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There are some begging questions from my readings on the saxophone. Here's one.

The descriptions of the physics of the saxophone that I have seen include parameters such a cone dimensions and tonehole placement. But I haven't seen key heights (pad to tonehole distance) included. Does the physics model assume that key heights are just beyond the distance where they would affect pitch, and so not discussed? Did Adolph Sax or any other manufacturer include key height requirements as integral to the engineering of the saxophone? To affect the pitch of a note wouldn't the saxophone engineer adjust the position of the tonehole or cone dimensions rather than introduce key height requirements? If key height requirements have been specified by saxophone engineers, shouldn't thay have been included with each saxophone? Shouldn't there exist some record of such requirements somewhere?

Secondly, I know that key heights can significantly affect pitch and tone. That is not in question. But it all leads me to think that if key height requirements are not part of the physics of the saxophone, then saxophone key heights should be setup by default at just beyond the point where they affect pitch or tone. Only then, if there are intonation problems, should one consider key height adjustments as a possible remedy. Is that correct? Thanks.
 

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The only manufacturer that I am aware of that publishes recommended key heights for their saxophones is Yamaha. (see attachment). There is also a "rule of thumb" that when a key height is raised to approximately 30% of the diameter of the tonehole raising it further will have no additional effect on raising the pitch or improving the tone. To me it makes little sense trying to design a saxophone tuned by raising and lowering key heights. The main reason is that when a key is lowered enough to bring down the pitch of a note, the venting is reduced and the timbre of the note is "stuffy".

I have seen discussions in which the 30% of the diameter is linked to the "end correction" of roughly 60% of the radius of the bore or opening that vents a note. The "end correction" is simply the distance the sound wave travels past the opening before it is reflected back toward the mouthpiece. Each wavelength of a note on a saxophone is twice the physical "sounding length" because of its journey up and back. A very elementary "entry level" book on saxophone acoustics is "The Saxophone is my Voice" by Ernest Ferron.

The question I am currently investigating is where the 30% of the diameter of the tonehole height is measured from---the edge of the pad above to outer rim of the tonehole or the center of the pad to the plane formed by the tonehole. The acoustical aspects of woodwind instruments by Nerveen has an interesting equation to calculate the effect on the pitch of a vented note when a brass disc suspended above a tonehole at various distances.
 

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all repairers that I know set the height with the same rule of thumb and only if the client requests a different setting will try to do anything in that direction.

The only shop ( that I am aware of) that has been conducting special studies and has a practice involving key height , Music Medic with their balanced venting method.

http://musicmedic.com/setting-key-heights-with-the-balanced-venting-method

This is absolutely great but in my view incompatible with either the production of saxophone or the repairs as conducted by most shops, because it takes a very long while to carry out.

In my opinion the practice of balanced venting should be done WITH the customer present in all phases because it should be tailored to his embouchure and mouthpiece and not the one of a technician whom may or may not be playing in a different way.
 

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(...) But it all leads me to think that if key height requirements are not part of the physics of the saxophone, then saxophone key heights should be setup by default at just beyond the point where they affect pitch or tone. (...)
As far as I can see, the Balanced Venting Method is a method to reach precisely this situation where nothing is gained by lifting each key cup further.
 

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it is an extremely complex process which done without the participation of its enduser misses one of the most important elements of the intonation itself.
 

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The saxophone sound is produced by standing waves. There is no wave traveling to a tone hole and reflecting back. Here is a good paper that explains it: http://newt.phys.unsw.edu.au/jw/pipes.html

A more complete study here: http://newt.phys.unsw.edu.au/jw/saxacoustics.html
A thorough reading of linked material would reveal this statement:
So we have devoted a whole page to comparing cylindrical and conical pipes and, if you want the details, you should read that page now. However, the result is this: the standing waves in a cone of length L have wavelengths of 2L, L, 2L/3, L/2, 2L/5... in other words 2L/n, where n is a whole number. The wave with wavelength 2L is called the fundamental, that with 2L/2 is called the second harmonic, and that with 2L/n the nth harmonic. [emphais added]
The clarinet which is a closed cylinder has a fundamental wavelength that is 4 times the length of the instrument meaning that the soundwave goes down and back twice. This is why a clarinet can play much lower than a soprano saxophone even though they have the same approximate length. A flute on the other hand is a cylinder open on both ends and has a wavelength of 2L like a conical closed pipe. Dividing the wavelength by whole number integers gives the wavelengths of the harmonics. On a closed conical tube they are 1 - fundamental, 2 - 2nd harmonic, 3 - 3rd harmonic, 4 - 4th harmonic and so on. For a closed cylinder like a clarinet the wavelengths of the harmonics are produced by dividing by odd numbered integers: 1, 3, 5, 7 etc. Fascinating stuff.
 

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I agree, which raises the question as to whether my tech is adjusting my key cups as low as possible while maintaining intonation and keeping the instrument free blowing, OR if they are adjusted higher than necessary.
 

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it is an extremely complex process which done without the participation of its enduser misse one of the most important elements of the intonation itself.
I used to think so myself, but upon closer study "the balanced venting method" is elegant in its simplicity, but one needs to understand saxophone regulation in order to see it. Let me try to explain.

Speaking only of keys on the upper and lower stacks which involve regulation with one another, there is a set pattern and sequence that takes place in order to remove "lost motion" where there is excess travel of a key before it contacts a second key it is meant to close.

I begin the sequence by setting the height of the RH F key. When this is regulated to close the F# and then the E and D keys are regulated to also close the F#, the key heights of the lower stack are set. In other words everything follows the height of the F key. Before moving to how the key heights on the upper stack are set by the height of the F, let's look at what Curt calls the "undervented" notes on the lower stack. These are notes that are vented through an open tonehole followed by a closed one. On the lower stack they are the F# (open hole - F followed by closed E key), the E (open hole D followed by closed Eb) and the D (open hole C followed by closed C#).

If any of these "undervented" notes are stuffy, the opening of the F key is increased and the notes are played again, repeating this process until all three "undervented" notes are clear.

The key heights of the upper stack are determined by the height of the F key through the regulation of the Bis. The sequence here is both the B and A keys are regulated to close the C (small keycup above the B), then the A key is adjusted to close the Bis. The arm from the Bis needs to travel its full distance until it just touches the adjusting screw from the F#, and the A key touch should have no "lost motion" before it contacts the Bis. Most of the time setting the key heights of the lower stack to make the "undervented" notes of the RH happy, also sets the key heights of the upper stack to fully vent the "undervented" notes up there. The upper stack "undervented" notes are C (open tonehole B followed by closed A), and A (open tonehole G followed by closed tonehole G#).

Should the removal of "lost motion" at the Bis fail to open the upper stack key heights enough to compensate for the "undervented" notes, then the upper stack can be opened more while not introducing "lost motion" by increasing the curvature of the arm extending from the Bis. Let me just add "there is no such thing as an "over vented note". :mrgreen: All of the other keys are "independent" and can just be opened enough to speak clearly with no problem.
 

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setting the height too low is way more perilous than setting them slightly too high.

The gain in speed in setting the key lower is measurable perhaps in milliseconds while the loss in volume is absolutely audible.

I asked my tech to lower the action because( I wrongly thought ) using flat resonators after having domed ones.

The volume reduction was definitely there (I didn’t really perceive or measure intonation changes) so I asked the tech to open up the key to where they were before and everything was better.
 

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.. meaning that the soundwave goes down and back twice.
With respect, that's wrong. The sound wave is stationery with a node at one end and anti-node at the other - the "no displacement" and maximum displacement points on a sine wave - which is quarter of a wavelength.

I'd have thought the bit of the site of relevance to the physics of tone holes is

http://newt.phys.unsw.edu.au/jw/musFAQ.html#end
The linked paper and, really, other discussions about end effects/corrections

https://en.m.wikipedia.org/wiki/End_correction
 

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With respect, that's wrong. The sound wave is stationery with a node at one end and anti-node at the other - the "no displacement" and maximum displacement points on a sine wave - which is quarter of a wavelength.

I'd have thought the bit of the site of relevance to the physics of tone holes is

http://newt.phys.unsw.edu.au/jw/musFAQ.html#end
The linked paper and, really, other discussions about end effects/corrections

https://en.m.wikipedia.org/wiki/End_correction
The stationnary wave can be seen as ("is") a superposition of two progressive waves travelling in opposing directions.
 

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I was referring to the model used in the linked site.
http://newt.phys.unsw.edu.au/jw/pipes.html

The bit where it says
"To compare cylindrical, conical, closed and open pipes, let's look first at diagrams of the standing waves in the tube."
Nothing in the website you quote contradicts the fact that the stationary wave is the superposition of two travelling waves (one incident, the other one reflected). This point of view (which was used by Saxoclese) is taught in standard textbooks in physics.
 

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I was referring to the model used in the linked site.
http://newt.phys.unsw.edu.au/jw/pipes.html

The bit where it says
"To compare cylindrical, conical, closed and open pipes, let's look first at diagrams of the standing waves in the tube."
The text accompanying the diagram reads:

Three simple but idealised air columns: open cylinder, closed cylinder and cone. The red line represents sound pressure and the blue line represents the amplitude of the motion of the air. The pressure has a node at an open end, and an antinode at a closed end. The amplitude has a node at a closed end and an antinode at an open end. These three pipes all play the same lowest note: the longest wavelength is twice the length of the open cyclinder (eg flute), twice the length of the cone (eg oboe), but four times the open length of the closed cylinder (eg clarinet). [emphasis added]. Thus a flutist (diagram at left) or oboist (diagram at right) plays C4 using (almost) the whole length of the instrument, whereas a clarinetist (middle) can play approximately C4 (written D4) using only half the instrument. If you have a flute or oboe and a clarinet, this experiment is easy to do. Play the lowest note on the flute or oboe, and then compare this with the lowest note on half a clarinet (ie removing the lower joint and bell). Important: in all three diagrams, the frequency and wavelength are the same for the figures in each row. When you look at the diagrams for the cone, this may seem surprising, because the shapes look rather different. This distortion of the simple sinusoidal shape is due to the 1/r term, which is discussed below.
 

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Saxoclese, now I think I understand Lesacks's point.
Your description of the clarinet in post #7 ("the soundwave goes down and back twice") is not accurate. At the mouthpiece tip you must have a speed node and at the bell (up to an end correction) you must have a pressure node ; with a cylinder a speed node is a pressure antinode and so the tube length must be (2n+1)/4 times the wavelength.
For a conical instrument the relevant quantity is not the pressure p but rather the product pr of the pressure p by the distance r from the apex of the cone ; in this case, both the apex of the cone and the bell (forget the end correction...) will be a node of the quantity pr. So the length of the tube will be n/2 times the wavelength. More precisely, the apex of the cone is not the mouthpiece tip, but the mouthpiece contains an additional volume which compensates for the difference.
 

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Saxoclese, now I think I understand Lesacks's point.
Your description of the clarinet in post #7 ("the soundwave goes down and back twice") is not accurate. At the mouthpiece tip you must have a speed node and at the bell (up to an end correction) you must have a pressure node ; with a cylinder a speed node is a pressure antinode and so the tube length must be (2n+1)/4 times the wavelength.
You've lost me there. I'm not sure what "n" is meant to represent? Let's address just the fundamental on a clarinet first before discussing the odd numbered harmonics. The sound wave in a clarinet travels to the opening and is reflected back to the mouthpiece, then it repeats this process. Down & back, down & back = travelling 4x the length. (Wavelength) W = 4L where L = length of the instrument. L = W/4.

For a conical instrument the relevant quantity is not the pressure p but rather the product pr of the pressure p by the distance r from the apex of the cone ; in this case, both the apex of the cone and the bell (forget the end correction...) will be a node of the quantity pr. So the length of the tube will be n/2 times the wavelength. More precisely, the apex of the cone is not the mouthpiece tip, but the mouthpiece contains an additional volume which compensates for the difference.
My understanding is that at the mouthpiece of a conical instrument the sound wave has a pressure anti-node (maximum pressure). At the bell or first open tone hole the sound wave has a pressure node (no pressure) also called velocity anti-node (maximum air movement) when this pressure node meets the atmospheric pressure after an end correction it is reflected back to the mouthpiece as a "rarefaction" presenting a "velocity node" at the mouthpiece, at which time the sequence begins again. This is clearly shown in the illustration at this link: Harmonics and the different instrument bores

In the addendum to aawi by cj nederveen he presents some interesting information on p.126 that I will summarize here and then quote: On the clarinet when the reed is "beating" the reed is open 50% of the time and closed 50% of the time. On a conical woodwind the closing is less than 50% of the time which is equal to the truncation of the cone.

After half an oscillation, the rarefaction has become a compression which reopens the reed. The time for a half oscillation is 2ro/c, which equals the time a pulse would need to travel to the fictitious apex and back. So the ratio between closing and opening time of the reed equals the ratio of the truncation to the tube length.
He further postulates that the increased reed open time of a saxophone may be one factor which helps to make the saxophone much louder than a clarinet. Fascinating stuff!
 

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You've lost me there. I'm not sure what "n" is meant to represent? Let's address just the fundamental on a clarinet first before discussing the odd numbered harmonics. The sound wave in a clarinet travels to the opening and is reflected back to the mouthpiece, then it repeats this process. Down & back, down & back = travelling 4x the length. (Wavelength) W = 4L where L = length of the instrument. L = W/4.

My understanding is that at the mouthpiece of a conical instrument the sound wave has a pressure anti-node (maximum pressure). At the bell or first open tone hole the sound wave has a pressure node (no pressure) also called velocity anti-node (maximum air movement) when this pressure node meets the atmospheric pressure after an end correction it is reflected back to the mouthpiece as a "rarefaction" presenting a "velocity node" at the mouthpiece, at which time the sequence begins again. This is clearly shown in the illustration at this link: Harmonics and the different instrument bores

In the addendum to aawi by cj nederveen he presents some interesting information on p.126 that I will summarize here and then quote: On the clarinet when the reed is "beating" the reed is open 50% of the time and closed 50% of the time. On a conical woodwind the closing is less than 50% of the time which is equal to the truncation of the cone.

He further postulates that the increased reed open time of a saxophone may be one factor which helps to make the saxophone much louder than a clarinet. Fascinating stuff!
The symbol "n" stands for an integer -fundamental: n=0 for the formula L=W(2n+1)/4 (open-closed cylinder) and n=1 for the formula L=Wn/2 (cone).

Though a standing wave can be analyzed as a superposition of two travelling waves, it is really more convenient to think in terms of standing waves (as is done in my previous post or on the website
http://newt.phys.unsw.edu.au/jw/pipes.html
quoted by Lesacks). If you really don't want to think in terms of standing waves:
-for the clarinet, the pressure wave is reflected with a sign change at the bell and without a sign change at the mouthpiece tip (in terms of the standing wave, the situation that you describe for the conical woodwind is indeed not for a conical woodwind: it is the situation for the clarinet)
-for a oboe or a saxophone, really the relevant variable is the product pr as in my last post (the explanation is mathemetical: express the Laplace operator in spherical coordinates). The quantity pr has a node both at the mouthpiece tip and at the bell. In terms of travelling waves, pr is reflected with a sign change at both ends.
 

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… Does the physics model assume that key heights are just beyond the distance where they would affect pitch, and so not discussed?…
Yes, i believe you are correct.

To affect the pitch of a note wouldn't the saxophone engineer adjust the position of the tonehole or cone dimensions rather than introduce key height requirements?
Yes, the position of the tone holes and body tube design are the primary factors for intonation. For me, raising or lowering key cups have made notes stuffy or un-stuffy, but never really solved an intonation "problem". Of course, If a key cup is extremely close to the chimney, the note can become flat, but I don't often see that.

If key height requirements have been specified by saxophone engineers, shouldn't thay have been included with each saxophone?
Yes, that would be a good idea. Perhaps it is not done because the manufacturers don't foresee users making their own adjustments.

I know that key heights can significantly affect pitch and tone. That is not in question.…
It's more about tone. Raising or lowering often has very little affect on pitch.
 
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