There is a strong correlation between musical skills, mathematics, and computation. This book explores these relationships and more from many different approaches. It is a collection of peer-reviewed publications from different authors. The common thread is that they all deal with music from a technical perspective. Some authors discuss mathematics, others physics, and some even discuss video games and how they relate to music. They are all trying to provide insight into an age-old question: What makes good music?

The intended audience for this book is people who have a working knowledge of music theory, can read sheet music, and also have a college-level background in mathematics. Others may still find certain sections of this book to be accessible.

The book is organized into five parts, each part containing three papers. The parts are named as follows:

(1) “Mathemusical Engagement”;

(2) “Mathemusical Creativity”;

(3) “Shaping Performance”;

(4) “Educating the Mathemusical”; and

(5) “Geometries.”

The first paper, “Without Our Consent,” explores the connections between famous pieces in classical music and mathematical patterns, asserting that there is beauty and elegance in both. For example, a proof is offered that Beethoven used Fibonacci series in his first piano sonata.

The next paper, “Approaches to Musical Expression in Harmonix Video Games,” is a short autobiography of the founders of the Harmonix video game company. This company is famous for musical video games such as Guitar Hero and Rock Band. They discuss all of their commercial software and its evolution over the years, explaining how their goal has always been to give the user the joy of playing music without the training that is typically required. There is an in-depth discussion of their various software constructs for allowing musical interaction and expression via controls that are perhaps more intuitive and forgiving than actual musical instruments.

The third paper in the first part, “Motion and Gravitation in the Musical Spheres,” explores the relationship between physics and musical compositions. It asserts that some pieces relate to the physical world, giving sensations of teetering on an edge, falling over the edge, moving swiftly through a crowded space, and more. It explores the relationship between certain patterns of notes and the laws of physics, mostly the universal law of gravitation.

A common theme throughout this first part is the idea that good music sets up expectations, and sometimes satisfies them, but other times goes in a different direction and does something unexpected. This is posited as a core component of good music.

Part 2, “Mathemusical Creativity,” explores the fairly modern practice of incorporating complex algorithms at a conscious level by the musical composer, either through the use of mathematics or, more commonly, through the application of mathematics in a computerized system. It introduces the notion of artificial creativity, which is the use of a computerized system to be creative, and how it can be used to augment human creativity. There can also be a learning aspect in which the computer learns from the human via machine learning, and the human might also learn from the computer, thus forming a natural and artificial collaborative approach to the creation of music.

Part 3, “Shaping Performance,” deals with analyzing live performance in a technical way with the assistance of computers. Some musical properties that can be analyzed include the appearance and number of musical patterns, changes in tempo, changes in dynamics, changes in key or time signature, and more. The hope is to find patterns or formulas that are in music in order to be able to categorize music, but more importantly to find those patterns or formulas that seem to make good music so that they can be applied to new compositions and performances.

Part 4, “Educating the Mathemusical,” offers a more detailed background of some of the technical terms used to describe different aspects of sound and music such as musical acoustics, tone, string vibration, and more. It also presents new ways of scientifically classifying and explaining aspects of musical performance such as “Tempo and Dynamic Analysis” and “Deep Integration Between Musical and Mathematical Thought.”

The final part, “Geometries,” offers a discussion of geometrical models that can be used to describe various aspects of music, such as pitch and time. It discusses the history of these concepts and modern tools for visualizing and utilizing these models.

In conclusion, this book is a wonderful achievement in exploring the intersection of musical and technical thought. It is geared toward an audience that is highly educated in both music and mathematics, but there are portions of the book that anyone with an interest in this space would find beneficial and fascinating.