on the art and
science of acoustic instruments
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Also available from the publisher at
Chronicle Books, San Francisco.
Cristiano M.L. Forster
All rights reserved.
I met Cris Forster more than thirty years ago. Shortly thereafter, I
saw him perform Song of Myself, his setting of Walt Whitman
poems from Leaves of Grass. His delivery was moving and
effective. Several of the poems were accompanied by his playing on
unique instruments — one an elegant box with many steel strings and
moveable bridges, a bit like a koto in concept; the other had a big
wheel with strings like spokes from offset hubs, and he rotated the
wheel as he played and intoned the poetry. I was fascinated.
that time, Cris has built several more instruments of his own design.
Each shows exquisite care in conception and impeccable craftsmanship
in execution. And of course, they are a delight to hear. Part of what
makes them sound so good is his deep understanding of how acoustic
musical instruments work, and part is due to his skill in working the
materials to his exacting standards.
another important aspect of their sound, and indeed one of the main
reasons Cris could not settle for standard instruments, is that his
music uses scales and harmonies that are not found in the standard
Western system of intonation (with each octave divided into twelve
equal semitones, called equal temperament). Rather, his music employs
older notions of consonance, which reach back as far as ancient Greek
music and to other cultures across the globe, based on what is called
just intonation. Here, the musical intervals that make up the scales
and chords are those that occur naturally in the harmonic series of
overtones, in stretched flexible strings, and in organ pipes, for
just intonation, the octave is necessarily divided into unequal parts.
In comparison to equal temperament, the harmonies of just intonation
have been described as smoother, sweeter, and/or more powerful. Many
theorists consider just intonation to be the standard of comparison
for consonant intervals. There has been a resurgence of interest in
just intonation since the latter part of the twentieth century,
spurred by such pioneers as Harry Partch and Lou Harrison. Even so,
the community of just intonation composers remains comparatively quite
small, and the subset of those who employ only acoustic instruments is
much smaller still. I know of no other living composer who has created
such a large and varied ensemble of high quality just intoned
acoustical instruments, and a body of music for them, as Cris Forster.
what he has done is not easy, far from it. The long process of
developing his instruments has required endless experimentation and
careful measurement, as well as intense study of the literature on
acoustics of musical instruments. In this way Cris has developed deep
and rich knowledge of how to design and build instruments that really
work. Also, in the service of his composing, Cris has studied the
history of intonation practices, not only in the Western tradition,
but around the world.
book is his generous offering of all that hard-earned knowledge,
presented as clearly as he can make it, for all of you who have an
interest in acoustic musical instrument design and/or musical scales
over time and space. The unifying theme is how mathematics applies to
music, in both the acoustics of resonant instruments and the analysis
of musical scales. The emphasis throughout is to show how to use these
mathematical tools, without requiring any background in higher
mathematics; all that is required is the ability to do arithmetic on a
pocket calculator, and to follow Cris’ clear step-by-step instructions
and examples. Any more advanced mathematical tools required, such as
logarithms, are carefully explained with many illustrative examples.
first part of the book contains practical information on how to design
and build musical instruments, starting from first principles of
vibrating sound sources of various kinds. The ideas are explained
clearly and thoroughly. Many beautiful figures have been carefully
conceived to illuminate the concepts. And when Cris gives, say,
formulas for designing flutes, it’s not just something he read in a
book somewhere (though he has carefully studied many books); rather,
you can be sure it is something he has tried out: he knows it works
from direct experience. While some of this information can be found
(albeit in a less accessible form) in other books on musical
acoustics, other information appears nowhere else. For example, Cris
developed a method for tuning the overtones of marimba bars that
results in a powerful, unique tone not found in commercial
instruments. Step-by-step instructions are given for applying this
technique (see Chapter 6). Another innovation is Cris’ introduction of
a new unit of mass, the “mica,” that greatly simplifies calculations
using lengths measured in inches. And throughout Cris gives careful
explanations, in terms of physical principles, that make sense based
on one’s physical intuition and experience.
latter part of the book surveys the development of musical notions of
consonance and scale construction. Chapter 10 traces Western ideas
about intonation, from Pythagoras finding number in harmony, through
“meantone” and then “well-temperament” in the time of J. S. Bach, up
to modern equal temperament. The changing notions of which intervals
were considered consonant when, and by whom, makes a fascinating
story. Chapter 11 looks at the largely independent (though sometimes
parallel) development of musical scales and tunings in various Eastern
cultures, including China, India, Indonesia, as well as Persian,
Arabian, and Turkish musical traditions. As far as possible, Cris
relies on original sources, to which he brings his own analysis and
explication. To find all of these varied scales compared and
contrasted in a single work is unique in my experience.
book concludes with two short chapters on specific original
instruments. One introduces the innovative instruments Cris has
designed and built for his music. Included are many details of
construction and materials, and also scores of his work that
demonstrate his notation for the instruments. The last chapter
encourages the reader (with explicit plans) to build a simple stringed
instrument (a “canon”) with completely adjustable tuning, to directly
explore the tunings discussed in the book. In this way, the reader can
follow in the tradition of Ptolemy, of learning about music through
direct experimentation, as has Cris Forster.
David R. Canright, Ph.D.
Del Rey Oaks, California