Koenig D.M., Fandrich D.D. Spectral Analysis of Musical Sounds with Emphasis on the Piano

Oxford University Press, 2015. — 395 p.This book addresses the analysis of musical sounds from the viewpoint of someone at the intersection between physicists, engineers, piano technicians, and musicians.
The study is structured into three parts. The reader is introduced to a variety of waves and a variety of ways of presenting, visualizing, and analyzing them in the first part. A tutorial on the tools used throughout the book accompanies this introduction. The mathematics behind the tools is left to the appendices. Part Two provides a graphical survey of the classical areas of acoustics that pertain to musical instruments: vibrating strings, bars, membranes, and plates. Part Three is devoted almost exclusively to the piano. Several two- and three-dimensional graphical tools are introduced to study various characteristics of pianos: individual notes and interactions among them, the missing fundamental, inharmonicity, tuning visualization, the different distribution of harmonic power for the various zones of the piano keyboard, and potential uses for quality control. These techniques are also briefly applied to other musical instruments studied in earlier parts of the book.Part 1 Some Basic Sound Waves and Some Simple Tools
An Introduction to Some Elementary Waves
The Basic Tools of Spectral Analysis
Analysis of Several Common Musical Sounds
Harmonics in Musical Sounds
Part 2 A Visual Analysis of Vibrating Objects (Strings, Membranes, Bars, Plates)
The Vibrating String
The Vibrating Bar
The Vibrating Membrane
The Vibrating Plate
Part 3 The Piano
An Introduction to Pianos
Some Individual Piano Notes and Their Interactions
The Missing Fundamental
Octave Stretching, Inharmonicity, and the Railsback Curve
Beating, Unisons, and Tuning
Two-Dimensional Graphical Metrics
Three-Dimensional Graphical Metrics
An Investigation into Hammer Knock and Key Striking
Evaluation of a Wapin Bridge Conversion
Similarities between Pianos and Repeatability of Data-Gathering Methods
Two Metrics Applied to Other Instruments
Use of the Metrics in Production and Development
Defining and Understanding Piano Tone