 The Clarinet BBoard
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Author: Keil
Date: 2001-03-22 03:03
I have to give a presentation on the physics behind clarinet playing such as being a closed end tube, harmonics, octaves, quality of tone, partials, fundamental notes, overblowing a 12th and so forth... i could really use help. I know the basics but somethings i'm not sure about. If you guys could help me by posting what accurate info you know that will really help me a lot. Especially info about harmonics, overblowing a 12th and fundamentals. Thanx!
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Author: joevacc
Date: 2001-03-22 03:14
Kiel,
A good book to have is... "Fundamentals Of Musical Acoustics" by Arthur H. Benade
ISBN 0-486-26484-X
Looking forward to the posts on this one!
Best,
jv
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Author: Nate Zeien
Date: 2001-03-22 04:15
Hmmm... Every time I get technical with this kind of thing, people seem to run away. :-) A couple questions for you, first... Do you want general acoustic principles of music, or do you want to concentrate on the specifics of the clarinet? Also, when does this presentation need to be given? How much info do you need? I could also recommend a couple of books, depending on how much time you have, as well. Let me know exactly what you want, and I'll probably start babbling... Unless of course it's something I don't know about, and then I keep my mouth shut. :-) Cheers! -- Nate Zeien
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Author: Gordon (NZ)
Date: 2001-03-22 12:54
Yes. Unless this excellent hyperphysics web site seems too elementary don't bother with Benade. It really is quite technical.
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Author: Don Poulsen
Date: 2001-03-22 13:02
I wonder why everyone concentrates on acoustics and harmonics and ignores the physics that cause sound to be produced in the first place? Without the reed vibration, which can be explained by the same principle that allows airplanes to fly and ping pong balls with "English" on them to curve, there would be no sound at all. I'm talking about Bernoulli's Principle, an explanation of which can also be found at the physics Web site.
Simply put, the velocity of the air passing over the reed causes a low-pressure zone on that side of the reed. The higher pressure on the other side of the reed forces the reed to close against the mouthpiece. Because air is no longer moving on the mouthpiece side of the reed, the pressures equalize and the reed springs back to the open position. Air starts moving past the reed again and the cycle starts over.
The tube we call a clarinet is, at its most basic, a device to control the frequency of the reed's vibration. (I know - I offended your aesthetic sensibilities with the last sentence, but right now I'm looking at it from a purely scientific viewpoint. When I play, I don't think about this stuff and just concentrate on the aesthetics.)
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Author: Stephen Froehlich
Date: 2001-03-22 13:40
Now don is sending everyone scrambling for their fluid dynamics text to look up the Bernoulii equations. I hope Keil doesn't need a great deal more than a first order description of this.
First order description:
The bernoulii effect causes the reed to move, which drives the end of the clyinder that the reed happens to close, and the frequency of the harmonic vibration of the air column is determined by the length of the tube. The cylinder is considered closed on the reed end because the surface there acts as an acoustic reflector (a wall). The air flow is nowhere near acoustic velocities, so it does not effect the vibration of the air column, only the bernoulii effect and other fluid dynamic forces driving the reed in the first place.
We're waaaaaay in nonlinear land already, I'd hate to try to include the bit where the reed shuts off its own air flow and causes the bernoulii effect to decrease, where the spring force of the reed takes over and it "springs" back into an open position and the air flow starts over again. Then there's the whole question of how that interacts with the resonant chamber known as the mouth and throat on the other side, etc.
All of this is why instrument making is more art than science, as is reed/moutpiece selection, and how to make a beautiful tone in general.
Now if only someone could explain to me what about the design of the Kohlert I bought from D. Spiegethal makes it the loudest bass I've ever heard much less played. It really has a saxaphone sized sound if you want it too.
Forgive the blabbering -- Stephen
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Author: Mario
Date: 2001-03-22 14:29
OK. This is really getting interesting.
Now, we understand what happens with the reed end of the tube (i.e.: why the reed closes) as a starting point of the process.
The reed closing creates a pulse (a pressure wave). This pulse travels to the open end of the tube (essentially where opened finger holes appear) AND BOUCES BACK (this is weird to understands and quite counter-intuitive). Using an electrical or fluid analogy, the pulse bouces back because there is a sharp impedence or pressure differential at the open end (from high to low pressure), causing a physical phenomenom called reflection.
Eventually (a few micro-second later) this returning pulse hits the reed AND OPENS IT. The brenoulli effects immediately takes over and closes it right away.
This is how the reed vibrates at the frequency of the tone being produced.
The beauty of all of that is the clarinet actually operates like a close-loop control system (lots of maths there) where the vibration of the reed is in fact modulated by the length of the tube through returning energy present in reflected pressure wave.
The period of this travel down and up the tube determines the frequency of the closing-opening cycle of the reed. For instance, playing clarion B create pulse trains that make the reed vibrates around 440 Hz.
Because the clarinet is a cylindrical closed pipe, the wave bounces back incurring a phase shift of 90 degrees (if I remember) (the mathematics for this are strange but quite exciting). Others winds such as sax and oboe (conical closed pipes) or the flute (cylindrical open pipe) do not incur phase shifts at the open end. This is why they overblow to even partial, while the clarinet overblows to odd partial.
The phase shift is also why a clarinet plays as low as it does. For a given tube length, a clarinet plays one octace lower than a flute or saxophone. Great maths here.
This returning pulse combines with pulse coming down and create stationary waves here and there, with all kinds of amplitude shapes. This is what provides colors, tone, tuning, resonance, etc.
A warm clarinet is sharper because warm air (lower pressure) encourages faster return.
Closing and opening holes down the tube affect color and tuning by shaping the location and form of the stationary waves. Clarinet makers spend a life-time figuring out the exact shape, location and dimensions of tone holes in order to build an instrument whose stationary waves promote even color, intonation, resistence, etc.
Just beautiful.
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Author: bob gardner
Date: 2001-03-22 15:36
I loved Don's coments on the reed. With out the reed we have NOTHING.
happy playing
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Author: Stephen Froehlich
Date: 2001-03-22 17:19
To comment on Mario's statement, it is counterintuitive for a wave to reflect when it goes from high impedance to low impedance. Its just not how we think of things, but the only reason is because we live in a world of air and walls and no other acoustic materials. In truth it is ANY impedance mismatch that occures on a length scale that is small compared to the wavelength itself that causes a reflection.
There are several examples of reflections when going from high to low impedance. The light reflecting off the top of the pool when you're underwater is an example. The same goes for sound going from water to air - that's why active sonar won't do any good finding surface ships. Another example is a string. A clarinet is essentially equivalent to a string you're holding on one end and that is free to move on the other. Lay it out on the table and wiggle the string - you can set up a standing wave. (or spin the string around in the air, this is the same deal, you can create odd harmonics)
Feynman gives a good discussion on the subject of reflection in his lay-man's book: QED
The mystery to me at this point is why a saxophone has even harmonics. I guess the conical shape curves the impedance such that it works like a cylinder closed on both ends, or is it just the gradual impedance shift?
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Author: Dee
Date: 2001-03-22 19:34
Stephen Froehlich wrote:
>
> The mystery to me at this point is why a saxophone has even
> harmonics. I guess the conical shape curves the impedance such
> that it works like a cylinder closed on both ends, or is it
> just the gradual impedance shift?
The key is that the sax (along with the oboe, English horn, and the brass instruments) have conical bores. A conical bore, whether closed at one end or open on both ends will give you the even harmonics.
The clarinet is unique (other than organ pipes) in acting like a cylinder closed at one end.
In other words, saxes, flutes, oboes, etc are "normal" and we are the oddballs.
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Author: Mario
Date: 2001-03-22 19:42
Hum. I am not at home these days so I will try to answer from memory here.
Why do closed-cylindrical pipes (and open cylindrical pipes for that matter) behave the way they do?
I is related to the end-tube effect of impedence mismatch, but is also related to energy dispersion. In a cylindrical closed-pipe, energy loss is linear, while in other kinds of pipes, energy loss is exponential (actually, a power of two). When pressure waves remain centered in a long cylinder, they keep their energy longer.
In conical pipes, the energy is spread on an expending plane (power of 2) and the energy is dissipated faster.
For a given conical tube length, a pressure wave has less energy remaining when it hits open holes, in comparison to a cylindrical tube. This affects the impedence differential, the energy of the returning wave, its phase shifts, the localisation of its stationary waves, etc. Sexy maths here again.
Strangely (but obviously if you look at the maths), the open cylinder (such as the flute) behaves the way closed conical tubes do. In fact, flutes, saxes and oboes have the same physics. The clarinet is out there, standing tall amongst lesser woodwinds with accoustic properties found only in majestic pipe organs.
There are very few shapes of pipes out there that can create stationary waves and closed-loop systems. We use three at this time (open cylinders, close conicals, closed cylinders). An open conical does not have stable states for instance and is useless as a shape for musical instruments.
However, by working from the maths, scientists have conceptualized what they call a Besnel pipe which is a pipe with a complex internal curvature based on Besnel functions. They have properties that would make them good shapes for musical isntruments. But they are mecanically challenging to build since they are all curves. It is why they do not exists at the moment. A Besnel pipe ressembles a snake that have swallowed a rabit: thin at the end, bulging in the middle, with curvature gradiants that only computer-driven machinery could produce.
If I were to do a Phd in Musical Accoustics, I would try to invent such as wind instrument.
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Author: Mario
Date: 2001-03-22 20:14
On the issue of Besnel shapes, it has been speculated that the bulging bell sometimes found on ancient instruments (Oboe d'amour, Clarinet d'amour as two instances) are crude approximation of Besnel shapes. These instruments have a velvety, almost mystical tone in the few long-tube notes that are affected by the bulging bell. Naturally, only three of four notes can be affected, and only for a small portion of the return path. In spite of that, the purety and magic of the resulting tones is almost erotic in feel. Hence the name "d'amour", since music taking advantage of the buldging end tended to be quite seductive or utterly sad - the kind of music you play while courting a beautiful woman, or while mending a broken heart.
We can only imagine the pure, sweet, mesmerizing tone of an instrument designed entirely around a Besnel pipe. BTW, a Besnel pipe overblow to odd partials. In its strangeness, it actually behaves like a clarinet.
Jonathan Cohler once told me that the clarinet is a freak instrument. Crual, but delightfully true!
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Author: Keil
Date: 2001-03-22 21:51
I have to make my presentation on the March 29th. I really need concentrated info on the clarinet. What's the significance of having even partials present or odd partials present? what does all of this translate to in the end when it comes to making a good tone? or the desired tone? do clarinets have fundamentals? do we do enharmonics like string instruments i.e. violin?
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Author: Stephen Froehlich
Date: 2001-03-22 23:07
I see now. I poked around Bill's link and I understand the conical tube now. (Enough, at least, that I don't feel compelled to work through the equations any more.)
What are examples of closed cylinder instruments?
This explains why, for example, a Sax can sound just like a euphonium when it wants to.
Another bit of interest that I dug up there: Traditionally, as I'm sure many of you know, the clarinet is the instrument that is thought to most resemble the human voice. The reason is that the vocal chords act like the reed and make the human voice cavity a closed cylinder (at least to a first approximation), which means that our voice also is dominated by odd harmonics.
I guess to make one, you'd have to do it brass / flute-style. First turn a form on a CNC lathe and then hammer a metal skin to the form. How radical are these curves?
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Author: Melanie
Date: 2001-03-23 04:30
To add more fuel to the fire:
One of the reasons my teacher cites for clarinets not needing vibrato is the fact that we have far more overtones ringing than our open pipe, conical bore cousins. This leads to a fuller, richer sound making vibrato unnecessary -- in many instances, it serves to beef up a harmonically dull sound. How does this work?
Melanie
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Author: Eoin McAuley
Date: 2001-03-23 08:06
Keil, you seem to be drowning in a mass of information, very little of it relevant to your presentation. Here's a summary.
1. The clarinet has a basically cylindrical shape.
2. Due to its shape and the construction of the mouthpiece, it plays with a peculiar acoustical property:
a) the fundamental note is an octave lower than you would expect
b) the even partials (notes an even multiple of the fundamental frequency) are very quiet
c) the odd partials (notes an odd multiple of the fundamental frequency) are strong.
This is unusual among musical instruments. The only other one that does this is the Krumhorn.
3. The sound produced, because of the lack of even partials, sounds different. (Insert your own description here - mournful, deep, warm etc). It looks approximately square wave shaped on an oscilloscope.
4. The sound is produced by a resonance between the air in the tube and the vibrating reed. A vibrating reed on its own will produce a squawk, that is, a note with many different frequencies in it. When tied to a column of air, it resonates, so it can only produce frequencies at multiples of the fundamental frequency of the tube of air.
5. The fundamental frequency of the tube of air is varied by changing its length. When you open a tone hole, you effectively shorten the tube until it is only from the mouthpiece to that hole. That is if the hole is a big one.
6. If you open a very small hole approximately one third of the way along the clarinet, you can force the clarinet to jump out of the fundamental vibration and start resonating at three times its normal frequency. This is overblowing into the Clarino register.
7. By opening two holes along the length, the register key hole and the L1 hole, you can force it to vibrate at 5 times the fundamental frequency. This is the lower altissimo range C# up to F#.
8. By opening three holes along the length at the right positions, you can get 7 times the fundamental frequency. Look at the standard fingering for altissimo G for an example.
All the best, and good look with your report.
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Author: Dee
Date: 2001-03-23 10:56
Stephen Froehlich wrote:
>
> ... Traditionally, as
> I'm sure many of you know, the clarinet is the instrument that
> is thought to most resemble the human voice.
Actually if you search deeper through greater timespans, there have been several instruments, when at the height of their popularity, were said to most resemble the human voice.
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Author: Stephen Froehlich
Date: 2001-03-23 12:13
OK, its time to actually answer Keil's questions:
> I have to make my presentation on the March 29th. I really need
> concentrated info on the clarinet. What's the significance of having
> even partials present or odd partials present?
The clarinet has the odd partials (fundamental, 3, 5, etc.) In short, it just sounds different. There are many fewer high harmonics than a trumpet for example.
When you add only odd harmonics, you get a waveform called a triangle wave, this is what the clarinet most closely resembles except that a triangle wave requires many higher harmonics.
It looks like; //////////
When you have all of the harmonics, you get a discontinuious wave form such as:
Sawtooth: /|/|/|/|/|/|/|
_ _ _
Square |_| |_| |_|
However, these require MANY of the higher harmonics. When a synthesist wants to make a "brass" sound, for example, they start with a sawtooth and then filter the higher harmonics down.
If you look carefully at different instruments at:
<A href="http://hyperphysics.phy-astr.gsu.edu/hbase/music/musinscon.html#c1">http://hyperphysics.phy-astr.gsu.edu/hbase/music/musinscon.html#c1</a>
you see that its a trade-off. Clarinets have higher harmonics than a sax or flute but are missing some in the middle.
> What does all of this translate to in the end when it comes to making a
> good tone? or the desired tone? do clarinets have fundamentals? do
> we do enharmonics like string instruments i.e. violin?
This simply translates into the sound of the clarinet. As you know, the technique of playing a sax is nearly identical to the clarinet, and saxes can (debatably) make a good tone. That's because the driving mechanism (reed/mouthpiece) is nearly identical.
The clarinet has a true fundamental. Examples of tones that don't have a strong root (again, see the link) are double-reeds and brass pedal tones. Poke around the website a little more.
OK, I must admit, I don't know what an enharmonic is.
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Author: Stephen Froehlich
Date: 2001-03-23 13:40
I don't know about Keil, but I'm learning an immense amount. Thanx everyone for correcting my rampant speculation. This explains why the clarinet and sax sound so much more similar in the upper register, the even harmonics don't seem to be damped nearly as much up there as they are in the fundamental register. Something tells me that this has to do with the compromise placement of the register hole, but I'm guessing.
One thing to note is that the graphs at GSU are linear, and at Ohio State are logarythmic.
So, what allows the even harmonics, the register hole? The reed opening? The bell? Or is it just the nonlinear nature of the system?
I have to admit, I'm still struggling to get my mind around all of this - even with a fizix degree under my belt.
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Author: Gordon (NZ)
Date: 2001-03-23 13:58
The 2nd & 3rd items form the end of the site map here may be of interest, although the sound quality seems bad.
http://library.thinkquest.org/19537/
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Author: Gordon (NZ)
Date: 2001-03-23 13:59
What amazing information on this thread. So much expertise, and presented with excitement. Wow!
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Author: Dee
Date: 2001-03-23 14:12
A sound that has *ONLY* odd partials produces a square wave form not triangular. Now since the clarinet does produce some even partials (although not accessible by the player), the clarinet waveform only approximates a square wave.
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Author: Nate Zeien
Date: 2001-03-23 21:33
Jeez! I was waiting until I had a little more time to write out a somewhat detailed post. I come back to do so, and look at what I've missed! Looks like I'll have to be faster next time. :-) -- Nate Zeien
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Author: Mark Charette
Date: 2001-03-24 02:47
A clarinet's body does not resonate like most stringed instruments; therefore there's no "fundamental pitch" of the clarinet. By humming into the f-holes of a violin or like instrument you can find the "fundamental pitch" (the natural resonance), which is also partly responsible for "wolf tones" on those instruments. The pitch of the produced sound on a clarinet is dependent on the effective air column length and mode of the driving system (reed/mouthpiece) alone.
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Author: Keil
Date: 2001-03-24 04:05
WOW!!! that's intense... this whole discussion has been and i'm sure will continue to be extremely helpful for me and anyone else in the future... thank you all.... please feel free to continue giving information. One can never know to much!
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Author: Jean Dagenais
Date: 2001-03-24 12:08
This is very very interesting!
One area that I am interested to know more about is how clarinetits control the quality/texture of the tone?
I know that a good clarinet/mf,reed, etc is of primary importance, but the part that is unique to each clarinetist is really fascinating.
I know that to produce a tone, I can control these variables: speed of air, lips pressure, jaws position, throat, tongue position,etc.and that I can get very distinctive sound when I vary these aspects.
What is really going on when I change these variables?
How does this impact the physics of the clarinet sound production system?
I suspect that I am impacting the harmonic & partials content of the tone, and also the frequency of the tone. I am also impacting the attack and decay, etc.
Any ideas or information about these aspects?
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Author: Rene
Date: 2001-03-24 13:20
Keil, while I would like to write about the physics of the air column in a clarinet versus an oboe (or a trumpet), I will defer that to some later point, when I have more time. It is involved. Also thinking in terms of reflection does not help much. it is a matter of getting a stable solution to a differential equation.
Instead I would answer one of your questions: The effect of having odd partials is that the clarinet overblows in wider intervals and thus has a much greater range then other instruments. To the expense that the clarinet has to use short throat tones to fill the gap between the basic and the clarion register. I guess everyone here knows that, but it has not been said in this thread.
Rene
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Author: Keil
Date: 2001-03-24 14:49
Rene, does that explain why our throat tones are considerably weaker than the rest of the clarinet's range? if so can you elaborate on why and how?
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Author: Don Poulsen
Date: 2001-03-24 17:08
Let's see how far I can step out on a branch before it starts breaking.
To try to start to answer Jean's questions as well as Keil's question regarding fundamental pitch, as Mark said, the clarinet itself does not have a fundamental pitch, but I would suspect that any given reed does. That pitch would be primarily controlled by the stiffness (mistakenly referred to as "hardness") of the reed, as well as its size and shape. (Now we are getting into solid mechanics whereas we have been primarily talking about fluid mechanics to this point.) The shape of the mouthpiece's opening and how your lips hold the reed are also going to affect how the reed vibrates and the frequencies it prefers. The tone that is produced is the combination of all the individual frequencies produced in their various amounts. A stiffer reed and narrower mouthpiece opening should favor higher harmonics, for example. And the narrowness of the opening affects the velocity of the air. The internal shape of the mouthpiece should also affect the velocities and pressures in the mouthpiece, which affect reed vibration. And everything plays off of everything else, like musicians jamming in a jazz ensemble.
In addition, I suspect that the reed tries to produce all of the harmonics, odd and even, but the tube we call a clarinet only likes the odd ones. However, it just doesn't do a perfect job of dampening the even ones, so they get produced to some extent.
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Author: Rene
Date: 2001-03-25 07:40
To keep this fascinating thread alive, the relatively short, but wide air column in the the throat register seems to me one of the reasons for its relative weakness. Adding to this is the compromise with the double use of the Bb and register key. By the way the long E/B is a compromise too, unless you have a clarinet with a special resonance mechanism. So its the expreme ranges, which are troublesome, it seems. Alas my claim that the great tonal range we enjoy is payed for.
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The Clarinet Pages
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