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PHYS 307

Prof Bishop

May 6 2013

Heidi Rechin

The Physics of Brass Playing

Among the multitude of brass players who can be found all over the world, many are

unaware of the physics and science that occurs each time their brass instrument produces a

sound. The physics of brass playing is surprisingly complex and the knowledge of this physics is

undoubtedly beneficial to amateur, student, and professional brass players alike. The science

behind brass playing is a progression that starts with the initial intake of air and continues with

the vibration of the lips as pressure is applied to the mouthpiece, then the movement of the air

through the brass tubing, and finally the tone production as it leaves the bell.

There are two main groups of brass instruments, the high brass and low brass. The high

brass category includes trumpets and French horns. The trombone, euphonium, and tuba are

considered the main instruments that make up the low brass category. The trumpet modernly has

three piston valves and a bore that is partly cylindrical and partly conical. The standard trumpet

is pitched in B-flat and it has a range of about three octaves starting at F-sharp 3 (below middle

C). Many orchestral players own multiple trumpets pitched in C or E-flat to assist transposition

and to sound with a different timbre. The cornet is commonly used in orchestral settings as well

and is very similar to the trumpet but it has a conical bore throughout its length while the

majority of the trumpet’s bore is cylindrical. The flugelhorn is a relative of the trumpet and is

frequently used by many trumpet players for its mellow tone. The French horn is a unique brass

instrument which is made of 17ft of tubing, which is the longest of the brass instruments besides

the tuba. The French horn is actually played while the player’s hand is inserted into the bell

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which is a quality that is exclusive to the French horn. This hand closure makes the horn a half-

step sharper than it would sound open and it increases the acoustic mass while lowering the

resonance. The most common French horn is the double horn, which has three lever operated

rotary valves plus a fourth valve to change the tuning of the tubing from F to B-flat.

The tuba is the lowest of the brass instruments and it is found in various pitches but most

commonly F, E-flat, C, and B-flat. The main tube of the B-flat tuba is approximately 18 feet

long. The tuba is an upright, piston-valved brass instrument containing a wide conical bore. The

euphonium is a relative of the tuba but it is smaller, with a higher range and mellower tone. Its

name is derived from the Greek word “euphonos” meaning “well-sounding”. The euphonium is

pitched in B-flat and traditionally has three, and sometimes four, piston valves. The trombone

sounds in a similar range to the euphonium and it is a predominantly cylindrical tube curved into

an elongated “s” shape. The tube is a complex series of taper, where the smallest taper is at the

mouthpiece and the largest is just before the bell flare. These tapers are carefully designed to

create an ideal intonation system. As opposed to other brass instruments which function based on

the opening and closing of valves, the trombone uses a slide. The slide extends the air column

and lowers the pitch as it is moved out.

The first component in the production of a tone from a brass instrument is the air intake.

To develop a good breathing and blowing technique a player has to train themself to breathe

correctly and to efficiently move their air through the horn. As opposed to the everyday

breathing one does to survive, the air intake before playing a brass instrument is very involved.

Ideally a brass player will fill their entire lungs before releasing the air, so students are often

taught to breathe from their lower diaphragm and expand upward. The amount of air intake

varies between the brass instruments, for example a tuba player will need more air than a trumpet

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player due to the larger amount of tubing. There is a threshold pressure that is required for any

note to sound on a brass instrument and the pressure increases with the pitch. There is an upper

limit to this pressure which also increases with the pitch.

N. H. Fletcher and A. Tarnopolsky completed a study in 1999 that reported extensive

measurements of blowing technique for a group of trumpet players. The study focused on three

experienced amateur players and one professional trumpet player.

The figure above shows the amount of blowing pressure used by the professional trumpet player

while playing a standard B-flat trumpet. The study reported that this professional trumpet player

was of solid physique and the highest blowing pressure that he used was about 25 kPa. This is

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much higher than the normal maximum blood pressure which is about 18 kPa, which explains

the players reported physiological complications while playing at this level (Fletcher).

The next topic of importance is what occurs as the brass player is releasing their air. As

soon as the air meets the lips which have formed a level of pressure to the mouthpiece, the lips

then vibrate; this can be referred to as the “lip reed”. Essentially the player’s lips are driven open

and closed by the oscillating sound pressure in the mouthpiece. As described by Newton and

Campbell, “The lips are destabilized by application of an overpressure from the lungs, causing a

pressure difference to be established between the mouth cavity and the mouthpiece. A complex

nonlinear coupling between the resulting airflow, the lips themselves and the resonances of the

instrument air column allows self-sustained oscillation and the production of a musical note”

(Newton). This can be visualized where the lips are like a valve moving in the direction of an

outward swinging door and the brass player’s lips can act as an acoustic generator within a

narrow frequency band. This resonance frequency is determined by a combination of vibrating

mass and muscle tension. The operation of this lip-valve generator is described in the study by N.

H. Fletcher and A. Tarnopolsky:

“Suppose that p0( f) is the threshold gauge pressure in the mouth for excitation of the lip

valve when producing a note of frequency f. If it is assumed that the lips are initially held

closed, then to a first approximation this pressure will be that which is needed to force the

lips open against the lip tension force T, and so will be proportional to T. If the vibrating

mass m of the lips were independent of their tension, then their resonant frequency f

would be proportional to (T/m)1/2, so that we should expect p0( f ) to be proportional to f

2. The structure of the soft tissue in the lips, however, is such that their vibrating mass m

decreases markedly with increasing muscular tension…It is a better approximation to

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write p0(f)=Kf, where K is a constant…Once the lips are forced open by a blowing

pressure p greater than p0, they oscillate in resonance with the instrument horn, because

the skilled player has chosen the tension to match the note he wishes to play. The lip

vibration is approximately sinusoidal, because the frequency is near resonance, and the

vibration amplitude is about equal to the equilibrium lip opening, so that the lips just

close once in each cycle. It is thus a reasonable assumption to write the linear opening x

of the lips as x=A(p-p0)(1+cos 2 ft), where p is the blowing pressure in the mouth and A

is another constant, the magnitude of which is inversely proportional to lip tension, and

thus to the frequency of the note being played” (Fletcher).

Michael J. Newton and Murray Campbell completed a study in 2008 which contrasted the

mechanical response of brass players’ lips and artificial lips. The used four semiprofessional

human players to study three notes played on a trombone. According to their analysis of the

function of the human lips, the player must adjust the tension and mass distribution of the lip

tissue in order to tune mechanical resonances so they usefully interact with the instrument.

Therefore, previous artificial models failed to be able to “lip” a note above and below the

relevant acoustical resonance frequency of the air column of the instrument as human lips can. In

this study they resolved this problem by ascribing two degrees of mechanical freedom to the lips,

similar to how the human vocal chords operate. The human embouchures that they studied

corresponded to three played notes, B1(pedal tone), B2, and F3, which are considered the lower

range of playable notes on the tenor trombone. In all three notes there was one dominant

resonance that consistently lied below the frequency of the played note which leads to the

suggestion that it acts like the outward striking reed of the Helmholtz. The image at the stop of

the following page shows a plot of three mechanical response curves obtained with the human

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lips using the video method. The played frequencies for each note are marked as vertical line and

the magnitude curves have been offset by 3 and 6dB for display purposes (Newton).

When these results were compared with the artificial lip there were general differences found.

The difference in Q values between real and artificial lips was likely due to the internal damping

of the lips. The human lips tissue is constructed from a lattice of skin and muscle cells containing

water, yet the artificial lips only consist of water surrounded by latex (Newton). This the study

did succeed in analyzing the human lips and were able to successfully reproduce this “lip reed”

process to an extent.

Once the lips have vibrated and created these self-sustained oscillations the brass

instrument then produces a sound specific to the shaping of the bore and flare of the bell. This

process can be explained rather simply. If the air is blown thought the brass instrument while the

player’s lips are vibrating at or close to one of the instrument’s resonant frequencies a standing

wave is set up in the air column. The feedback from the excited air column drives the lips to

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sustain the vibration and this produces a complex musical tone with a fundamental frequency

close to one of the instrument’s actual resonance modes. If the tension in the lips is increased it

will excite a higher resonance in the air column, such as a string vibrates. The following image

shows the complex waveforms produced by the trombone and trumpet (LoPresto).

A clear tone on a brass instrument that is pleasing to the listener takes years to develop

and is a very complex topic. A brass player really has to visualize this ideal sound or tone and

practice every day to try to create it. Brass instruments are known for their ability to allow the

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musician to change tone “colors” and timbre based on artistic choices. The sound of a brass

instrument is characterized by a spectrum which is somewhat weak in the upper harmonics of

quiet playing but is gradually enriched in the upper harmonics as the dynamic level is increased.

When a player reaches a very loud, high dynamic level at the peak of a crescendo the brightness

of the sound is equally increased and this timbre is often referred to a full, “brassy” sound. One

of the main elements that contribute to this “spectral enrichment” in brass instruments is the

distributed nonlinear effect from sound propagation in the bore. This results in a waveform that

leaves from the mouthpiece and becomes progressively more distorted as it travels along the

duct. This effect occurs at the very loudest dynamic playing, but still occurs in a lesser extent at

lower dynamic levels. The potential for this nonlinear wave propagation to occur in a brass

instrument at a given dynamic level can be referred to as the “brassiness potential, and it is

relatice to the bore profile and bore diameter of the instrument. Instruments such as the trumpet

or trombone, which have long cylindrical sections of tubing, have a more significant nonlinear

wave propagation than brass instruments such as the euphonium or flugelhorn (Myers). The

following image compares an upstretched cylinder with the stretched coordinates of a relatively

narrow trumpet bell and a more rapidly-expanding flugelhorn bell. If the same particle velocity

was isjected at the left end, the sound in all three ducts would have achieved the same degree of

nonlinear distortion when it arrives at the right end.

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In Myer’s article The Effects of nonlinear sound propagation on the characteristic timbres of

brass instruments, he provides a ratio explaining the “brassiness potential parameter”:

“For a brass instrument whose sounding length is divided into N sections with arbitrary

lengths , the brassiness potential parameter B can be approximated by

where is the bore diameter at the start of the nth section and is the

diameter at the exit of the final section. It is found that physical measurements of the bore

at ten or more points along the length of the tubing give sufficient accuracy. Axial length

measurements following the mid bore line round bends in the tubing can be done with an

accuracy of 3% or better. The minimum bore is usually accessible to direct

physical measurement, and can be determined to 0.2mm (typically within 3% accuracy).

Bore measurements along the length of the tube can be estimated to 1% attuning-slides

and other points of separation, and by estimates of bell wall thickness elsewhere

(typically to 0.2 mm). The wider tubing of the bell flare makes relatively little

contribution to nonlinear propagation effects, and precision is less important here than in

the proximal (narrower) part of the bore. The final factor in the calculation of B is the

equivalent cone length. For instruments in playing regimes the intended playing pitch is

well known and the equivalent cone length can be derived from the nominal pitch and the

design pitch standard. In most cases the playing pitch can be estimated by one means or

another to within half a semitone, giving an uncertainty in equivalent cone length of less

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than 63 %. Since the brassiness parameter varies widely between families of instruments,

its utility is not compromised by errors of the order of 3%.” (Myers)

A study by Emilie Poirson had a similar outline and it focused on the brightness of

trumpet tones. The main variable found to affect the brightness of the tone was the depth of the

mouthpiece, so they tested this with 2 notes from a musician at a piano dynamic level (MP), a

mezzo forte level (MF), and an artificial mouth at a forte level (AM). In this study they cut out

differences created by the shape of the cup, thickness of the rim, and width of the throat and back

bore, by developing a special mouthpiece for which just a single geometric parameter, the depth

of the mouthpiece cup, can be controlled. To do this the mouthpiece had a micrometer screw

which increased the mouthpiece cup depth by .5 mm each turn. The image below shows the cross

section of the mouthpiece with two positions of depth, shallow (T0, left) and deep (T10, right).

In this study they incorporated the brightness of tone with the input impedance of the trumpet,

which was based on the impedance sensor described in Dalmont and Bruneau in 1991. The

impedance sensors used were linear with two entries and the signals were influenced by both the

pressure and volume velocity. Two kinds of measurements made. The first was called “narrow-

band measurements,” which corresponds to measurements made step by step from 50 to 150 Hz,

using a step equal to 1 Hz. The second was called “broadband measurement,” and it corresponds

to measurements made from 4 Hz step by step to 4096 Hz using a step equal to 4 Hz. The

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narrow-band measurements were used in order to extract the resonance frequencies and their

associated parameters as the quality factor and the impedance magnitude value. The following

image shows the measured dimensionless input impedance (magnitude in dB and phase) of the

trumpet with the “shallow” mouthpiece T0 dotted and with the “deep” mouthpiece T10

continuous.

This study concluded that that the artificial mouth and the simulations give results

coherent with those of the musician concerning the perception of differences of timbre. The

distinguishability between sounds is of the same order for the artificial mouth, the simulated

tones, and the musician. One of the significant findings was that the musician is not reproducible

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enough and creates difference of timbre of the same order as the difference produced by the

depth change in the mouthpiece. The artificial mouth was found to be an essential device to

study of the quality of wind instruments, for the conception of new instruments, and for the

validation of realistic simulated tools. The main component in the brightness of tone is the

magnitude of the impedance peak corresponding to the second harmonic (Poirson).

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Works Cited

Fletcher, N. H., and A. Tarnopolsky. "Blowing Pressure, Power, and Spectrum in Trumpet

Playing." The Journal of the Acoustical Society of America 105.2 (1999): 874-81. Print.

LoPresto, Michael C. "Experimenting with Brass Musical Instruments." Physics Education 38.4

(2003): 300-08. Print.

Myers, Arnold, Robert W. Pyle, Joël Gilbert, Murray D. Campbell, John P. Chick, and Shona

Logie. "Effects of Nonlinear Sound Propagation on the Characteristic Timbres of Brass

Instruments." Journal of the Acoustical Society of America 131.1 (2012): 678-88. Print.

Newton, Michael J., Murray Campbell, and Jöel Gilbert. "Mechanical Response Measurements

of Real and Artificial Brass Players Lips." The Journal of the Acoustical Society of

America 123.1 (2008): EL14-L20. Print.

Poirson, Emilie, Jean-François Petiot, and Joël Gilbert. "Study of the Brightness of Trumpet

Tones." The Journal of the Acoustical Society of America 118.4 (2005): 2656-666. Print.