NOTE: all the flute sound samples were performed by Comaci Boschi on 26/10/2007. Sound engineer: Valerio Carboni.

Structure of the instrument

The modern flute is the transverse flute: it consists of two cylindrical sections of metal tube joined by a short conical section. The sections fit into one another and together form a tube about 65 cm long. The total length of the tube can be changed slightly by pulling the head joint out of, or pushing it further into, the body of the instrument, so that it can be tuned.

Flute	"exploded" view	keys

part 1	part 2	part 3

The first cylindrical section, closed at one end, has on its side the embouchure with the air inlet hole. The conical section connects the first part to the second cylindrical section, which is longer and has a slightly larger diameter. The second cylindrical section, open at its end, carries the tone holes. On the outside of this section a system of levers and valves is used to open and close the holes.

How the sound is produced

• As in all wind instruments, the sound is produced by turning a steady air flow generated by the player's breath into an oscillating flow, and by amplifying the pressure wave thus produced through the resonance of the body of the instrument. The pressure that the player must build up in the mouth for the sound to start exceeds atmospheric pressure by about 1% (about 1 kPa). Higher notes require the jet to oscillate between inside and outside more often. The player achieves this by tightening the lips and adjusting their position relative to the embouchure (that is, by changing the angle at which the air flow strikes the edge of the embouchure).
• The way in which the steady flow is "broken" and made to oscillate differs from that used in other instruments such as the clarinet and the oboe, because it does not use a reed. The flow is in fact directed towards an edge of the embouchure, much as one does when "playing" an empty bottle. However, while in the case of the bottle the main resonance is the Helmholtz resonance of the (empty part of the) bottle, in the flute the resonance is that of a cylindrical pipe, whose effective length at any given moment depends on which holes are closed and which are open. Once the base frequency is fixed, determined by the overall length of the pipe, all the notes of the equal-tempered scale can be produced by operating the keys so as to close the holes.

The source of the oscillations

Schematically, the formation of sound in the flute can be summarised in the following stages.

1. The steady air flow produced by the player, channelled into the embouchure, breaks against a sharp edge. A particular hydrodynamic phenomenon governs the motion of the fluid, which, instead of splitting into equal parts, typically oscillates, passing alternately from one side to the other. Every time the flow is directed into the instrument it produces a pressure pulse above atmospheric pressure, while every time it is directed outwards it produces a rarefaction.
2. The train of successive compressions and rarefactions at regular intervals forms a pressure wave in the air contained in the instrument, that is, a progressive sound wave, which travels along the tube and is reflected at its ends.
3. Acoustically, the flute behaves like a tube open at both ends (for details see the next section)
4. The very hole that splits the air flow acts as the main radiator of the sound, coupling the oscillations of the air inside the resonance tube with the surrounding air. Only part of the energy coming from the player is actually radiated as sound from the tone holes and the end opening; much more is dissipated, because of hydrodynamic friction, during the many reflections undergone by the standing waves inside the tube.

Tuning and resonances

• The air column in which standing waves are set up inside the flute is an example of a one-dimensional system; the physics of this system is in many ways analogous to that of the strings of string instruments, and is illustrated in detail in the pages: natural frequencies of pipes, normal modes of a string, reflection in strings.
• In the flute, as in the other woodwinds, the effective length of the air column, and therefore the pitch of the note produced, is controlled by the player by closing the appropriate holes. Clearly the effective length of the pipe can only be shortened starting from the total length of the instrument. The lowest note that can be produced is C₄ (261.6 Hz).
• The most elementary way of obtaining a pipe length shorter than the overall length of the instrument is to close all the holes starting from the one nearest the embouchure up to a certain point, and leave all the following ones open. In this way, the first open hole corresponds roughly to the effective length of the pipe. To a first approximation, in fact, the first open hole forms a "short circuit" with the outside air, that is, a point where the pressure wave is reflected as it would be at an open end. At the hole the air is practically "free", and its pressure is always equal to atmospheric pressure.
• More correctly, however, using the electroacoustic analogy, we should say that the hole is an element of very low inductance. That is, it actually behaves as a short circuit only at low frequencies, while at high frequencies its response is more complex.
• This complex behaviour can be seen by observing that the sequence of several open holes in the flute (as in the other woodwinds) has the properties of a high-pass filter. When the musician uses fingerings with many consecutive open holes, the instrument tends to attenuate frequencies roughly above 2000 Hz. To explore this behaviour interactively, follow the instructions on the page experiments on sound tubes.
• In the modern instrument the holes are spaced so as to reflect the intervals of the equal-tempered scale; however, small deviations from the "preset" tones can be obtained by changing the incoming air flow, for example by tightening the lips, or by changing the angle of attack at the embouchure.

The chromatic scale contains 12 tones, while the flautist uses only 9 fingers (the right thumb is used to hold the instrument). How is it possible to produce all the notes?

The solution lies in the complex system of levers housed on the outside of the instrument. Its function is precisely to allow a single finger to operate several holes at the same time.

How the timbre is formed

The flute normally plays by exciting the fundamental resonance of the air column contained between the embouchure hole and the last open hole along the pipe. The sound is rather pure, and excites only a few other normal modes of the air column, corresponding to the first higher harmonics of the fundamental.

There are two different exceptions to this situation, for completely different reasons:

1. when one of the register holes is used: in this case the timbre changes because some series of harmonics are suppressed (see the example at the end of the previous section)
2. when playing very loudly: in this case the system does not respond linearly, and non-harmonic components may appear in the spectrum, that is, frequencies that are not integer multiples of the fundamental. Anharmonic effects are common to all sound tubes, and are due to the fact that real tubes deviate from the ideal conditions listed on the page natural frequencies of pipes. In particular, for example:
   1. they are not exactly one-dimensional: they have a finite diameter (this effect becomes more noticeable the higher the resonance frequency excited)
   2. their cross-section is not exactly uniform (in general they consist of several sections with small differences in geometry)

Acoustic characteristics

Excerpts of live performance

A short passage from Syrinx by C. Debussy was recorded in an almost reverberation-free room by a microphone very close to the instrument. The sample faithfully corresponds to what is heard at a short distance from the instrument, but does not reproduce the listening conditions in a concert hall. The sound is very faithful to the original, but very "dry". The right and left channels are identical copies of the same signal.

waveform	spectrogram	Audio
		FL_SampleDry.mp3 Flute: from "Syrinx" by C. Debussy ("dry" version)

An elementary electronic manipulation of the sample consists in introducing dynamic compression of the sound, that is, automatically reducing the difference between the loudest and the softest sounds, so as to even out its dynamics. Note that the right and left channels now show small differences. The net effect is to introduce a "virtual listening environment", which simulates a slightly reverberant real room and therefore reproduces more faithfully the sound one would hear in a concert hall. The sound seems richer overall, although all the pitches and note durations are unchanged with respect to the "dry" sample.

waveform	spectrogram	Audio
		FL_SAMPLE.mp3 Flute: from "Syrinx" by C. Debussy (version with dynamic compression)

Intonation

Intonation, that is, the production of sounds of definite pitch corresponding to the notes of a scale, is achieved in the flute mainly by changing the effective length of the resonating pipe by means of the keys. The lowest note that can be played is determined by the maximum length of the pipe, obtained by closing all the holes, and corresponds to C₄ at about 262 Hz. Progressively opening the holes "short-circuits" the air inside the pipe with the air outside. However, the strength of the breath, the tension of the lips and the angle at which the air flow strikes the embouchure also play an important role in the fine adjustment of the pitch.

waveform	spectrogram	Audio
		FL_Labbra.mp3 In this example the pitch is slightly modulated by changing the position of the lips, but not the position of the fingers

Harmonics and resonances

The main resonance of the flute corresponds to the fundamental mode of its pipe (the mode whose wavelength is twice the effective length of the pipe). However, by varying the air flow into the instrument, the player can also excite the higher modes. These correspond to the series of harmonics of the fundamental note. Note that the component with the most energy (lighter colour) at the n-th step corresponds to the n-th harmonic of the fundamental note. The last harmonic is so close in frequency to the next one that both are excited at the same time.

waveform	sonogram	Audio
		FL_Armonici.mp3 Natural harmonics on the flute

A curious way to perceive the instrument's own resonance is... not to play it. Simply by operating the keys that close the holes, one can hear a "pitched noise" in a descending scale. What happens is that the small impact between the key and the pipe is enough to transmit a pulse to the air inside it. The impact produces an almost white noise of very short duration (corresponding to an impulsive excitation). The pipe does the rest, selecting and amplifying the frequencies corresponding to its own resonance.

In the diagrams below the taps are evident: in the time domain they appear as small cusps, while in the frequency domain they appear as horizontal lines. However, by amplifying the signal, increasing its frequency resolution and raising the visibility threshold, another spectrum is obtained that clearly shows the presence of weak peaks in a harmonic sequence.

waveform	Audio
	FL_Tasti.mp3 Flute: noise for different pipe lengths
sonogram	highlighted sonogram

The attack of the sound

As with many other instruments, in the flute the control over the sound lasts for the whole duration of the note. This means in particular that the same note can take on ever-changing characteristics over time. In the simple example given here we tried to vary only one characteristic, leaving all the others almost unchanged. The same note is played with the same intensity, first with a very short attack time, then with a longer one. The attack time, we recall, is the time in which a sound passes from the transient regime to a steady state, and it depends partly on the type of external excitation and partly on the time constant of the instrument itself. The graph as a function of time shows that in the first case the sound reaches steady state in less than about 0.1 s, while in the second it takes almost 0.5 s.

waveform	spectrogram	Audio
		FL_Attacco.mp3 Flute: hard attack, soft attack

Special effects

Flutter-tonguing is an effect obtained by pronouncing the letter "r" while playing. The result is a rapid amplitude modulation, with a variation of about 2 dB at a frequency of about 25 Hz (that is, about 4 hundredths of a second pass between two consecutive maxima), compared with the roughly 830 Hz of the note played (a G#₅).

waveform	spectrogram	Audio
		FL_Frullo.mp3 Flute: flutter-tonguing

Different registers

The sonogram analysis makes it clear that the spacing of the harmonics doubles at each octave. It is less easy to tell whether the three Cs are simply the same sound with harmonics of double frequency, or whether they are completely different sounds. To decide this we computed the time-averaged spectrum of each note, and then divided by 2 and by 4 the frequencies of the two higher Cs; the amplitude of the fundamental was also normalised, so that the three spectra can be compared on the same scale. It is clear that the harmonics decay faster the higher the fundamental. On reflection, it is surprising that the human ear recognises that the three sounds are produced by the same instrument.

waveform	spectrogram
	FL_Ottave.mp3 Flute: C in three different octaves
sonogram	normalised spectra

Vibrato

In this sample you can hear the difference between the sound without and with vibrato. The diagrams make it clear that this is a simultaneous modulation of amplitude and frequency. The amplitude modulation is more perceptible and, as can be seen from the waveform diagram, spans a range of about 3 dB at a frequency of about 6 Hz. In the sonogram the frequency modulation is evident above all in the higher harmonics. The fundamental oscillates by about 26 Hz at the same frequency as the amplitude modulation.

waveform	spectrogram	Audio
		FL_Vibrato.mp3 Flute: sustained note without and with vibrato

Musical features

Introduction

We all know the timbre of the flute and its traditional use in classical and popular music; recently, however, research into the technical possibilities of the instrument has pushed into hitherto unexplored territory. Examples of this are the very personal interpretation of J. S. Bach's Bourrée by Jethro Tull and the innovative approach to the instrument of the contemporary composer S. Sciarrino, who has dedicated an entire cycle of works to the flute.

The Jethro Tull approach

Jethro Tull revisit Bach's piece in a jazz style, adding pizzicati, staccati, tongue strokes, flutter-tonguing, coughs, and even playing while singing into the instrument (which thus becomes a kind of resonating body for the voice).

Salvatore Sciarrino's research and the "window form"

S. Sciarrino, from Come vengono prodotti gli incantesimi

Far from the improvisational attitude of the Jethro Tull flautist (the Scot Ian Anderson), Sciarrino instead integrates this new articulatory vocabulary into a completely different linguistic context. The composer himself coined the term "window form" (“forma a finestre”) to better frame the organising principle of many of his compositions; this principle consists in characterising a musical gesture with extreme clarity and then switching suddenly to another, equally well-characterised gesture, like a cut in a film, and the game is based on the discontinuous and surprising alternation of two or more musical "characters". Naturally the "cut" comes when you least expect it, perfectly in tune with a contemporary logic (think of zapping with the remote control, which opens windows onto even very distant dimensions of space and time, or of the windowed graphical interface of modern PCs, based on the same principle). In Canzona di ringraziamento Sciarrino alternates a particular articulation obtained with key tremolos with another based on high harmonics, while in Come vengono prodotti gli incantesimi the jet-whistle (a violent sweep of harmonics) "cuts", alternates with and finally replaces an ostinato of tongue-ram (tongue strokes). As well as being interesting from a formal point of view, Sciarrino's research is perhaps even more so from the point of view of timbre, inventing instrumental gestures so meaningful that they evoke strange creatures, wild beasts, the insistent chirping of cicadas and many other situations on the border between the real and the imaginary.

S. Sciarrino, from Canzona di ringraziamento

Remarks and links

• Construction details of the shape of the instrument can affect its timbre. Much less relevant from this point of view, on the other hand, is the particular metal from which the instrument is made. Indeed, the oscillation of the air column inside it is coupled very weakly to the oscillation of the metal tube, because of the large difference in acoustic impedance.

• We invite you to read the fundamental page Sound and resonance, where you will find the general principles of how a musical instrument works. Reading it will help you better appreciate the peculiarities of the instrument described on this page

• In our 2D Waves virtual laboratory you can explore the formation of reflected waves and their dependence on the shape of the pipe and on the position of the instrument's holes. The page experiments on sound tubes describes some guided experiments.