Mathematics of Music and Art

Arturo Portnoy, Ph.D., is a Professor of Mathematical Sciences at the University of Puerto Rico at Mayaguez. He 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.

“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)

• 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.