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Discussion Starter #1
This topic relates to the issue common to saxophones in which the neck suffers some degree of "pull down" which results in the area of the tube at the bend becoming elliptical. The essential question is whether this has a measurable or significant effect upon the soundwave that passes through this elliptical area.
 

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As a slight clarification of the terms of the issue there are two distinct considerations:

-the effect of the shape of the tube's cross section, (elliptical vice circular).

-the effect of the constriction imposed by the reduction in area centered on the bend when the tube is rendered oval, (on the order of a 3% decrease for a bend which would render a 1" tube 1.08 by .9 <rounded>- a moderate but clearly visible pull down).
 

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This topic relates to the issue common to saxophones in which the neck suffers some degree of "pull down" which results in the area of the tube at the bend becoming elliptical. The essential question is whether this has a measurable or significant effect upon the soundwave that passes through this elliptical area.
I like this one, lets hear the science. I'm all for it, not opinions, real science.
 

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what is "vice circular"
The effect on the sound wave of the shape of the tube- i.e. two tubes both the same cross sectional area with one circular in cross section and one oval.

On an ideal neck a cross section taken perpendicular to the center axis of the neck as it curves would be circular (the curved nature of the neck presents all sorts of analytic issues of course- as the wave "sees" (as some put it) the curve with a larger volume than indicated by the simple cross section area times length measurements might otherwise indicate). That same cross section, taken at the same spot and also perpendicular to the center axis of the neck, would be oval on a pulled down neck.

It would also be smaller in area representing a constriction.

Were the neck made so that it had an oval cross section in the first place with the same cross sectional area as the cylindrical/ circular neck what would the effects be?
 

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Discussion Starter #7
I'm sorry Henry, but you explanation is even more confusing. Did you mean "elliptical versus circular" instead of "elliptical vice circular"?

I have had very little trig and no calculus in my schooling, so you are obviously more well versed in this area than I am.

It would seem to me that when a circle is made elliptical that the perimeter (circumference) does not change. That can be demonstrated by a strip of paper taped at the ends to form a circle. However, as you indicated in the other thread, the area by some complex formula does get smaller. That implies that what is lost in the diameter of the shrunken axis is not entirely made up in the diameter of the expanded axis.

My thinking at this point is that it would be interesting to make a garden hose woodwind with no tone holes and clamp the tube halfway closed at different areas along its length and listen for changes in the pitch and/or timbre of the sound.

It would be great if Antoine would weigh in to share his insight on this topic.
 

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AHA- my apologies on misunderstanding your question. While you were actually learning how to skillfully play the sax I was squandering the few brain cells at my disposal on Latin and math. That I now spend a great deal of my time squalling away on the sax vice reading Virgil shows who made the better long term choice...

Vice, as an English preposition, (from vix) , means "in place of". My apologies for my stilted use of the language- I mean nothing by it- it's just, for good or for ill, how I think.

While the decrease in area as a circle is squished is a pain to compute precisely, just think of what happens when you take it to the extreme. The tube is closed off, and as the height approaches zero the width isn't two times what it was, but 1.57 times what it was since the starting circumference is diameter times pi.

So you don't know exactly what it is inbetween- but you can be certain that it's smaller. My "3% for a 10% squish, (say one inch down to .9 inches)" earlier is a ballpark figure- not an exact one.

This IS an interesting topic- but (as in "except") for extreme cases I'd be surprised to hear that an oval tube and a cylindrical tube of the same cross sectional area performed differently from an acoustic standpoint- but I've surely been surprised before.

The degree to which a constriction affects the tuning of notes with pressure nodes in the vicinity (feel free to stamp on my terminology in relation to nodes) is also of interest. For years I've avoided even moderate pull down with a supertitious awe of unknown but surely terrible effects. It may be that any effect from a technical point of view, is liable to be well below the noise level for all but really severe cases. I look forward to a reasoned discussion of the topic.
 

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Why not do the taste test? Take some well-chewed gum and reduce the diameter at the bend of the neck by varying amounts and see what happens. Nederveen's book contains a formula for figuring the acoustic effects of toroidal bends, and IIRC neither the bends in a normal neck nor a slight increase due to pulldown are significant acoustically.
 

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It seems to me that wouldn't be an acurate test. You're reducing the width while not simulatenously increasing the height, no?
 

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It seems to me that wouldn't be an acurate test. You're reducing the width while not simulatenously increasing the height, no?
Within reason, the shape is not significant, only the cross-sectional area, so it would give a good idea of the effect of pulldown, which reduces that area in the affected region.
 

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Discussion Starter #13
You can have an ellipse with the same area or perimeter of a given circle, never both, or it would be identical to the circle. Making a round neck oval must decrease the cross-sectional area of the affected region, so it alters the pitch for the established reasons.
Thank you for that clarification. In light of Kymarto's observation that it is the area, not the shape that is the most significant factor, a logical conclusion might be that the notes which contain pressure anti-nodes in the area of reduced volume will experience a slight rise in pitch.
 

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This topic relates to the issue common to saxophones in which the neck suffers some degree of "pull down" which results in the area of the tube at the bend becoming elliptical. The essential question is whether this has a measurable or significant effect upon the soundwave that passes through this elliptical area.
When a neck suffers some degree of "pull down", it is reduced in volume to some extent where the bend occurred. This has measurable and significant effects.

The shape of the cross-section (circular, elliptical, triangular, squared, ...) do not matter.

The curvature of the neck has negligible effects (contrarily to the curvature of the elbow).

On an ideal neck a cross section taken perpendicular to the center axis of the neck as it curves would be circular...
No. A circular cross section is not acoustically superior to any other shape such as ellipsis or even squares, they will behave the same if they have the same area.

Were the neck made so that it had an oval cross section in the first place with the same cross sectional area as the cylindrical/ circular neck what would the effects be?
This is actually the case. Saxophone necks have non-cylindrical cross sections where they are bent. Some years ago, I unsoldered all parts from an alto neck (Selmer Series II, never pulled down) to measure the dimensions:
View attachment 28112
as an example, the external diameters, as measured top-down versus right-left, for one cross-section are 19.5mm diameter and 20.4mm diameter. The actual shape of the cross-section is probably not an ellipse but some non-circular shape, more or less symmetric, a bit egg-shaped or something else, as are most real things, non-ideal.

This does not matter, what matters is the cross-sectional area as a function of the distance along the spine of the instrument.

If you "pull-down" your neck, the area will be reduced, this will have acoustic consequences.

My thinking at this point is that it would be interesting to make a garden hose woodwind with no tone holes and clamp the tube halfway closed at different areas along its length and listen for changes in the pitch and/or timbre of the sound.

It would be great if Antoine would weigh in to share his insight on this topic.
Well, I don't think it is worthwhile to make a garden-hose experiment. It would be difficult to relate any finding with what would occur on a saxophone, plus, clamping half-way is very radical.

Why not do the taste test? Take some well-chewed gum and reduce the diameter at the bend of the neck by varying amounts and see what happens. Nederveen's book contains a formula for figuring the acoustic effects of toroidal bends, and IIRC neither the bends in a normal neck nor a slight increase due to pulldown are significant acoustically.
I think this is a much better approach for testing the effect. I already did many such experiments. I encourage anyone to test this out, in some cases of bad neck design, you may even improve the response of your horn. Isn't it well known anyway that you can change (for the best or the worse) the response of your instrument with small modifications to the volume of the neck different positions?

Also, why not take two necks with very similar response and "pull-down" on one? Then, you can compare what happen. Ideally, you need to have a few good players to test it independently, we should never trust ourself too much, we have a tendency to only listen to what we already believe in....

Making a round neck oval must decrease the cross-sectional area of the affected region, so it alters the pitch for the established reasons.
Yes.
Thank you for that clarification. In light of Kymarto's observation that it is the area, not the shape that is the most significant factor, a logical conclusion might be that the notes which contain pressure anti-nodes in the area of reduced volume will experience a slight rise in pitch.
Not exactly. If the area is reduced in the vicinity of the bend, so is the volume of the neck. Reducing the volume of the neck raises the pitch of the first register, so that you will pull out your mouthpiece to tune properly. This will lower the pitch of the second register. If the "pull-down" is relatively important, you'll notice it in the palm-keys.

Also, such volume perturbations will affect every notes to a varying extent, not only those with an anti-node located exactly at the perturbation. See Eq, (35.10) from Nederveen's book, there is a cosine relation to the distance of a pressure node.
 

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Discussion Starter #15
Thank you Antoine. I feel as if we owe you tuition for this course on acoustics. Your participation is much appreciated. If I understood your last post correctly, a significant "pull down" at the curvature of the neck would result in the octaves being too narrow rather than too wide for the left hand notes in particular.

A related question would be what would the general effect upon the tuning be if a neck's taper were decreased over its entire length to the mouthpiece opening?
 

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No. A circular cross section is not acoustically superior to any other shape such as ellipsis or even squares, they will behave the same if they have the same area.



This is actually the case. Saxophone necks have non-cylindrical cross sections where they are bent. Some years ago, I unsoldered all parts from an alto neck (Selmer Series II, never pulled down) to measure the dimensions:
View attachment 28112
as an example, the external diameters, as measured top-down versus right-left, for one cross-section are 19.5mm diameter and 20.4mm diameter. The actual shape of the cross-section is probably not an ellipse but some non-circular shape, more or less symmetric, a bit egg-shaped or something else, as are most real things, non-ideal.

This does not matter, what matters is the cross-sectional area as a function of the distance along the spine of the instrument.

If you "pull-down" your neck, the area will be reduced, this will have acoustic consequences.
Thank you for the clarification. The reference to an "ideal circular cross section" was to the cosmetic model seemingly pursued by manufacturers and expected by consumers rather than a reference to some acoustic design ideal.

Whatever the form- and a perfect ellipse is no more (probably substantially less) likely than a close to perfect circle- any change from a pulldown is clearly almost certain to result in a reduced area.

Do you have any rule of thumb feel for how great a reduction in cross sectional area would have to be (as a %) before it probably becomes a significant factor, (everything affects everything to one degree or another but some effects are simply below the practical noise level).

I suppose I'll bum some chewing gum off my daughter and see what I can see.
 

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Do you have any rule of thumb feel for how great a reduction in cross sectional area would have to be (as a %) before it probably becomes a significant factor, (everything affects everything to one degree or another but some effects are simply below the practical noise level).
This is a good question. It is not obvious to determine what is significant from what is not without actually playing the horn. We are doing a lot of measurements and comparison between instruments and prototypes in search for objective criteria that would tell us what is significant from what is not, what makes an instrument better, what makes it worse.

So, I can make some calculations to estimate what size of a change may have a non-negligible effect though this may only be possible in some undetermined future.

From casual "blu-tack" experiments, it appears that a 1 cubic centimeter (cc) amount added in the bent portion of an alto neck definitely affect the playing behavior (negatively), though this was not following a scientific method. With less than 0.1cc, it was difficult to tell if something changed.

Anyone willing to add some "blu-tack" to their neck and share what changed in the behavior of their horn? Make sure to measure as accurately as possible the volume of the added material!

Great to have you here Antoine!
My pleasure.
 
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