Chapter 1. Introduction: “Is that a real subject?”
Chapter 2. Underpinnings I: Good vibrations
2.1.1 Linearity and sine waves
2.2 Frequency analysis and modes
2.2.1 Fourier series
2.2.2 The undamped harmonic oscillator
2.2.3 Linearity for small vibration
2.2.4 Degenerate modes of a drum
2.2.5 Vibration frequency response
2.2.6 Frequency spectrum of a hammer tap
2.2.7 Vibration damping
Chapter 3. When does a structure become a musical instrument?
3.1 Harmonics and non-harmonics
3.1.1 Vibration of an ideal stretched string
3.2 Building blocks: beams, plates and shells
3.2.1 Bending beams and free-free modes
3.2.2 Synthesising percussion sounds
3.2.3 Plate vibration
3.2.4 The modal density of a vibrating plate
3.2.5 Rayleigh’s principle
3.3.1 Rayleigh’s principle and tuning a marimba bar
3.4 Church bells
3.5 Steel pans and the musical saw
3.5.1 Time-average holography
3.5.2 Waveguide reflection: the beam on an elastic foundation
3.6 Tuned drums
3.6.1 Vibration modes of a circular drum
UNDER CONSTRUCTION…
Chapter 5 Strings, mainly plucked
5.1 Stringed instrument overview
5.1.1 Averaging and the coherence function
5.1.2 Coupling a string to the instrument body
5.3 Signature modes and formants
5.3.1 The bridge hill: a resonator near the driving point
5.3.2 Skudrzyk’s method
5.4 Synthesising plucked string sounds
5.4.1 Motion of a plucked string as a modal sum
5.4.2 Waves on a string: d’Alembert’s solution
5.4.3 Natural frequencies of a stiff string
5.4.4 Energy loss in a string: internal damping
5.4.5 Energy loss in a string: air damping
5.4.6 Frequency responses for string synthesis
5.5 An extreme case: the banjo
5.5.1 The “square banjo” model