1. Lecture 12 String Instruments: (Violin Family) Guitar
                                                                                 
Lecture 12
String Instruments:
(Violin Family)
Guitar
Woodwind Instruments:
Single reed
Double reed
(Air reed)
Instructor: David Kirkby

2. Review of Lecture 11
We discussed how reflections and absorption modify the sound you hear, and how the Precedence Effect helps you sort out the complex results.
We completed the second part of this course which dealt with the Perception of Sound, and started the third part which deals with Production of Musical Sound.
We studied the orchestral strings as examples of the string instruments.
Physics of Music, Lecture 12, D. Kirkby

3. The Guitar
The guitar is an older instrument than the violin, and probably originates from Egypt over 3000 years ago. The modern guitar usually has six strings tuned to E2, A2, D3, G3, B3, E4 (intervals of a 4th, 4th, 4th, 3rd, 4th).
Physics of Music, Lecture 12, D. Kirkby

4.                                                                  
                                                       
Guitar Construction
Like the violin, the guitar has a thin top plate (~2.5mm). The guitar has more substantial structural reinforcement inside its body:
Physics of Music, Lecture 12, D. Kirkby

5. Air escapes from the guitar body through a large round hole under the strings (compare with the violin f-holes). The guitar neck is fitted with frets to make finger positioning easier. Guitars are usually plucked (or picked) and not bowed.
Physics of Music, Lecture 12, D. Kirkby

6. Guitar Body Vibrations
                                                                 
                                                                 
                                                                 
Guitar Body Vibrations
At high frequencies, most of the guitar’s sound is produced by vibrations of the thin top plate alone. At low frequencies, both the top and back plates vibrate to change the volume of air contained in the body, and therefore pump air out through the sound hole.
These images show Chladni patterns for a guitar top plate:
Physics of Music, Lecture 12, D. Kirkby

7. Electric Guitar and Bass
The electric guitar and bass usually have solid bodies and so cannot produce a useful amount of sound by string vibrations alone.
Instead, a wire coil (pickup) senses the disturbance of a magnetic field due to the vibrations of the nearby metal string. The pickup generates an electronic signal that varies in synch with the motion of the string vibrating over it.
Physics of Music, Lecture 12, D. Kirkby

8. Other String Instruments
There are many other string instruments that we will not have time to cover…
Physics of Music, Lecture 12, D. Kirkby

9. Guitar Demonstration
Listen to the guitar being played (thanks to John Nuch).
We will analyze the guitar’s sound using the freeware Spectrogram software for windows:
Look for:
The attack transients and slow decay in the envelope.
The change in timbre from attack to decay.
The change in timbre depending on pluck location.
Compare finger and pick.
Physics of Music, Lecture 12, D. Kirkby

10. Woodwind Instruments
Woodwinds are one of two groups of instruments that are played by blowing into them (the other group is brass instruments). Examples of woodwind instruments are the flute, clarinet, saxophone, oboe, and bassoon.
The common features of woodwind instruments are:
A vibrating “reed” at the mouthpiece end
An air column open at the far end
Tone holes along the air column
Woodwinds were originally made of wood.
Physics of Music, Lecture 12, D. Kirkby

11. Energy Flow and Feedback
The source of energy in a woodwind instrument is a player’s breath.
There are two resonators in a woodwind: the reed and the air column. The resonant frequencies of the reed are much higher than those of the air column. The two resonators interact through a feedback process.
The player transfers energy directly to the reed, and then some of this energy, in turn, is stored in the air column. Less than 1% of the player’s energy is radiated as sound.
Physics of Music, Lecture 12, D. Kirkby

12. Woodwind Categories
The woodwind instruments divide naturally into three categories according to the type of reed they use:
Single-reed instruments (clarinet, saxophone)
Double-reed instruments (oboe, bassoon)
Air-reed instruments (flute, whistle)
cane
reeds
Arundo Donax
Physics of Music, Lecture 12, D. Kirkby

13. Woodwinds in the Orchestra
Physics of Music, Lecture 12, D. Kirkby

14. Listen to these samples of the four orchestral woodwinds:
(from
Physics of Music, Lecture 12, D. Kirkby

15. Single Reed Instruments: Clarinet
Physics of Music, Lecture 12, D. Kirkby

16. Single Reed Instruments: Saxophone
The saxophone is a recent addition to the woodwinds (invented in 1846 by Adolphe Sax).
Alto sax
Baritone
sax
Soprano sax
Tenor sax
Physics of Music, Lecture 12, D. Kirkby

17. Double Reed Instruments: Oboe
Double reeds are formed from a folded piece of cane:
English horn
Physics of Music, Lecture 12, D. Kirkby

18. Double Reed Instruments: Bassoon
bocal
Contrabassoon
Physics of Music, Lecture 12, D. Kirkby

19. Standing Waves in the Air Column
All woodwinds have one end open, which must therefore be an anti-node for any standing waves in the air column (assuming that all finger holes are covered).
The boundary conditions at the mouthpiece end depend on the type of reed being used:
Cane reed instruments are essentially closed: the mouthpiece is a node.
Air reed instruments are essentially open: the mouthpiece is an anti-node.
Physics of Music, Lecture 12, D. Kirkby

20. Standing Waves Review Air reed Cane reed f1=v/2L 2f1 3f1 4f1 f1=v/4L
Physics of Music, Lecture 12, D. Kirkby

21. Boundary Conditions: Pitch and Timbre
The two main differences between these boundary conditions are that:
The cane reeds have a lower fundamental frequency for the same length of instrument. The clarinet and flute are about the same length but the clarinet’s lowest note is about an octave lower than the flute’s.
The cane reeds are (ideally) missing all even harmonics
The lack of even harmonics influences the timbre of the instrument in a characteristic way. Compare these sounds:
Fundamental only
11 first harmonics
6 first odd harmonics
Physics of Music, Lecture 12, D. Kirkby

22. Air-Reed Interactions
The air column and mouthpiece reed are both resonant systems, each with their own resonant frequencies.
A common feature of the woodwind instruments is that the reed’s resonant frequencies are much higher than the air column’s resonant frequencies.
How do the reed and the air column interact to determine the overall resonant response of the instrument?
Physics of Music, Lecture 12, D. Kirkby

23. There are 3 possibilities:
Since the energy source (breath) is a noisy source, energy is available to the instrument over a wide range of frequencies.
There are 3 possibilities:
Reed vibrations dominate the overall response
Air column vibrations dominate the overall response
Both reed and air column vibrations coexist
String instruments also consist of two primary resonators (strings and body) whose vibrations coexist to produce sound.
Physics of Music, Lecture 12, D. Kirkby

24. The air column is a more massive resonator than the reed.
In woodwind instruments, two factors combine to ensure that the air column vibrations dominate the instrument’s response:
The air column is a more massive resonator than the reed.
The reed resonance is of lower quality because of damping (e.g., due to the player’s lips on a cane reed).
The process by which one resonator takes over and forces the other resonator into non-resonant vibrations is called feedback.
Physics of Music, Lecture 12, D. Kirkby

25. Example: Feedback in a Clarinet
When you blow gently through a clarinet mouthpiece, your breath goes through unimpeded.
As you blow harder, your air pressure forces the reed to partially close.
Physics of Music, Lecture 12, D. Kirkby

26. A pulse of air sent down the instrument from the mouthpiece has a negative reflection from the open end.
t = 0
High breath pressure closes reed
t = L/v
t = 2L/v
Low mouthpiece pressure closes reed
When this negative pulse returns to the mouthpiece, it creates suction that pulls the reed closed and cuts off the flow of air into the instrument.
Physics of Music, Lecture 12, D. Kirkby

27. The negative pulse is reflected from the mouthpiece and makes another round trip. This time, the negative reflection restores the original positive pulse.
t = 2L/v
Low breath pressure opens reed
t = 3L/v
t = 4L/v
High mouthpiece pressure opens reed
The returning pulse pushes the reed open when it gets back to the mouthpiece, a time 4L/v after the initial pulse.
Physics of Music, Lecture 12, D. Kirkby

28. Clarinet Feedback Loop
The reed and air column are in synch when the reed vibrates at f = v/4L. The effects of the pressure inside the mouthpiece provides positive reinforcement (or feedback) to the effects of the player’s breath pressure.
High breath pressure closes reed
Low mouthpiece pressure closes reed
High mouthpiece pressure opens reed
Low breath pressure opens reed
Physics of Music, Lecture 12, D. Kirkby

29. Effects of Tone Holes
So far, we have assumed that all the finger holes are closed so that we have a simple air column.
Actual Length
Real woodwind instruments have holes along the length of their air column. We call these tone holes or finger holes.
How does the presence of tone holes change the resonant response of the air column?
Physics of Music, Lecture 12, D. Kirkby

30. Open finger holes change the effective length of the air column
Open finger holes change the effective length of the air column. A small hole has a negligible effect while a large hole (hole diameter > instrument diameter) completely opens the instrument to the air at the hole position.
Effective Length
Effective Length
This is the purpose of tone holes: to change the fundamental resonant frequency (note) of the instrument.
Physics of Music, Lecture 12, D. Kirkby

31. Most fingerings have all holes closed up to a certain distance from the mouthpiece, and then all remaining holes open.
Effective Length
In realistic instruments, the size of the holes is somewhere in between the limiting cases, so we cannot ignore the section of the instrument with open holes.
Physics of Music, Lecture 12, D. Kirkby

32. Open holes let low frequency sounds out more easily than high frequency sounds. Why? The hole contains its own small air column, and so is also a resonator. At low frequencies, we are driving this small air below its resonant frequency and it responds in phase, allowing sound to escape. At high frequencies, we are driving above the resonant frequency of the small air column and it responds out of phase, preventing air from escaping.
Physics of Music, Lecture 12, D. Kirkby

33. The net result of the open tone holes is to let low frequency sounds escape but trap the high frequency sounds.
This means that the boundary condition at the open end now depends on frequency: the instrument looks longer to higher frequency sound. As a result, the timbre of an instrument will depend on the number of open holes in a particular fingering.
Physics of Music, Lecture 12, D. Kirkby

34. Effect of Closed Tone Holes
Closed tone holes add bumps to the otherwise smooth inside surface of the instrument.
These bumps slow sound waves down slightly, changing the velocity v in this formula for the frequencies of each standing wave:
fn = n (v / 4L) , n = 1,3,5,…
An decrease of v is mathematically equivalent to an increase in L.
Physics of Music, Lecture 12, D. Kirkby

35. Register Holes
Most fingerings have all tone holes closed up to some point, and then the remaining holes open.
Some holes are specially positioned to create a node that kills the fundamental standing wave, and forces the air column to vibrate at a higher harmonic.
These are called register holes and are made small enough that the holes further down the instrument can still be used to change the effective length.
The purpose of register holes is to allow the instrument to be played in more than one register.
Physics of Music, Lecture 12, D. Kirkby

36. Effect of Register Hole on Standing Waves
Air
reed
f1=v/2L
2f1
3f1
4f1
Cane
reed
f1=v/4L
3f1
5f1
7f1
Physics of Music, Lecture 12, D. Kirkby

37. Ideally, there should be one register hole for each fingering
Ideally, there should be one register hole for each fingering. In practice, there are only a few register holes that are shared by all fingerings.
The oboe effectively has 3 register holes, the saxophone has two and the clarinet one. As a result of this compromise, the timbre of an instrument can be quite different in different registers.
Physics of Music, Lecture 12, D. Kirkby

38. Cylindrical and Conical Bores
The flute and clarinet have cylindrical bores with diameters of about 19mm and 15mm respectively.
The oboe, bassoon and saxophone have conical bores with opening angles of 1.4o, 0.8o, and 3o - 4o respectively. (A 2o cone angle corresponds to a widening of 7mm for every 10cm of length).
How does this tapering of the air column change the instrument’s sound?
Physics of Music, Lecture 12, D. Kirkby

39. Standing Waves in a Conical Bore
A tapered air column has resonances at essentially the same frequencies as a cylindrical air column that is open at both ends. Surprisingly, this is still a good approximation even when the cone is cut short and does not taper all the way to a point.
Physics of Music, Lecture 12, D. Kirkby

40. Bells
Clarinets and saxophones have a bell section at the end with a curved flare (as opposed to a conical flare).
The bell has relatively little effect on the instrument’s timbre, except for the lowest notes (where almost all tone holes are closed).
One of the roles of the bell for low notes is to approximate the effect that an extra length with open tone holes would have, thus matching the timbre of higher-pitched notes.
Physics of Music, Lecture 12, D. Kirkby

41. Formants
Some resonances are not sharply peaked near one frequency, but instead spread over a broad range of frequencies. Example: resonances of a shower stall.
Broad resonances are called formants, and play a role in the timbre of woodwind instruments (formants play an even more important role in speech and singing).
Look for formants in the frequency spectra of these sounds:
Clarinet (formants at Hz, Hz)
Oboe (formants at 1400 Hz, 3000 Hz)
Bassoon (formants at Hz, Hz)
Physics of Music, Lecture 12, D. Kirkby

42. Summary
We studied the cane reed instruments (single and double reed) as examples of the woodwind family.
Woodwind instruments use feedback from an oscillating air column to control the flow of air into an instrument.
We studied the following effects on timbre:
All harmonics or only odd harmonics
Open tone holes
Flared bell
In the next lecture, we will finish our study of woodwinds with the air reed instruments.
Physics of Music, Lecture 12, D. Kirkby