The textbook provides both profound technological knowledge and a comprehensive treatment of essential topics in music processing and music information retrieval (MIR). Including numerous examples, figures, and exercises, this book is suited for students, lecturers, and researchers working in audio engineering, signal processing, computer science, digital humanities, and musicology. The book consists of eight chapters. The first two cover foundations of music representations and the Fourier transform―concepts used throughout the book. Each of the subsequent chapters starts with a general description of a concrete music processing task and then discusses―in a mathematically rigorous way―essential techniques and algorithms applicable to a wide range of analysis, classification, and retrieval problems. By mixing theory and practice, the book’s goal is to offer detailed technological insights and a deep understanding of music processing applications. As a substantial extension, the textbook’s second edition introduces the FMP (fundamentals of music processing) notebooks, which provide additional audio-visual material and Python code examples that implement all computational approaches step by step. Using Jupyter notebooks and open-source web applications, the FMP notebooks yield an interactive framework that allows students to experiment with their music examples, explore the effect of parameter settings, and understand the computed results by suitable visualizations and sonifications. The FMP notebooks are available from the author’s institutional web page at the International Audio Laboratories Erlangen.
This is an excellent book that goes into a basic level of music theory and explores the math of the music analysis in great detail. It's an impressive collection of the equations that allow one to describe music using math. The really amazing part is the collection of jupyter notebooks that accompany the book (spoiler alert: you don't need to buy the book to access the notebooks). The authors have done an amazing job putting this all together.
OTOH, I have to admit, I'm hard pressed to understand who this book is for. It is a textbook and the target audience is for graduates and high level undergrads in math, but unless they're steeped in a lot of experience with synthesizer sound design, it is hard for me to get how they will be motivated to learn the material other than the necessity to get a good grade. At the same time, a musical practitioner with a decent math background (here I'm talking about me) isn't given sufficient musical motivation to work through the math. Do I really need to understand Hilbert spaces in order to understand what's going on? Maybe I do, but it's often not clear why.