The Flute and its Mechanics
By: Kevin Bellows
December 12, 2011
Kevin Bellows is studying electrical engineering at the University of
Southern California. After completing his Bachelor of Science degree,
he plans to continue at USC to earn his master’s degree.
Author’s contact information:
25677 Paseo Lauro Court
Valencia, CA 91355
(661) 645-8909
kbellows@usc.edu
ABSTRACT: The flute’s origins date back 35,000 years to instruments made of bone.
While the design, fabrication, and, of course, materials of the flute have evolved since that
time, the instrument has had immense staying power. Through its vast overhaul in the
nineteenth century by Theobald Boehm, it became a much more intelligently engineered
instrument. The science behind how tones are produced on the instrument is discussed in
this article, as is the importance of the flute family at large.
Key words: flute, Boehm, resonance.
Origins
Music—the universal language. It’s something that has been ingrained into our lives for tens of
thousands of years, dating back to our prehistoric ancestors. In 2009, an archaeology group in
Germany dug up a flute made of bone dated over 35,000 years old [1]. One year earlier, the same
archaeology group found pieces of ivory flutes [1]. These ancient flutes are the oldest that are
currently known to humankind, with the bone flute holding the individual record [1].
Figure 1: Ancient flute dating back 35,000 years [2].
To this day, the flute is a very popular wind instrument. Though many types of flutes exist
throughout the world, the most prevalent in Western music is the transverse Boehm flute. This
type of flute, which is popular in bands and orchestras, is typically made from silver due to the
material’s combination of enjoyable tone quality and affordability. Gold and platinum are also
sometimes the main basis of a flute, although the acoustical qualities of silver allow it to be
played in a more musically nuanced manner [3]. This typical type of flute, called the transverse
flute, is held horizontally with the player’s arms extended to the right side of his or her body.
Anatomy of the Flute
The flute has undergone an extensive transformation from its ancient bone ancestor through the
present day. Theobald Boehm, a nineteenth-century flutist, is credited with developing the basis
for the current design. In 1831, Boehm wrote the following in reference to the flutes played by
his contemporaries (example shown below): “There is no doubt that many artists have carried
perfection to its last limits on the old flute, but there are also unavoidable difficulties, originating
in the construction of these flutes, which can neither be conquered by talent nor by the most
persevering practice” [4].
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Figure 2(a): A flute, c. 1827, made before
Boehm began his modifications to the flute
[4]. The labels indicate the function of each
tone hole. Some tone holes were normally
open and were covered directly by the
fingers, while others were normally closed
and were opened by pressing upon a lever
mechanism.
Figure 2(b): Default finger positions on the
modern flute, which has sixteen tone holes
controlled by eight fingers and one thumb.
The left thumb rests on a key on the side of
the flute, whereas this is a view of the top.
The right thumb never activates any key.
Basic photo of flute from [5].
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Those older flutes were designed primarily for ease of playing—the keys were spaced and sized
such that the fingers could seal the holes without trouble—rather than for the best possible sound
[4]. Considering this sound problem to be unfixable in the old design, Boehm set out to revamp
the entire system to allow for a superior sound. For example, he increased the size of the tone
holes [4]. Their enlarged size meant that the fingers could no longer cover them directly, so he
placed a mechanism of keys over the holes which, when depressed, would seal them [4]. Keys
also became necessary because after Boehm’s changes to the space between each tone hole, the
key mechanism allowed the musician to close certain out-of-reach holes, as depicted below [4].
Figure 3: The two keys indicated on this modern flute act together. The musician’s finger is able
to easily reach the key on the left, but the tone hole is placed underneath the key on the right for
optimal sound. Through a mechanical connection in the mechanism of the instrument, the player
depresses the key on the left in order to close the hole on the right.
The Flute as a Resonator
Let’s take a look at an analogy to better understand intuitively what happens to the air column
inside a flute. Consider a young child in a playground being pushed in a swing [6]. Everyday
experience will tell the adult doing the pushing to apply force to the swing at a particular time.
The adult would not push when the swing is at the center of a forward arc nor when the swing is
currently traveling backward. The adult would push at the specific moment when the swing has
reached its peak height after completing a backward arc. This is the time when a force applied
will generate the greatest forward speed. Depending on the length of the cable connecting the
seat to the suspension bar, the time taken to complete an arc will change [6]. Thus, the time in
between each push by the adult (and, thus, the frequency of pushing) will vary accordingly.
Figure 4: The most logical time to push a swing is when it is at the end of a backward arc [6].
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A similar phenomenon occurs inside a flute. When a flutist’s breath causes the air inside a flute
to vibrate at a particularly effective frequency, known as a resonant frequency, the wave created
undergoes a large increase in amplitude, or volume, analogous to the height achieved by the
child’s swing [7]. This increase in amplitude is what causes a particular pitch to be heard. A
particular frequency corresponds to a particular pitch interpreted by the ear, so each note played
on the flute is generated by a different resonant frequency.
A flute produces the desired notes as a result of the interaction between the musician’s air stream
and the column of air inside the flute [8]. This interaction leads to oscillations at the particular
frequencies where the air column has the least resistance to vibration [8]. The frequencies at
which these minimum resistances occur—the resonant frequencies—are determined by the
length of the instrument, similar to how the length of the cable determines the optimum pushing
frequency for a swing. A change in pitch is caused by changing the fingering, or the combination
of tone holes that are closed, since this changes the effective endpoint of the instrument.
On the flute, many fingerings can produce more than one pitch each, however. This means that
each fingering must correspond to more than one resonant frequency. The player can produce
various pitches with a single fingering by changing the manner in which the air is blown, namely
by changing the blowing pressure and the air jet length [8]. A note is played most easily when
the time for the air to travel across the embouchure hole, the hole which is blown across, is about
half the time it takes for the wave inside the flute to complete one cycle of oscillation [8]. Thus,
to prevent a particular pitch from sounding, the time taken for the air to travel across the
embouchure hole can be dropped below this threshold [8].
Figure 5: The head joint of a flute. The lips rest against the metal, and air is blown out of the
mouth and across the hole, as indicated by the yellow arrow.
In order to decrease the time for the air stream to cross the embouchure hole, the musician has
two options: move the position of the lips forward closer to the far end of the hole to decrease the
jet length, or use greater blowing pressure to speed up the air [8]. This decrease in distance
traveled or increase in speed of air will shorten the time taken for the air to cross the embouchure
hole. As a result, the first (lowest) resonant frequency will be skipped over, and a note will be
produced at the next highest resonant frequency. The note produced at this higher resonant
frequency is known as the second harmonic. By varying the degree to which the musician
changes the air stream, he or she can play a third or fourth harmonic instead. By varying the
fingerings and the way the air stream is blown, a flutist can play over a range of more than three
octaves.
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The Flute Family
While the flute, also referred to as the concert flute, is the main member of the flute family, there
are many other members, some of which can be seen in the image below. For example, the
piccolo is a smaller version of the flute that sounds one octave higher than the flute. The larger
the instrument, the lower the pitch, so the instruments that are much larger than the flute play
pitches that are quite low. The fingerings are the same for each member of the flute family, but
the player’s mouth must adjust to each instrument individually due to the difference in size. This
size difference is found in the embouchure hole, in the diameter of the instrument, and in the
length of the instrument. The larger the diameter and length, the more air required by the
musician. Playing a bass flute, for example, requires a much heavier use of air than playing a
concert flute. Additionally, playing on a larger instrument with a larger embouchure hole
requires a looser, more open formation of the lips in order to produce a sound.
Figure 6: A selection of members of the flute family. From top to bottom: bass flute, alto flute,
concert flute with B foot, concert flute with C foot (which we’ve been focusing on), E-flat flute,
piccolo. [9]
The flute and piccolo are by far the most widely-used members of the flute family today, but the
other members are used in certain instances, such as in musical compositions for flute choir.
There are some pieces that are composed for multiple flutists without any additional
accompaniment, and oftentimes these pieces will require multiple concert flutes and, for
example, a single alto flute.
The flute family has come a long way in 35,000 years, and it has managed to maintain its
importance in the world of music. With its uniquely rich, brilliant tone quality and its key
mechanism facilitating flourishes of notes in impressively fast succession, the flute family
maintains the ability to be played in a delicate fashion or in a much more commanding one. Due
to its magnificent sound, the flute family has earned a spot as a melodic staple in bands and
orchestras across the world.
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[1] A. Reynolds. (2010, January/February). “Top 100 stories of 2009.” Discover. [Online].
Available: http://www.discovermagazine.com/2010/jan-feb/051 [Oct. 11, 2011].
[2] H. Jensen. “World’s oldest flute shows first Europeans were a musical bunch.” Discover.
[Online]. Available: http://blogs.discovermagazine.com/80beats/2009/06/24/worlds-oldestflute-shows-first-europeans-were-a-musical-bunch/ [Oct. 11, 2011].
[3] P. Bate. “Materials and manufacture,” in The Flute: A Study of its History, Development and
Construction, 1st ed. London: Ernest Benn Ltd., 1969, ch.12, p. 201.
[4] N. Toff. “A brief history of the flute,” in The Flute Book, 2nd ed. New York: Oxford, 1996,
ch. 4, pp. 48-55.
[5] (2011, January 25). Why I started this blog. [Online]. Available:
http://www.practicemusicright.com/2011/01/25/why-i-started-this-blog/
[6] T. D. Rossing. “Resonance,” in The Science of Sound, 1st ed. Reading: Addison-Wesley,
1983, ch. 4, p. 49.
[7] D. Kleppner and R. J. Kolenkow. “The harmonic oscillator,” in An Introduction to
Mechanics, 1st ed. Boston: McGraw-Hill, 1973, ch. 10, sec. 3, p. 423.
[8] T. D. Rossing. “Woodwind instruments” in The Science of Sound, 1st ed. Reading: AddisonWesley, 1983, ch. 12, sec. 9, p. 227.
[9] (2007, November 24). Instruments of the orchestra [Online]. Available: http://wolfswiki.
pbworks.com/w/page-revisions/12430902/Instruments%20of%20the%20Orchestra
[10] M. Chasin and D. Hayes. (2010 March). “Music for the Hearing Care Professional: Relating
Musical Principles to Audiological Principles.” The Hearing Review. [Online]. 17(3), pp.
20-25. Available: www.gale.cengage.com [Oct. 11, 2011].
[11] J. Wolfe. Open vs closed pipes (flutes vs clarinets) [Online]. Available: http://www.phys.
unsw.edu.au/jw/flutes.v.clarinets.html
[12] I. Cossette, et al. (2010, July/August). “From Breath to Sound: Linking Respiratory
Mechanics to Aeroacoustic Sound Production in Flutes.” Acta Acustica United with
Acustica. [Online]. 96(4), pp. 654-67. Available: www.ingentaconnect.com [Oct. 11, 2011].
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Multimedia ideas:
-Clip on YouTube taken from the Discovery Channel: “How It’s Made – Flute” (URL:
http://www.youtube.com/watch?v=DHSu0trGkRg) to supplement “Anatomy of the Flute.”
-Video of how each finger controls the keys on the flute to supplement or replace figure 3.
-Video of a flute choir, including various members of the flute family to supplement the final
section (“The Flute Family”).
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