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The Physics of Music Physics 15 University of California, Irvine
Lecture 13 § Woodwinds: air reeds § Brass Instruments
Instructor: David Kirkby (dkirkby @uci.edu)
Air Reed Examples of air reed instruments include the flute, recorder, and whistles.
In an air reed instrument, a thin jet of air plays the role of the cane reed(s) of other woodwind instruments.
The air reed has two main components: Air jet Sharp edge
Physics of Music, Lecture 13, D. Kirkby
Air Jets and Edges An air jet striking a sharp edge will be deflected to one side of the edge.
If the jet is centered on the edge, turbulence can cause it to switch back and forth between sides in a chaotic way.
The coupling of an air jet with an edge produces sound of its own, which we describe as wind whistling or aeolian tones. These tones are inharmonic and noisy.
Physics of Music, Lecture 13, D. Kirkby
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Instructor: David Kirkby dkirkby@uci.edu
Miscellaneous I will be traveling on Nov 26 (Tuesday before Thanksgiving). There will be a guest lecture, Prof. David Casper.
Problem Set #7 (the last one) will be handed out next Thursday (Nov 21) but not due for two weeks.
No office hours 1011am on Wednesday Nov 27 (afternoon hours are still OK).
Physics of Music, Lecture 13, D. Kirkby
Air Jets and Turbulence As fast air is forced out through your lips, it comes in contact with the stationary surrounding air. This contact triggers turbulent eddies to form, which in turn disturb the flow pattern.
Physics of Music, Lecture 13, D. Kirkby
When an air jet and edge are coupled to a resonator (such as an air column), the frequency selectivity of the resonator can harness the chaotic jetedge vibrations to store energy at harmonic frequencies.
The jetedge (air reed) vibrations are reinforced and synched to the air columns vibrations by a feedback mechanism (similar to the other reed instruments).
In this case, the feedback relies on the direction of air flow in the standing wave rather than pressure pulses.
Physics of Music, Lecture 13, D. Kirkby
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The resonant frequencies of the mouthpiece are fixed, but the player can adjust the resonances of the air column and of his lips.
A lot of the physics of brass instruments repeats what we have already learned for woodwinds, but there are also some surprises.
The Physics of Music Physics 15 University of California, Irvine
Air Reed Instruments: Flute
Air Reed Instruments: Recorder The recorder is similar to the flute, but has a built in channel to produce an air jet and direct it at an edge.
Instructor: David Kirkby dkirkby@uci.edu
Physics of Music, Lecture 13, D. Kirkby
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Physics of Music, Lecture 13, D. Kirkby
Physics of Music, Lecture 13, D. Kirkby
Examples of brass instruments are the trumpet, trombone, french horn and tuba.
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Brass Instruments Brass instruments are the second of two groups that are played by blowing into them (the other group is woodwind instruments).
Physics of Music, Lecture 13, D. Kirkby
Physics of Music, Lecture 13, D. Kirkby
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Flute Demonstration Listen for the following effects (thanks to Ye Seul Yi): Does the flute timbre include even harmonics? How does the timbre change for quiet vs loud playing? How does the timbre change with register? How does vibrato work?
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Physics of Music, Lecture 13, D. Kirkby
The common features of a brass instrument are: A player’s vibrating lips A mouthpiece and mouthpipe An air column open at the far end A flared bell
Energy Flow and Feedback The source of energy in a brass instrument is a player’s breath.
The recorder is unusual among woodwinds because it has a reverse conical bore that tapers away from the mouthpiece.
Try this quiz before we get started: How do all the twists and turns of a brass instrument affect its sound? A trumpet is about 3 times longer than a clarinet. How do you expect their lowest notes to compare? A cylindrical brass (eg ,trumpet) should only have odd harmonics and sound like a clarinet. Does it? Why do woodwinds have many (>10) keys but brass instruments can make do with only 3 valves?
There are three main resonators in a brass: the player’s lips, the mouthpiece and mouth pipe, and the air column.
The Physics of Music Physics 15 University of California, Irvine
Brass Families Brass instruments can be grouped according to whether they are mostly cylindrical or conical:
Cylindrical: trumpet, trombone, french horn
Conical: cornet, baritone, tuba
Physics of Music, Lecture 13, D. Kirkby
Listen to these samples of orchestral brasses: (fromhttp://www. discovereso .com/woodwinds. htm)
Physics of Music, Lecture 13, D. Kirkby
Cylindrical Brasses: Trombone
Physics of Music, Lecture 13, D. Kirkby
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Instructor: David Kirkby dkirkby@uci.edu
Brasses in the Orchestra
Physics of Music, Lecture 13, D. Kirkby
Cylindrical Brasses: Trumpet
piccolo trumpet Physics of Music, Lecture 13, D. Kirkby
Cylindrical Brasses: French Horn
http://www.huntington.edu/music/gallery/gallery%20pages/orchestra.htm Physics of Music, Lecture 13, D. Kirkby
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The Physics of Music Physics 15 University of California, Irvine
Conical Brasses: Tuba Family
tuba Physics of Music, Lecture 13, D. Kirkby
Sousaphone
flugelhorn
baritone
Comparison of Air Columns Since the twists and turns do not matter, we can unroll the brasses to compare their air columns (bells omitted):
Trumpet (53+87=140cm)
Trombone (170 +105=275cm)
French horn (193+182=375cm)
Tuba (0+536=536cm)
Physics of Music, Lecture 13, D. Kirkby
First, check the frequency spectrum of a “PVC trumpet”.
What is the lowest harmonic? Does it agree with the expected f1= v/4L ?
Are even harmonics suppressed, as expected for open+closed boundary conditions?
Since the PVC trumpet plays as expected, what is different about a real trumpet?
Physics of Music, Lecture 13, D. Kirkby
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Instructor: David Kirkby dkirkby@uci.edu
Standing Waves in the Air Column The air column in a brass instrument is open at the bell end and closed at the mouthpiece end.
If it were straight, a brass instrument should be similar to a clarinet (ignoring the difference between a reed and a mouthpiece for now).
But brass instruments have their air columns coiled up in many loops, in order to make them more compact for their length. How does this affect their sound?
Listen to the PVC “brasses” to hear the effect of adding twists and turns to the air column…
Physics of Music, Lecture 13, D. Kirkby
The trumpet is about 3 times longer than a clarinet and has the same boundary conditions (open+closed).
This means that the frequency of a trumpet’s lowest note should be about 1/3 of the frequency of the clarinet’s lowest note (D3).
Instead, the trumpet’s lowest note (E3) is slightly higher than the clarinet’s lowest note!
Why??
Physics of Music, Lecture 13, D. Kirkby
The important differences between a real trumpet and the PVC trumpet are: The mouthpiece and mouth tube The bell
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Both of these features change the effective length of the air column.
But what really matters is that they change the effective length differently for different frequencies…
Physics of Music, Lecture 13, D. Kirkby
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You will perceive this pitch
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play these overtones 3 4 5
A trumpet would be out of tune (inharmonic overtones) if we removed either the bell or the mouthpiece. The trumpet’s lowest resonance is out of tune with the other overtones, and so is not musically useful (or physically sustainable) The lowest harmonic resonance of a trumpet is about 3 times higher in frequency than the fundamental frequency we would expect for a simple air column of the same length.
What have we learned?
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Physics of Music, Lecture 13, D. Kirkby
Why isn’t there an instrument like the bugle for the woodwinds? The reason is that reed instruments are optimized to play pitches corresponding to low harmonics of the air column, while brasses are optimized to play high harmonics.
f1f2 Physics of Music, Lecture 13, D. Kirkby
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This is the only option on a bugle, but still allows you to play a limited selection of music.
One method for playing different notes is to adjust the tension in your lips which increases their resonant frequency and then, in turn, excites a higher overtone of the air column.
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C D E F G A B C D E F G A B C D E F G A B
Physics of Music, Lecture 13, D. Kirkby
Instructor: David Kirkby dkirkby@uci.edu
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frequency
frequency
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34567891011 frequency
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Both of these elements subtly adjust the odd harmonic spectrum to give an almost even+odd spectrum at a new fundamental frequency:
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The bell on a brass instrument behaves like the open holes on a woodwind instrument and shortens the instrument’s effective length for low frequencies, while leaving the high frequencies alone.
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As a result, a “woodwind bugle” would have its notes too spread out to be useful: bugle “woodwind bugle”
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Physics of Music, Lecture 13, D. Kirkby
+ bell
cylinder
+ mouth piece
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Physics of Music, Lecture 13, D. Kirkby
Physics of Music, Lecture 13, D. Kirkby
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Pedal Tones It is actually possible to play a note that is perceived to have the pitch of the mistuned fundamental, by exciting the 2nd, 3rd, 4th, … harmonics and letting your brain fill in the missing fundamental. This is called a pedal tone .
How do these two effects work together to fill in the even harmonics?
The mouthpiece and mouthpipe are a constriction of the air column and have the opposite effect: they resonate around 800 Hz and increase the instrument’s effective length at high frequencies, while leaving the low frequencies alone.
Playing Different Notes So far, we have focused on the air column, and not mentioned how different notes are selected.
For example: http://www.f a s.org/man/dod101/sys/land/bugle.htm
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f3
f6
f5
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The Physics of Music Physics 15 University of California, Irvine
frequency
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Piston style (trumpet,tuba) Physics of Music, Lecture 13, D. Kirkby
An empty bottle is essentially a “woodwind bugle”.
Compromises The fingering chart tells us to press down valves #1 and #2 to reach the third semitone down.
Rotary style (french horn)
C D E F G A B C D E F G A B C D E F G A B
Brass instruments traditionally have only 3 valves. Why is this enough if the woodwinds need >10 to cover each register?
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Trumpet Fingerings How much should each valve increase the length of the instrument by?
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Physics of Music, Lecture 13, D. Kirkby
Physics of Music, Lecture 13, D. Kirkby
The reason is that the size of a register is determined by the spacing of the harmonics being used: trumpet (7 semitones) clarinet (19 semitones) flute,oboe (12 semitones)
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f1f2 Physics of Music, Lecture 13, D. Kirkby
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Pressing down valve #2 should lower the pitch byone semitone. This is equivalent to stretching the length by 1/12 2 = 1.06. So if the original length is 100cm, the extra length should be 6cm.
Pressing down valve #3 should lower the pitch bytwo 2/12 semitones. This is equivalent to stretching by 2 = 1.12, or adding 12cm.
Try to blow overtones on one. How many can you get?
Physics of Music, Lecture 13, D. Kirkby
We have already calculated that this adds 6+12 = 18cm to the length.
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Most of the brasses do this with fingeractuated valves that add an extra length of tube when they are pressed down:
Trumpet Valve Fingerings Pressing down a valve makes the instrument longer, and so lowers the fundamental frequency. (This is opposite to what happens with a woodwind, where finger holes make the instrument shorter and raise the fundamental frequency.) 1 2 3 X X X X X X X X X X X
Valves The second method for changing the pitch is to alter the physical length of the instrument.
The Physics of Music Physics 15 University of California, Irvine
Instructor: David Kirkby dkirkby@uci.edu
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What went wrong? Intervals require multiplying by some ratio, but valves involve adding some length. These are impossible to reconcile exactly, so some compromise is necessary (just like for the woodwind register holes).
Physics of Music, Lecture 13, D. Kirkby
3/12 Butthreesemitones requires a stretch of 2 or= 1.19, an extra 19cm.
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The Physics of Music Physics 15 University of California, Irvine
Trombone Slide The trombone uses a different strategy and does not need valves (although some trombones have a trigger valve anyway).
This gives the player complete freedom to play any frequency within a range, but also the responsibility to find the right ones!
The full extent of the trombone’s slide motion is usually divided into seven steps that are a semitone apart.
Physics of Music, Lecture 13, D. Kirkby
The bell of a brass instrument reflects low frequencies but allows high frequencies to escape easily. This is a doubleedged sword since, without reflections, standing waves do not have a chance to build up: Internal spectrum External spectrum
frequency frequency Demonstration: listen to these two timbres side by side.
Physics of Music, Lecture 13, D. Kirkby
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Instructor: David Kirkby dkirkby@uci.edu
Sound Escape So far, we have been discussing the standing waves within the air column. You would only actually hear these using a microphone place inside the instrument.
To explain the sound that escapes from the air column and reaches your ears, we must understand how sound gets out of the instrument.
For the brass instruments, there is only one way out: through the bell.
Physics of Music, Lecture 13, D. Kirkby
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Construction Materials Does a flute made from gold sound better than one made from steel? How about a clarinet made of metal instead of wood? Most musicians believe that some materials sound better than others. Most physicists disagree. It is difficult to perform objective double blind tests for many instruments, since this requires that both the performer and the listener are unable to identify the material (except by listening). See these interesting results: http://iwk .mdw.ac.at/Forschung/ pdf_dateien/2001e_ Widholm_ISMA_ Floeten .pdf Physics of Music, Lecture 13, D. Kirkby 40
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