Flute acoustics: measurement, modelling and design - School of ...

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Chapter I
Introduction
The world will never starve for want of wonders; but only for want of wonder.
G. K. Chesterton
1.1 INTRODUCTION TO FLUTE ACOUSTICS
Music and musical instruments have long fascinated physicists and philosophers. The simple
numerical basis of musical harmonies is a striking example of the concordance between mathematics
and aesthetics, and for many philosophers the mathematical theory of harmony has
served as a metaphor for the quantitative understanding of the universe. For Pythagoras (c. 6th
century BC) musical harmonies were the key to understanding the cosmos. The Pythagoreans
likened planetary orbits to huge strings on which the universe itself made a kind of music—
the ‘Harmony of the Spheres’. The orbits of each planet were related to those of its neighbours
by a simple musical interval. This concept, although superseded by modern cosmology, captured
the imagination of poets and scientists alike. The celestial music featured in the work of
Shakespeare, Milton and Donne:
The spheres have music, but they have no tongue,
Their harmony is rather danced than sung . . .
(Donne 1971, p. 333) and inspired Donne’s contemporary Kepler to devise his famous laws of
planetary motion (Koestler 1959). Musical analogies also feature in Bohr’s model of the atom
which led to modern quantum physics.
Quite apart from the influence of music in physics and philosophy, many scientists have
been interested in music and musical instruments in their own right.
In the 19th century
Helmholtz and Rayleigh laid the foundations of musical acoustics and psychoacoustics. Many
problems in musical acoustics are surprisingly complex and involve the interplay of physics,
culture and psychology. Some musical instruments are a direct creative development of a scientific
discovery—one thinks of the electric guitar and Faraday’s law—and instrument makers
have historically made active use of scientific and technological developments.
Most musical instruments are made with many different (and sometimes conflicting) goals
in mind. Instruments are usually required to play in tune over a wide range of pitches with
reasonable timbal uniformity over the range (although in some musical traditions notes with
different timbre are used for musical effect). In the case of the flute and other woodwind instruments
the several dozen notes playable on the instrument are made when the player covers
various holes in the instrument or operates various keys and the design of such instruments
is constrained by the necessity for a relatively simple, responsive fingering mechanism. Inevitably,
single holes on the instrument contribute to the production of more than one note,