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Overblowing wind instruments

by bcrowell
Tags: instruments, overblowing, wind
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bcrowell
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Dec7-12, 07:09 PM
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Wind instruments exhibit overblowing: http://en.wikipedia.org/wiki/Overblowing

Naively, I would expect that if one, for example, blew harder on a whistle, or blew at a different angle on a flute, the result would be as follows. You produce some noise spectrum, which becomes a different noise spectrum when you change how you blow. This noise spectrum drives the air column, which has a series of discrete resonances at frequencies fo, 2fo, 3fo, ... (or possibly only the odd multiples, if the boundary conditions are asymmetric). The air column responds strongly at those frequencies, with amplitudes that are proportional to the noise spectrum at those frequencies and also proportional to the strengths of the resonances. The spectrum that results contains frequencies fo, 2fo, 3fo, ..., and overblowing only changes the relative strengths of the harmonics, which means there is only a change in timbre, not a change in pitch. The pitch still corresponds to that of the fundamental fo. The timbre varies continuously as a function of how you blow. It should be impossible to produce a change in pitch without the use of a register hole or register key.

What really happens is that, e.g., for symmetric boundary conditions, overblowing produces a set of frequencies 2fo, 4fo, 6fo, ... The odd multiples of fo are eliminated completely. The period of the sound is now 1/(2fo), and the musical pitch corresponds to 2fo. The change in pitch is discontinuous as a function of how you blow. A register hole or register key makes the instrument easier to play fluently, but you can overblow without needing to use the register hole/key.

Why is this?

It seems like the effect must be some nonlinearity in the system. Is it a mouthpiece/reed effect, or is it an effect that happens because of the behavior of the air column, tone holes, radiation patterns from the tone holes and bell, ... ?

If it's a complicated, nonlinear mouthpiece/reed effect, are there any examples that are easy to understand?
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Studiot
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Dec8-12, 03:55 AM
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Good morning, bcrowell.

Firstly you need to distinguish between reeded and plain-pipe wind instruments.

You will find a mathematical discussion of the harmonic distribution in both types in chapter 9of

The Dynamical Theory of Sound by
Sir Horace Lamb
sophiecentaur
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Dec8-12, 04:52 AM
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That wiki article suggests that the direction of the injected air stream is responsible for finding the overblow mode. That sounds a convincing argument to me - you are just changing the boundary conditions so different overtones will be favoured..

mahur
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Dec8-12, 07:30 AM
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Overblowing wind instruments

theorethical study is misleading.
I play woodwind instruments and I very well know owerblowing makes the pitch higher.
owerblowing triggers upper harmonics plus makes the pitches higher.
for example lets assume you blow 1f then when you owerblow you get a little bit higher than 2f.
the woodwind instruments can be fine tuned by lips and diaphram.
a woodwind instrumentist should have a good ear sensitivity.
sophiecentaur
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Dec8-12, 10:32 AM
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Quote Quote by mahur View Post
theorethical study is misleading.
I play woodwind instruments and I very well know owerblowing makes the pitch higher.
owerblowing triggers upper harmonics plus makes the pitches higher.
for example lets assume you blow 1f then when you overblow you get a little bit higher than 2f.
the woodwind instruments can be fine tuned by lips and diaphram.
a woodwind instrumentist should have a good ear sensitivity.
Its how the overtones are 'triggered', that interests us. Overtones are not necessarily exact harmonics, remember - certainly not in wind instruments, as you have found. Actual air pressure / volume and the direction will make a difference to the effective length (where the resonance actually begins in the pipe - hence the resonance frequency).

Something that surprises me and is sort of relevant here: when you listen to orchestral pieces with Organ, the pitch of the organ seems to wander noticeably (to my ear at least). The opening of 'Also Sprach Zarathustra' by Richard Strauss is an example. The low organ note dies away and goes off tune - and it's not just one particular recording. I could expect an old disc recording speed to be affected by volume, one way or another but on a modern recording? Perhaps it's to do with the air pressure from the blower sagging after a sustained low note @forte.
AlephZero
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Dec8-12, 03:31 PM
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Your attempt at an explanation seems to leave out the key feature, which is the coupling between the oscillations in the pipe, and the air flow being blown across (note, across, not into!) the blowing hole.

The easiest instrument to study scientifically is the pipe organ, because it is entirely mechanical. Start here: http://www.ausgo.unsw.edu.au/music/p...etcher1976.pdf

Actually, the real "start" of the theory was the paper by Ising and Cremer (ref 1) in the above, but I've never been able to find an English translation. They came up with a non-dimensional parameter (the Ising number) which basically relates the time it takes the air-stream to cross the blowing hole of the pipe, and the period of the resonance of the pipe.

It's a slightly soberinig thought about the scientific method that people were designing pretty sophisticated wind instruments for thousands of years before anybody "really understood" how they worked. For example there was a very popular view expressed by organ builders, even in the early 20th century, that the speed of sound in a pipe must depend on the diameter of the pipe, since pipes with the same length and different diameters produce different pitches. (Of course that is correctly explained by the impedance of the air outside the end of the pipe, which is the cause of the "end correction" in simple physics experiments).

For flute acoustics, see http://www.phys.unsw.edu.au/music/flute/, and there is work on other wind instruments by the same research group.

For more on the science of pipe organs, google "johan liljencrants" (note that he died recently, so websites, links, etc may be in a state of flux)
bcrowell
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Dec8-12, 04:21 PM
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Thanks, AlephZero, for the links to the Fletcher paper and the flute page. I didn't find any specific discussion of overblowing in either of them, but the Fletcher paper does clearly state that there are two linear systems (jet and pipe) which interact in a nonlinear way. It seems like there's no conceivable way in which overblowing could happen if there were no nonlinearity in the system, so I guess that's it. I assume there must be something analogous for other instruments, e.g., nonlinear interaction between the reed/mouthpiece of a saxophone and the saxophone's air column.

Does this all sound right?

It would be nice to get some more specific insight into why overblowing occurs.
AlephZero
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Dec8-12, 06:03 PM
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Try this, including some experiments on overblown pipes. http://www.ece.uvic.ca/~bctill/paper...ltman_1976.pdf
As their introduction rightly says, "this involves the interaction between three different phenomena none of which are well understood".

The interaction between the air jet and the pipe depends on the instrument. Flue organ pipes are usually designed not to overblow, by choosing the right proportionns of blowing slot width, air pressure, and cut-up height (as defined by Fletcher), but I have seen a demo (by an organ builder, not a CFD specialist) of an ordinary-looking cylindrical pipe that sounded its first 6 harmonics in turn as the wind pressure was slowly changed.

There are a few types of flue organ pipes that produce mainly their first harmonic (2x or 3x the fundamental frequency) but they usually have a small hole bored in the pipe at the antinode of the fundamental frequency, to "kill" the fundamental resonance.

For reed organ pipes, the frequency is controlled entirely by the mechanical vibrations of the reed. The size and shape of the pipe acting as a resonator greatly affects the tone quality, but it is not necessarily tuned to the reed frequencyy. If may be double the fundamental length. Small amounts of (nonlinear) resonanace at 0.5, 1.5, etc times the dominant frequency don't affect the perception of the pitch, but they create a "fatter" tone quality (Heavy metal guitarists have discovered the same acoustic principle!) Some organ reed pipes have resonators of various weird and wonderful shapes that are not "tuned" to the fundamental reed frequency at all.

Woodwind reed instruments (and brass, where the player's lips form the reed) work the opposite way to reed organ pipes. The reed does not have any strong resonance itself. If you take the mouthpiece off the instrument you can "squeak" it at pretty much any frequency, just like blowing on a blade of grass as a reed. The resonances of the pipe are much more complicated than an organ pipe because of the finger holes, and for high frequency notes they depends more on the size and spacing between the holes than on the total length of the pipe. The player can control the wind pressure to match the frequency of the reed "sqeak" to the dominant resonance of the pipe. Large mismatches can produce intentional sqeaks and growls (listen to any good jazz sax or trumpet player).

There are a few so-called "capped reed" instruments (e.g. bagpipes) which have similar design to modern woodwind instruments, but the blowing pressure comes from bellows and a plenum chamber like an organ. Usually they do not have any capability to overblow (unless they are wrongly adjusted!), and the range of notes is therefore limited range compared with other wind instruments, i.e. to about a 2:1 frequency range.
bcrowell
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Dec8-12, 08:23 PM
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Quote Quote by AlephZero View Post
Woodwind reed instruments (and brass, where the player's lips form the reed) work the opposite way to reed organ pipes.[...] The resonances of the pipe are much more complicated than an organ pipe because of the finger holes, and for high frequency notes they depends more on the size and spacing between the holes than on the total length of the pipe.
This doesn't sound right to me. The basic physics of the tone holes in an instrument like the saxophone is that they simply shorten the effective length of the air column by terminating it at the first open hole. For any given fingering, the resonances are simple. They are just the multiples of the frequency corresponding to the one for which half a wavelength equals the distance from the mouthpiece to the first open tone hole. There are various complications, such as cross-fingerings, but that's the physics story in a nutshell.
AlephZero
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Dec9-12, 02:36 PM
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Quote Quote by bcrowell View Post
This doesn't sound right to me. The basic physics of the tone holes in an instrument like the saxophone is that they simply shorten the effective length of the air column by terminating it at the first open hole.
That is much too oversimplified. Get a simple wind instrument with no "keys", like a recorder or a tin whistle, so "what you see is what you get", and measure the hole positions along the length of the pipe. Compare with elementary theory for an open pipe termiated at the first open hole. The correlation between the two will be close to zero. (You can probably do this from a picture of an instrument, if you have access to a real one)

For a more realstic physical model, you have to treat the pipe as a branched system with the acoustic travelling wave partially reflected from every sound hole position. Even for "closed" holes, the cavity in the wall of the pipe has a significant effect on the acoustic impedance of the pipe, because it acts in a similar way to a step change in the pipe diameter (or more pedantically, as two step changes, one at each "side" of the hole).
sophiecentaur
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Dec10-12, 10:25 AM
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Quote Quote by AlephZero View Post
That is much too oversimplified. Get a simple wind instrument with no "keys", like a recorder or a tin whistle, so "what you see is what you get", and measure the hole positions along the length of the pipe. Compare with elementary theory for an open pipe termiated at the first open hole. The correlation between the two will be close to zero. (You can probably do this from a picture of an instrument, if you have access to a real one)
Absolutely right. When you learn to play the recorder 'properly', to get some of the notes right, you do it by covering additional holes lower down the tube. I never could fathom a systematic rule for it but it is necessary so there's more to it than just the length from mouthpiece to hole.
AlephZero
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Dec10-12, 12:29 PM
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Quote Quote by sophiecentaur View Post
Absolutely right. When you learn to play the recorder 'properly', to get some of the notes right, you do it by covering additional holes lower down the tube. I never could fathom a systematic rule for it but it is necessary so there's more to it than just the length from mouthpiece to hole.
Since humans don't have 12 fingers, there is always a tradeoff in making an instrument that will play a chromatic scale in tune. In fact there are (at least) three different "standards" for recorder fingering, and the hole positions and diameters are different for each. This page http://www.moeck.com/cms/index.php?id=194&L=1 has pictures of two of them.
bcrowell
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Dec10-12, 09:01 PM
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Quote Quote by AlephZero View Post
That is much too oversimplified. Get a simple wind instrument with no "keys", like a recorder or a tin whistle, so "what you see is what you get", and measure the hole positions along the length of the pipe. Compare with elementary theory for an open pipe termiated at the first open hole. The correlation between the two will be close to zero. (You can probably do this from a picture of an instrument, if you have access to a real one)
OK, I have a recorder I can use at work, and a convenient setup for measuring frequencies for a student lab, so I'll try it. When you claim "close to zero" "correlation," what exactly are you claiming? Are you claiming that even for a C scale (i.e., essentially just opening the holes one at a time, starting from the bottom), there will be close to zero correlation in the statistical sense of correlation (i.e., a small R^2 value)? I'd definitely bet a six-pack against that. Or are you just claiming that my simple explanation fails to explain stuff like cross-fingerings (which I specifically said it wouldn't do)? Or are you claiming that a C scale will just not give detailed quantitative agreement with my simple explanation (which wouldn't surprise me)?

I suspect that we just have differing ideas of how much simplification is too much.
AlephZero
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Dec10-12, 10:07 PM
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Quote Quote by bcrowell View Post
Or are you claiming that a C scale will just not give detailed quantitative agreement with my simple explanation (which wouldn't surprise me)?
Take the dimeusions of the "Nova N601 Descant" from http://www.dolmetsch.com/ourrecorders.htm. They don't give the overall length of the instrument, but there is stlll enough data to give an idea of the discrepancies from simple theory.

The first thing to notice is that the distance between the holes is almost constant, not decreasing logarithmically as simple theory would predict.

Make the reasonable assumption that the length of pipe below the lowest note is about 24mm, and the overall length is 304mm. By simple theory, the octave (hole 1) should be at 152mm, but it's actually at 145. That's about 0.8 of a semitone out compared with simple theorh.

On the other hand, if you treat the pipe and holes as a branched waveguide, it is possible to get an accurate mathematical model. It's hard to follow all the details on this page http://www.chrysalis-foundation.org/...tone_holes.htm without the earlier chapters of the book (which are not online) or the references, but compare the calculated and actual dimensions of a flute in table 8.1 - all within 1mm except for one hole (and he explains the reason for that qualitatively). This is still using "only" 19th-century modelling (as used by Boehm to redesign wind instruments), not a computer based "digital waveguide" model which is now the standard way to do physics based modelling of mosucal instruments.

Incidentally Tables 8.2(a) and (b) show the effect of the hole diameter on the hole positions. In that example, altering the diameter changes the required tube length by about 3%, which would correspond to half a semitone pitch change on the simple model.
AlephZero
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Dec10-12, 10:26 PM
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I guess this illustrates the difference between physics and engineering. A physicist mght be quite content with an explanation that is qualitatively correct and accurate to a few percent. On the other hand, if an engineer wants to simulate real or imagined musical instruments, and given that the difference between an equally tempered fitfh and a "pure" fifth is about 0.02 of a semitone, or about 0.1% frequency difference, a model that can't be made to work to that level of accuracy doesn't have much practical use.
bcrowell
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Dec10-12, 11:01 PM
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I see. Yeah, interesting cultural divide there :-) You should probably be glad that people like me aren't building the bridges you drive on.

I'm looking forward to doing the experiment. Should be fun.
dlgoff
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Dec11-12, 01:06 AM
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This may be of interest.

http://www.phys.unsw.edu.au/music/clarinet/

e.g. from Introduction to clarinet acoustics



and from How Do Woodwind Instruments Work?

sophiecentaur
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Dec11-12, 03:28 AM
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Quote Quote by bcrowell View Post
OK, I have a recorder I can use at work, and a convenient setup for measuring frequencies for a student lab, so I'll try it. When you claim "close to zero" "correlation," what exactly are you claiming? Are you claiming that even for a C scale (i.e., essentially just opening the holes one at a time, starting from the bottom), there will be close to zero correlation in the statistical sense of correlation (i.e., a small R^2 value)? I'd definitely bet a six-pack against that. Or are you just claiming that my simple explanation fails to explain stuff like cross-fingerings (which I specifically said it wouldn't do)? Or are you claiming that a C scale will just not give detailed quantitative agreement with my simple explanation (which wouldn't surprise me)?

I suspect that we just have differing ideas of how much simplification is too much.
The holes in the recorder will have different sizes. That implies that someone has already taken into account the failure to follow a simple rule, I think. I think one reason that a recorder is designed so specifically may be to remove the skill required for accurate note production. That's why it works so well (adequately) in groups of relatively unskilled child players playing in 'simple keys'. Oh god - twinkle twinkle again!!!


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