1. Introduction. -- The goals of this book -- What exactly is a piano? -- The way a physicist thinks -- Organization of this book -- 1. A brief introduction to waves and sound. -- What is a wave? -- Sound as a wave -- The spectrum of sound -- Spectrum as a real musical tone -- Pitch -- How the ear detects sound -- Combining two waves: beats -- 3. Making a musical scale. -- It all starts with the octave -- Using a logarithmic scale of frequency and pitch -- Pythagorus and the importance of musical intervals -- Constructing a musical scale -- Measuring the distance between notes: Cents -- 4. Why the piano was invented: a little history. -- The harpsichord -- The clavichord -- Hitting strings with hammers: the pantaleon -- The invention of the piano -- Acceptance of the piano -- The evolutionary road ahead -- 5. Making music with a vibrating string. -- The ideal string and some of its properties -- Standing waves -- The shape of a grand piano -- Designing the strings -- Waves on real strings: the effect of string stiffness -- Real strings: what have we learned and where do we go next? -- 6. Hitting strings with hammers. -- What happens when a hammer hits a string? -- The design of piano hammers -- The hammer-string collision and the importance of contact time -- The hammer-string collision and the importance of non-linearity -- Where should the hammer hit the string? -- Longitudinal string vibrations -- Holding the string in place: the agraffe and capo tasto bar -- Connecting the key to the hammer: design of the piano action -- The Viennese action: an example of an evolutionary dead end -- 7. The soundboard: turning string vibrations into sound. -- Designing the soundboard -- Vibration of the soundboard -- The soundboard as speaker -- The rest of the piano: contributions of the rim, lid, and plate --

8. Connecting the strings to the soundboard. -- Decay of a piano tone -- Damping of a piano tone part 1: motion of a single string and the effect of polarization -- Damping of a piano tone part 2: how the strings act on each other through the bridge -- Making sound from longitudinal string motion -- Motion of the bridge and its effect on the frequencies of string partials -- 9. Evolution of the piano. -- In the beginning: key features of the first piano -- Why did the piano need to evolve? -- The piano industry on the move -- The industrial revolution and its impact on the piano -- The shape of a piano: fitting everything into the case -- On the nature of evolutionary change -- 10. Psychoacoustics: how we perceive musical tones. -- Physics and human senses: the difficulties in putting them together -- Hermann von Helmholtz and his long shadow -- Range of human hearing and the range of a piano -- Pitch perception and the missing fundamental -- Consonance and dissonance of musical tones: implications for piano design -- 11. The magic of Steinway. -- The piano in our culture -- The Steinway family and the rise of the company -- Steinway and Sons' role in the development of the piano -- Marketing and the Steinway legend -- Rise and fall of the family business -- The Steinway brand today -- Why is a Steinway piano so special? -- 12. What physics can and cannot teach us about pianos. -- Physics lesson -- Perceptual lessons -- The evolutionary future of the piano -- Finding the right piano -- Definitions of common terms.