lecture 13 woodwinds: air reeds brass instruments instructor: david kirkby ([email protected])

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Lecture 13 Woodwinds: air reeds Brass Instruments Instructor: David Kirkby ([email protected])

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Page 1: Lecture 13 Woodwinds: air reeds Brass Instruments Instructor: David Kirkby (dkirkby@uci.edu)

Lecture 13Woodwinds: air reedsBrass Instruments

Instructor: David Kirkby ([email protected])

                                                                                 

Page 2: Lecture 13 Woodwinds: air reeds Brass Instruments Instructor: David Kirkby (dkirkby@uci.edu)

Physics of Music, Lecture 13, D. Kirkby 2

MiscellaneousI 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 10-11am on Wednesday Nov 27 (afternoon hours are still OK).

Page 3: Lecture 13 Woodwinds: air reeds Brass Instruments Instructor: David Kirkby (dkirkby@uci.edu)

Physics of Music, Lecture 13, D. Kirkby 3

Air ReedExamples 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

Page 4: Lecture 13 Woodwinds: air reeds Brass Instruments Instructor: David Kirkby (dkirkby@uci.edu)

Physics of Music, Lecture 13, D. Kirkby 4

Air Jets and TurbulenceAs 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.

Page 5: Lecture 13 Woodwinds: air reeds Brass Instruments Instructor: David Kirkby (dkirkby@uci.edu)

Physics of Music, Lecture 13, D. Kirkby 5

Air Jets and EdgesAn 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. Thesetones are inharmonic and noisy.

Page 6: Lecture 13 Woodwinds: air reeds Brass Instruments Instructor: David Kirkby (dkirkby@uci.edu)

Physics of Music, Lecture 13, D. Kirkby 6

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 jet-edge vibrations to store energy at harmonic frequencies.

The jet-edge (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.

Page 7: Lecture 13 Woodwinds: air reeds Brass Instruments Instructor: David Kirkby (dkirkby@uci.edu)

Physics of Music, Lecture 13, D. Kirkby 7

Air Reed Instruments: Flute

Page 8: Lecture 13 Woodwinds: air reeds Brass Instruments Instructor: David Kirkby (dkirkby@uci.edu)

Physics of Music, Lecture 13, D. Kirkby 8

Air Reed Instruments: RecorderThe recorder is similar to the flute, but has a built in channel to produce an air jet and direct it at an edge.

The recorder is unusual among woodwinds because it has a reverse conical bore that tapers away from the mouthpiece.

Page 9: Lecture 13 Woodwinds: air reeds Brass Instruments Instructor: David Kirkby (dkirkby@uci.edu)

Physics of Music, Lecture 13, D. Kirkby 9

Flute DemonstrationListen 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?

Page 10: Lecture 13 Woodwinds: air reeds Brass Instruments Instructor: David Kirkby (dkirkby@uci.edu)

Physics of Music, Lecture 13, D. Kirkby 10

Brass InstrumentsBrass instruments are the second of two groups that are played by blowing into them (the other group is woodwind instruments).

Examples of brass instruments are the trumpet, trombone, french horn and tuba.

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

Page 11: Lecture 13 Woodwinds: air reeds Brass Instruments Instructor: David Kirkby (dkirkby@uci.edu)

Physics of Music, Lecture 13, D. Kirkby 11

A lot of the physics of brass instruments repeats what we have already learned for woodwinds, but there are also some surprises.

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?

Page 12: Lecture 13 Woodwinds: air reeds Brass Instruments Instructor: David Kirkby (dkirkby@uci.edu)

Physics of Music, Lecture 13, D. Kirkby 12

Energy Flow and FeedbackThe source of energy in a brass instrument is a player’s breath.

There are three main resonators in a brass:•the player’s lips,•the mouthpiece and mouth pipe, and•the air column.

The resonant frequencies of the mouthpiece are fixed, but the player can adjust the resonances of the air column and of his lips.

Page 13: Lecture 13 Woodwinds: air reeds Brass Instruments Instructor: David Kirkby (dkirkby@uci.edu)

Physics of Music, Lecture 13, D. Kirkby 13

Brass FamiliesBrass instruments can be grouped according to whether they are mostly cylindrical or conical:

Cylindrical: trumpet, trombone, french horn

Conical: cornet, baritone, tuba

Page 14: Lecture 13 Woodwinds: air reeds Brass Instruments Instructor: David Kirkby (dkirkby@uci.edu)

Physics of Music, Lecture 13, D. Kirkby 14

Brasses in the Orchestra

Page 15: Lecture 13 Woodwinds: air reeds Brass Instruments Instructor: David Kirkby (dkirkby@uci.edu)

Physics of Music, Lecture 13, D. Kirkby 15

Listen to these samples of orchestral brasses:

(from http://www.discovereso.com/woodwinds.htm)

Page 16: Lecture 13 Woodwinds: air reeds Brass Instruments Instructor: David Kirkby (dkirkby@uci.edu)

Physics of Music, Lecture 13, D. Kirkby 16

Cylindrical Brasses: Trumpet

piccolo trumpet

Page 17: Lecture 13 Woodwinds: air reeds Brass Instruments Instructor: David Kirkby (dkirkby@uci.edu)

Physics of Music, Lecture 13, D. Kirkby 17

Cylindrical Brasses: Trombone

Page 19: Lecture 13 Woodwinds: air reeds Brass Instruments Instructor: David Kirkby (dkirkby@uci.edu)

Physics of Music, Lecture 13, D. Kirkby 19

Conical Brasses: Tuba Family

tuba Sousaphonebaritone

flugelhorn

Page 20: Lecture 13 Woodwinds: air reeds Brass Instruments Instructor: David Kirkby (dkirkby@uci.edu)

Physics of Music, Lecture 13, D. Kirkby 20

Standing Waves in the Air ColumnThe 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 effectof adding twists and turns to the air column…

Page 21: Lecture 13 Woodwinds: air reeds Brass Instruments Instructor: David Kirkby (dkirkby@uci.edu)

Physics of Music, Lecture 13, D. Kirkby 21

Comparison of Air ColumnsSince 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)

Page 22: Lecture 13 Woodwinds: air reeds Brass Instruments Instructor: David Kirkby (dkirkby@uci.edu)

Physics of Music, Lecture 13, D. Kirkby 22

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??

Page 23: Lecture 13 Woodwinds: air reeds Brass Instruments Instructor: David Kirkby (dkirkby@uci.edu)

Physics of Music, Lecture 13, D. Kirkby 23

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?

Page 24: Lecture 13 Woodwinds: air reeds Brass Instruments Instructor: David Kirkby (dkirkby@uci.edu)

Physics of Music, Lecture 13, D. Kirkby 24

The important differences between a real trumpet and the PVC trumpet are:

•The mouthpiece and mouth tube•The bell

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…

Page 25: Lecture 13 Woodwinds: air reeds Brass Instruments Instructor: David Kirkby (dkirkby@uci.edu)

Physics of Music, Lecture 13, D. Kirkby 25

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.

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.

How do these two effects work together to fill in the even harmonics?

Page 26: Lecture 13 Woodwinds: air reeds Brass Instruments Instructor: David Kirkby (dkirkby@uci.edu)

Physics of Music, Lecture 13, D. Kirkby 26

Both of these elements subtly adjust the odd-harmonic spectrum to give an almost even+odd spectrum at a new fundamental frequency:

1 2 3 4 5 6 7 8 11

frequencycylinder

9 10

+ bell frequency

+ mouthpiece

frequency

1 2 3 4 5 6

Page 27: Lecture 13 Woodwinds: air reeds Brass Instruments Instructor: David Kirkby (dkirkby@uci.edu)

Physics of Music, Lecture 13, D. Kirkby 27

What have we learned?

•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.

Page 28: Lecture 13 Woodwinds: air reeds Brass Instruments Instructor: David Kirkby (dkirkby@uci.edu)

Physics of Music, Lecture 13, D. Kirkby 28

Pedal TonesIt 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.

frequency

1 2 3 4 5 6

play these overtones

You will perceive this pitch

Page 29: Lecture 13 Woodwinds: air reeds Brass Instruments Instructor: David Kirkby (dkirkby@uci.edu)

Physics of Music, Lecture 13, D. Kirkby 29

Playing Different NotesSo far, we have focused on the air column, and not mentioned how different notes are selected.

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.

This is the only option on a bugle, but still allows you to play a limited selection of music.

For example:

http://www.fas.org/man/dod-101/sys/land/bugle.htm

Page 30: Lecture 13 Woodwinds: air reeds Brass Instruments Instructor: David Kirkby (dkirkby@uci.edu)

Physics of Music, Lecture 13, D. Kirkby 30

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.

As a result, a “woodwind bugle” would have its notes too spread out to be useful:

C D E F G A B C D E F G A B C D E F G A B

f1 f2 f4f3 f5 f6 f8

bugle“woodwind bugle”

Page 31: Lecture 13 Woodwinds: air reeds Brass Instruments Instructor: David Kirkby (dkirkby@uci.edu)

Physics of Music, Lecture 13, D. Kirkby 31

An empty bottle is essentially a “woodwind bugle”.

Try to blow overtones on one. How many can you get?

Page 32: Lecture 13 Woodwinds: air reeds Brass Instruments Instructor: David Kirkby (dkirkby@uci.edu)

Physics of Music, Lecture 13, D. Kirkby 32

ValvesThe second method for changing the pitch is to alter the physical length of the instrument.

Most of the brasses do this with finger-actuated valves that add an extra length of tube when they are pressed down:

Piston style(trumpet,tuba)

Rotary style(french horn)

Page 33: Lecture 13 Woodwinds: air reeds Brass Instruments Instructor: David Kirkby (dkirkby@uci.edu)

Physics of Music, Lecture 13, D. Kirkby 33

Brass instruments traditionally have only 3 valves. Why is this enough if the woodwinds need >10 to cover each register?

The reason is that the size of a register is determined by the spacing of the harmonics being used:

C D E F G A B C D E F G A B C D E F G A B

f1 f2 f4f3 f5 f6 f8

flute,oboe (12 semitones)clarinet (19 semitones)

trumpet (7 semitones)

Page 34: Lecture 13 Woodwinds: air reeds Brass Instruments Instructor: David Kirkby (dkirkby@uci.edu)

Physics of Music, Lecture 13, D. Kirkby 34

Trumpet Valve FingeringsPressing 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 XX - XX X X

low

er

pit

ch

Page 35: Lecture 13 Woodwinds: air reeds Brass Instruments Instructor: David Kirkby (dkirkby@uci.edu)

Physics of Music, Lecture 13, D. Kirkby 35

Trumpet FingeringsHow much should each valve increase the length of the instrument by?

Pressing down valve #2 should lower the pitch by one semitone. This is equivalent to stretching the length by 21/12 = 1.06. So if the original length is 100cm, the extra length should be 6cm.

Pressing down valve #3 should lower the pitch by two semitones. This is equivalent to stretching by 22/12 = 1.12, or adding 12cm.

Page 36: Lecture 13 Woodwinds: air reeds Brass Instruments Instructor: David Kirkby (dkirkby@uci.edu)

Physics of Music, Lecture 13, D. Kirkby 36

CompromisesThe fingering chart tells us to press down valves #1 and #2 to reach the third semitone down.

We have already calculated that this adds 6+12 = 18cm to the length.

But three semitones requires a stretch of 23/12 = 1.19, or an extra 19cm.

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).

Page 37: Lecture 13 Woodwinds: air reeds Brass Instruments Instructor: David Kirkby (dkirkby@uci.edu)

Physics of Music, Lecture 13, D. Kirkby 37

Trombone SlideThe 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.

Page 38: Lecture 13 Woodwinds: air reeds Brass Instruments Instructor: David Kirkby (dkirkby@uci.edu)

Physics of Music, Lecture 13, D. Kirkby 38

Sound EscapeSo 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.

Page 39: Lecture 13 Woodwinds: air reeds Brass Instruments Instructor: David Kirkby (dkirkby@uci.edu)

Physics of Music, Lecture 13, D. Kirkby 39

The bell of a brass instrument reflects low frequencies but allows high frequencies to escape easily. This is a double-edged sword since, without reflections, standing waves do not have a chance to build up:

frequency frequency

Internal spectrum External spectrum

Demonstration: listen to these two timbres side by side.

Page 40: Lecture 13 Woodwinds: air reeds Brass Instruments Instructor: David Kirkby (dkirkby@uci.edu)

Physics of Music, Lecture 13, D. Kirkby 40

Construction MaterialsDoes 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