The Mathematics of Music and Art

Arturo Portnoy (Autor)

Buch | Hardcover

XXIV, 129 Seiten

2023
Springer International Publishing (Verlag)
978-3-031-34439-8 (ISBN)

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This book explores the relationships between music, the sciences, and mathematics, both ancient and modern, with a focus on the big picture for a general audience as opposed to delving into very technical details. The language of music is deciphered through the language of mathematics. Readers are shown how apparently unrelated areas of knowledge complement each other and in fact propel each other's advancement. The presentation as well as the collection of topics covered throughout is unique and serves to encourage exploration and also, very concretely, illustrates the cross- and multidisciplinary nature of knowledge. Inspired by an introductory, multidisciplinary course, the author explores the relationships between the arts, sciences, and mathematics in the realm of music. The book has no prerequisites; rather it aims to give a broad overview and achieve the integration of the three presented themes. Mathematical tools are introduced and used to explain various aspects of music theory, and the author illustrates how, without mathematics, music could not have been developed.

Arturo Portnoy, Ph.D., is a Professor of Mathematical Sciences at the University of Puerto Rico at Mayaguez. His is also Co-Director of the Puerto Rico Mathematical Olympiads. He received his B.Sc. in Applied Mathematics at the Instituto Tecnológico Autónomo de México (1992) and his M.Sc. (1994) and Ph.D. (1997) at Rensselaer Polytechnic institute. His areas of interest include inverse problems, mathematical modeling, optimization, regularization, math education, and math Olympiads. He also explores the use of technology to increase efficiency, transparency, and consistency in teaching mathematics.

Preliminaries.- The pigeonhole principle.- Continued fractions.- Pythagoras and music.- Temperaments of the scale.- Patterns in music.- Analysis and synthesis of music.- Beats, resonance, and tuning.- Digital music and information.- Last thoughts.

"The book is understandable for beginners: The most important notions are explained (irrationality, logarithms, musical notation etc., golden ratio, binary representation of numbers etc.). It is a fine book that can be recommended." (Eberhard Knobloch, zbMATH 1535.00043, 2024)

Erscheinungsdatum	30.07.2023
Reihe/Serie	Synthesis Lectures on Mathematics & Statistics
Zusatzinfo	XXIV, 129 p. 65 illus., 45 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	168 x 240 mm
Gewicht	431 g
Themenwelt	Kunst / Musik / Theater ► Musik ► Musiktheorie / Musiklehre
Themenwelt	Mathematik / Informatik ► Mathematik
Schlagworte	Continued fractions • digital information • Fourier series • Harmonic Analysis • Mathematics • Music analysis • Pattern Analysis • Pigeon Hole Principle • Pythagoras
ISBN-10	3-031-34439-1 / 3031344391
ISBN-13	978-3-031-34439-8 / 9783031344398
Zustand	Neuware