the orchestra 4. Consonance and dissonance 5. Scales and temperaments: the fivefold way 6. More scales and temperaments 7. Digital music 8. Synthesis 9. Symmetry in music Appendices A. Answers to almost all exercises B. Bessel functions C. Complex numbers D. Dictionary E. Equal tempered scales F. Frequency and MIDI chart I. Intervals J. Just, equal and meantone scales compared L. Logarithms M. Music theory O. Online papers P. Partial derivatives R. Recordings W. The wave equation

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