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

2. Physics of Music, Lecture 13, D. Kirkby2 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 10-11am on Wednesday Nov 27 (afternoon hours are still OK).

3. Physics of Music, Lecture 13, D. Kirkby3 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

4. Physics of Music, Lecture 13, D. Kirkby4 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.

5. Physics of Music, Lecture 13, D. Kirkby5 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.

6. Physics of Music, Lecture 13, D. Kirkby6 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.

7. Physics of Music, Lecture 13, D. Kirkby7 Air Reed Instruments: Flute

8. Physics of Music, Lecture 13, D. Kirkby8 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. The recorder is unusual among woodwinds because it has a reverse conical bore that tapers away from the mouthpiece.

9. Physics of Music, Lecture 13, D. Kirkby9 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?

10. Physics of Music, Lecture 13, D. Kirkby10 Brass Instruments Brass 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 players vibrating lips A mouthpiece and mouthpipe An air column open at the far end A flared bell

11. Physics of Music, Lecture 13, D. Kirkby11 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?

12. Physics of Music, Lecture 13, D. Kirkby12 Energy Flow and Feedback The source of energy in a brass instrument is a players breath. There are three main resonators in a brass: the players 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.

13. Physics of Music, Lecture 13, D. Kirkby13 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

14. Physics of Music, Lecture 13, D. Kirkby14 Brasses in the Orchestra

15. Physics of Music, Lecture 13, D. Kirkby15 Listen to these samples of orchestral brasses: (from http://www.discovereso.com/woodwinds.htm)http://www.discovereso.com/woodwinds.htm

16. Physics of Music, Lecture 13, D. Kirkby16 Cylindrical Brasses: Trumpet piccolo trumpet

17. Physics of Music, Lecture 13, D. Kirkby17 Cylindrical Brasses: Trombone

18. Physics of Music, Lecture 13, D. Kirkby18 Cylindrical Brasses: French Horn http://www.huntington.edu/music/gallery/gallery%20pages/orchestra.htm

19. Physics of Music, Lecture 13, D. Kirkby19 Conical Brasses: Tuba Family tuba Sousaphone baritone flugelhorn

20. Physics of Music, Lecture 13, D. Kirkby20 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…

21. Physics of Music, Lecture 13, D. Kirkby21 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)

22. Physics of Music, Lecture 13, D. Kirkby22 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 trumpets lowest note should be about 1/3 of the frequency of the clarinets lowest note (D 3 ). Instead, the trumpets lowest note (E 3 ) is slightly higher than the clarinets lowest note! Why??

23. Physics of Music, Lecture 13, D. Kirkby23 First, check the frequency spectrum of a PVC trumpet. What is the lowest harmonic? Does it agree with the expected f 1 = 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?

24. Physics of Music, Lecture 13, D. Kirkby24 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…

25. Physics of Music, Lecture 13, D. Kirkby25 The bell on a brass instrument behaves like the open holes on a woodwind instrument and shortens the instruments 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 instruments effective length at high frequencies, while leaving the low frequencies alone. How do these two effects work together to fill in the even harmonics?

26. Physics of Music, Lecture 13, D. Kirkby26 Both of these elements subtly adjust the odd-harmonic spectrum to give an almost even+odd spectrum at a new fundamental frequency: 1234567811 frequency cylinder 910 + bell frequency + mouth piece frequency 1 2345 6

27. Physics of Music, Lecture 13, D. Kirkby27 What have we learned? A trumpet would be out of tune (inharmonic overtones) if we removed either the bell or the mouthpiece. The trumpets 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.

28. Physics of Music, Lecture 13, D. Kirkby28 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. frequency 1 2345 6 play these overtones You will perceive this pitch

29. Physics of Music, Lecture 13, D. Kirkby29 Playing Different Notes So 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

30. Physics of Music, Lecture 13, D. Kirkby30 Why isnt 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: CDEFGABCDEFGABCDEFGAB f1f1 f2f2 f4f4 f3f3 f5f5 f6f6 f8f8 bugle woodwind bugle

31. Physics of Music, Lecture 13, D. Kirkby31 An empty bottle is essentially a woodwind bugle. Try to blow overtones on one. How many can you get?

32. Physics of Music, Lecture 13, D. Kirkby32 Valves The 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)

33. Physics of Music, Lecture 13, D. Kirkby33 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: CDEFGABCDEFGABCDEFGAB f1f1 f2f2 f4f4 f3f3 f5f5 f6f6 f8f8 flute,oboe (12 semitones) clarinet (19 semitones) trumpet (7 semitones)

34. Physics of Music, Lecture 13, D. Kirkby34 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 lower pitch

35. Physics of Music, Lecture 13, D. Kirkby35 Trumpet Fingerings How 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 2 1/12 = 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 2 2/12 = 1.12, or adding 12cm.

36. Physics of Music, Lecture 13, D. Kirkby36 Compromises The 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 2 3/12 = 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).

37. Physics of Music, Lecture 13, D. Kirkby37 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 trombones slide motion is usually divided into seven steps that are a semitone apart.

38. Physics of Music, Lecture 13, D. Kirkby38 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.

39. Physics of Music, Lecture 13, D. Kirkby39 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 Internal spectrumExternal spectrum Demonstration: listen to these two timbres side by side.

40. Physics of Music, Lecture 13, D. Kirkby40 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