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Overblowing wind instruments

  1. Dec 7, 2012 #1

    bcrowell

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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?
     
  2. jcsd
  3. Dec 8, 2012 #2
    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
     
  4. Dec 8, 2012 #3

    sophiecentaur

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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..
     
  5. Dec 8, 2012 #4
    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.
     
  6. Dec 8, 2012 #5

    sophiecentaur

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    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.
     
  7. Dec 8, 2012 #6

    AlephZero

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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/people/publications/Fletcher1976.pdf [Broken]

    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)
     
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  8. Dec 8, 2012 #7

    bcrowell

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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.
     
  9. Dec 8, 2012 #8

    AlephZero

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    Try this, including some experiments on overblown pipes. http://www.ece.uvic.ca/~bctill/papers/numacoust/Coltman_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.
     
  10. Dec 8, 2012 #9

    bcrowell

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    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.
     
  11. Dec 9, 2012 #10

    AlephZero

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    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).
     
  12. Dec 10, 2012 #11

    sophiecentaur

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    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.
     
  13. Dec 10, 2012 #12

    AlephZero

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    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.
     
  14. Dec 10, 2012 #13

    bcrowell

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    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.
     
  15. Dec 10, 2012 #14

    AlephZero

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    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/flute_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.
     
  16. Dec 10, 2012 #15

    AlephZero

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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.
     
  17. Dec 10, 2012 #16

    bcrowell

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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.
     
  18. Dec 11, 2012 #17

    dlgoff

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  19. Dec 11, 2012 #18

    sophiecentaur

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    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!!!
     
  20. Dec 11, 2012 #19

    bcrowell

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    Here's my data from the plastic toy recorder we had in the physics stockroom. I don't think it's meant to be a real, usable musical instrument. (For one thing, it's virtually impossible to get the damn thing to speak on the high notes unless you start on a low note and run up a scale to the high one. This is kind of interesting in its own right, since it seems physically similar to overblowing -- an effect that clearly can't be explained by any simple, linear model.)

    f (Hz),open holes,b (cm),note,v/2b (Hz)
    590,0,29.6,1,574
    655,1,25.1,2,677
    730,2,23.1,3,736
    780,3,21,4,810
    870,4,18.9,5,899
    995,5,16.7,6,1018
    1020,6,14.4,b7,1181

    This is in CSV (comma-separated value) format, which people should be able to read into a spreadsheet program, but I think it's more or less readable as is. The first column is the measured frequency. The second is the number of open holes. The third is the distance from the tip of the mouthpiece to the center of the first open hole (or to the end of the tube). The fourth column is the frequency v/2b predicted by the simple model I proposed, which is that the frequency is determined by simply truncating the length of the sound column to the first open hole and taking that as half a wavelength.

    I would say that the agreement between theory and experiment is reasonably good. The agreement is not good enough that you could use v/2b as your sole mathematical rule for building a good, practical instrument that plays in tune, but I think it's good enough to say that the theory is basically right as a first approximation, and further corrections can be taken as perturbations on top of that.

    The first-open-hole model predicts that it doesn't matter what holes you close or open below the first open one. This seems to be more or less true on this instrument, but not exactly true. I observe that if I finger a note near the top of this scale and then close and open various holes that are farther from the mouthpiece, I sometimes get no change in pitch and sometimes get a drop of a quarter-tone or a semitone.

    On this piece-of-**** instrument, the holes that your index fingers rest on are slightly smaller than the others.
     
  21. Dec 11, 2012 #20

    bcrowell

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    dlgoff's #17 is interesting, because it shows how a nonlinearity enters in the case of a reed instrument. However, it's not obvious to me how that nonlinearity produces overblowing.

    I found a book that discusses overblowing very clearly in instruments such as recorders, bamboo flutes, and whistles: Backus, The acoustical foundations of music, Norton, 1969, pp. 184-186. These instruments work based on edge tones at the mouthpiece. Here's a brief online description of an edge tone: http://hyperphysics.phy-astr.gsu.edu/hbase/music/edge.html To me this example is very transparent. The edge tone occurs because of a flow of air that is binary in nature. The air either flows past one side of the knife-edge or the other. This binary object "wants" to do its 010101... oscillation at some frequency, but it has to accomodate itself to the air column, which only has certain resonant frequencies. In overblowing, this square-wave vibration occurs at a harmonic of the air column's fundamental frequency. The square wave has Fourier components at all the multiples of that, and some or all of these components match up with the resonances of the air column.
     
  22. Dec 11, 2012 #21

    AlephZero

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    There are two strange things about your experiment. With all holes closed, the discrepancy in frequency is the opposite way to all the other results. And the discrepancy for the highest note is much bigger than the rest (15% compared with 2 or 3%).

    I'm not sure what "the tip of the mouthpiece" means. The start of the vibrating air column is the "window" or rectangular slot before the finger holes. The bevelled edge of the "window" is the lip that created the edge tone, if you believe in edge tones.

    Did you see the comment by Benade in your hyperphysics link on edge tones? It's easy to measure the edge tone frequency of an organ pipe. If you put some cotton wool in the pipe to damp its resonance you can hear the edge tone. As Benade says, the observed edge tone frequencies are much too high for the coupled system to "pull" the edge tone frequency to match a resonance of the pipe. For some styles of organ pipe voicing, you can hear the edge tone as a transient sound at the start of the note. If it is at a harmonic of the pipe frequency, it is more like the 5th or 6th harmonic than the first.

    FWIW the usual problem with recorders being reluctant to playing some notes is just internal dirt. A quick blast with a high pressure air line might fix that problem!

    Plastic recorders come in all qualities, from complete junk up to instruments used by professionals. For folk music, they have advantages over wood - the sound is louder and brighter, for outdoor use they are much less temperamental about humidity or even rain, and they are a lot more resistant to accidental damage.
     
  23. Dec 11, 2012 #22

    bcrowell

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    This doesn't surprise me, because b is being defined differently in that case than in the others. That one is measured to the end of the tube rather than to the center of an open tone-hole.

    Yeah. Actually, looking at standard recorder fingerings on the web, nobody seems to use the one with all tone holes open. Also, the set of tone holes on this instrument is different than on a normal recorder. It only has 6, not 7 or 8.

    "Tip" means the very end, the point farthest from the bottom of the tube. I'm sure you're right that the window would be more appropriate than the tip. (Backus calls this the "mouth.")
     
  24. Dec 11, 2012 #23

    AlephZero

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    That would explain the lowest note result, because your "measured" tube length is clearly longer than the acoustic length, unless there is a huge end correction factor for some reason.

    Whatever model of the physics you use, the acoustic length of the tube should always be longer than the actual length. That's what made me curious about your lowest note.

    .
    So it's probably not a recorder, but a "tin whistle" made from of plastic. Actually that would explains why all the frequencies looked strange. The most common recorders have lowest note C (523 Hz) and the only other likely possibility is F. Tin whistles usually have the lowest note D (587 Hz) which is fairly close to what you measured.

    Your hypothesis is that a tone hole acts like open end of a tube. I don't see that it matters that you are using non-standard fingerings. You are comparing the measured frequency with a mathematical model of the pipe, not with any particular musical scale.

    It would be nice to know the tube lengths measured from a more correct end point. The pattern of the discrepancies from your hypothesis might then be more revealing.
     
  25. Dec 12, 2012 #24

    sophiecentaur

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    This is certainly a complex topic. You haven't even got onto Timbre yet!
     
  26. Dec 14, 2012 #25
    The tube does not just choose the note within a wide noise spectrum or between several harmonics produced independently by the reed or blowhole. It determines how the reed or blowhole behaves to create just the emitted note.

    Easier to understand with a reed. During one oscillation period of the air column, when the pressure is minimum, it attracts the reed to close the mouthpiece, thus reducing the air throughput. When pressure is high, the reed is pushed open to increase the throughput. The reed that brings air when pressure is high brings the negative impedance that lets the air column oscillate by providing power to it.

    For this, the reed must act as a spring, not a mass. In other words, its resonant frequency must be quite higher than the emitted note.

    In a blowhole, the negative impedance relates with the time needed by air to cross the hole (hence the air pressure). It's similar to some power vacuum tubes: pressure deviates the air jet, but once the jets arrives at the bevel, the pressure has already changed, hence the negative resistance.

    Though, at a flute, we change also the thickness of the jet and its angle.

    ------------------------------------

    You shouldn't try to understand pitch vs length on a recorder, because the bore is not cylindrical nor even conical. It's first straight, then converging, in order to overblow in tune despite other effects, first of them the inductance of the narrower blowhole.

    As well, narrow toneholes are inductive and produce a lower note. Just look where the overblow hole is located at the clarinet, but it produces a (bad) lower note on the fundamental because it's narrow and long hence inductive. One reason more against understanding through a recorder, or even worse, a bassoon, which works as an ocarina (Helmholtz resonator) in its short notes.

    Take a flute, you can explain the pitch then. Or a clarinet also, but its bore isn't really cylindrical, nor its toneholes big.

    The flute has a conical headjoint, but only to combine with the extra volume near the stop and the inductance of the blowhole, in order to tune the overblow.

    ------------------------------------

    The inductance of narrow toneholes makes them less effective in stopping the wave there, so lower holes matter and can define half-tones.

    Narrow toneholes are also extremely important for sound quality. They define losses, frequency response, and even a very nonlinear behaviour at the bassoon. After wide holes improved the flute, all best manufacturers tried them on all instruments and consistently failed.

    The clarinet has gotten and kept holes more or less at the proper places, but not really big. The oboe and the bassoon had to keep very small holes to sound good, even at the Heckel design.

    Narrower holes explain most of the Tarogato's sound, different from a soprano saxophone. Notice the many small holes at its bellow.

    One nice bassoon attempt by TriƩbert can be seen in Brussels' museum.

    ------------------------------------

    The part with negative conductance the creates the oscillation has also a susceptance. This is personal thought, not widely known. Again easier to grasp at a reed than a flute, and can be experimented convincingly when playing a saxophone, or even better a bassoon.

    As higher pressure in the tube pushes the reed away, the mechanical movement also increases the air volume in the tube. This is equivalent to a capacitance. Not a small one: similar to the tuning volume in a saxophone's mouthpiece, or to its missing volume at the truncated cone.

    This susceptance is in parallel with the reed's negative conductance and with the admittance of the air column. It influences the pitch AND the overblow.

    A harder reed (best combined with a less open mouthpiece) needs more pressure for the same movement hence produces a smaller susceptance. Same for a narrower reed and mouthpiece. They pitch the instrument higher. Little bit at the clarinet, important at the saxophone, huge and obvious at the bassoon, where musicians tune the reed by cutting it.

    It is this susceptance that prevents the instrument from overblowing when not desired. The susceptance must be big enough to short-circuit the negative conductance, so that the reed can't compensate the column's losses at the harmonic, and oscillation occurs at the fundamental only.

    Now, if you press the reed more firmly, first the pitch rises because the free-moving part of the reed is shorter hence the reed's susceptance decreases, and then the note jumps to the overtone.

    Which means that the reed and the mouthpiece must match the instrument. With parts from an alto saxophone, you can't overblow a bassoon.

    ------------------------------------

    Back to the wide toneholes: timber gets bad when the reed is too efficient, because the reed closes and opens too brutally then. Similar to a bagpipe then.

    The musician adjusts his lip pressure for that, but only if the instrument allows it. The losses at the air column must match approximately the reed's negative conductance. As the closer reed is needed to produce higher notes, the negative conductance changes, and the tube's losses must still match the reed and mouthpiece. This is true when bridging to the second mode, and needs shorter notes to have narrower holes than long notes - can be observed at real instruments.

    This equilibrium would be necessary when playing soft and loud. The clarinet achieves it, the saxophone doesn't.

    Narrow holes also de-tune the higher harmonics which then are attenuated as they don't resonate any more. Softer sound, emission less easy. Harmonics alignment is knowingly paramount to make an easy instrument, but because the reed's susceptance varies with the note, the manufacturer can't tune the overblow perfectly and align the harmonics.

    ------------------------------------

    Octave holes help a lot by killing the resonance at the fundamental (or generally the unwanted mode. Early saxophones had independent octave keys that helped the third overtone if wanted).

    For that, the opening doesn't suffice, as it would only change the pitch. They must also bring losses big enough to prevent oscillation, even though the reed would provide the negative conductance. This part is better documented in books.

    ------------------------------------

    Cross-fingerings can be partially understood as better octave holes, always at the optimum location, possibly combining several of them, to define strongly the allowed vibration mode.

    But they're more. As the frequency increases, tone holes get less efficient in producing a short-circuit, because of their inductance - more so if they're narrow. More well-situated open holes add their effects to produce a good sound reflection, while closed holes in between keep the vibration.

    At higher notes, the length corrections by the tone holes and the reed and mouthpiece are huge, so the distance between the cross-fingering holes is easier to compare with the note's pitch.

    My apologies for the long post, it's a passion...
     
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