Physics of the Piano

Why does a piano sound like a piano? A similar question can be asked of virtually all musical instruments. A particular note - such as middle C - can be produced by a piano, a violin, a clarinet, and many other instruments, yet it is easy for even a musically untrained listener to distinguish between these different instruments. A central quest in the study of musical instruments is to understand why the sound of the "same" note depends greatly on the instrument, and to elucidate which aspects of an instrument are most critical in producing the musical tones characteristic of the instrument. The primary goal of Physics of the Piano is to investigate these questions for the piano. The explanations in this book use a minimum of mathematics, and are intended for anyone who is interested in music and musical instruments. At the same time, there are many insights relating physics and the piano that will likely be interesting and perhaps surprising for many physicists.

Nicholas J. Giordano, Sr. is Hubert James Distinguished Professor of Physics at Purdue University, Indiana. He joined the Department of Physics there as an Assistant Professor in 1979, becoming an Associate Professor in 1982 and Full Professor in 1985. He served as an Assistant Dean of Science from 2000-2003, and became Head of the Department of Physics in 2007. His research includes nanoscience and conduction in small metallic systems, micro- and nanofluidic systems, musical acoustics, and computational biophysics. He was an Alfred P. Sloan Foundation Fellow (1979-1983), received a Computational Science Education Award from the U.S. Department of Energy in 1977, and was named Indiana Professor of the Year by the Carnegie Foundation for the Advancement of Teaching in 2004.

Introduction	p. 1
The goals of this book	p. 1
What exactly is a piano?	p. 3
The way a physicist thinks	p. 5
Organization of this book	p. 6
A brief introduction to waves and sound	p. 9
What is a wave?	p. 9
Sound as a wave	p. 10
The spectrum of a sound	p. 12
Spectrum of a real musical tone	p. 14
Pitch	p. 17
How the ear detects sound	p. 19
Combining two waves: Beats	p. 20
Making a musical scale	p. 23
It all starts with the octave	p. 23
Using a logarithmic scale for frequency and pitch	p. 25
Pythagoras and the importance of musical intervals	p. 26
Constructing a musical scale	p. 28
Measuring the distance between notes: Cents	p. 33
Why the piano was invented: A little history	p. 35
The harpsichord	p. 35
The clavichord	p. 38
Hitting strings with hammers: The pantaleon	p. 41
The invention of the piano	p. 42
Acceptance of the piano	p. 44
The evolutionary road ahead	p. 45
Making music with a vibrating string	p. 47
The ideal string and some of its properties	p. 47
Standing waves	p. 50
The shape of a grand piano	p. 52
Designing the strings	p. 53
Waves on real strings: The effect of string stiffness	p. 57
Real strings: What have we learned and where do we go next?	p. 62
Hitting strings with hammers	p. 65
What happens when a hammer hits a string?	p. 65
The design of piano hammers	p. 66
The hammer-string collision and the importance of contact time	p. 69
The hammer-string collision and the importance of nonlinearity	p. 73
Where should the hammer hit the string?	p. 76
Longitudinal string vibrations	p. 79
Holding the string in place: The agraffe and capo tasto bar	p. 80
Connecting the key to the hammer: Design of the piano action	p. 81
The Viennese action: An example of an evolutionary dead end	p. 85
The soundboard: Turning string vibrations into sound	p. 89
Design of the soundboard	p. 89
Vibration of the soundboard	p. 92
The soundboard as a speaker	p. 98
The rest of the piano: Contributions of the rim, lid, and plate	p. 103
Connecting the strings to the soundboard	p. 105
Decay of a piano tone	p. 105
Damping of a piano tone part 1: Motion of a single string and the effect of polarization	p. 107
Damping of a piano tone part 2: How the strings act on each other through the bridge	p. 110
Making sound from longitudinal string motion	p. 113
Motion of the bridge and its effect on the frequencies of string partials	p. 113
Evolution of the piano	p. 115
In the beginning: Key features of the first pianos	p. 115
Why did the piano need to evolve?	p. 117
The piano industry on the move	p. 119
The industrial revolution and its impact on the piano	p. 121
The shape of a piano: Fitting everything into the case	p. 123
On the nature of evolutionary change	p. 124
Psychoacoustics: How we perceive musical tones	p. 127
Physics and human senses: The difficulties in putting them together	p. 127
Hermann von Helmholtz and his long shadow	p. 128
Range of human hearing and the range of a piano	p. 129
Pitch perception and the missing fundamental	p. 130
Consonance and dissonance of musical tones: Implications for piano design	p. 133
The magic of Steinway	p. 137
The piano in our culture	p. 137
The Steinway family and the rise of the company	p. 139
Steinway and Sons' role in the development of the piano	p. 141
Marketing and the Steinway legend	p. 145
Rise and fall of the family business	p. 146
The Steinway brand today	p. 148
Why is a Steinway piano special?	p. 149
What physics can and cannot teach us about pianos	p. 151
Physics lessons	p. 151
Perceptual lessons	p. 152
The evolutionary future of the piano	p. 153
Finding the right piano	p. 155
Definitions of common terms	p. 157
References	p. 163
Index	p. 169
Table of Contents provided by Ingram. All Rights Reserved.

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