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My review of the 30% Rule for pad height; perhaps someone will find it useful. In the saxophone world, a common rule or assumption about key pad heights is: a pad height (measured at high side of pad) of 30% of the tonehole diameter is (approximately) a height below which pitch and tone will start to be affected, and above which there is no effect.

The origin of the 30% rule is apparently derived from the automotive engine world (where I have dabbled) and refers to a simplified model of valve lift height to port diameter that doesn't restrict flow. Actual ratios applied depend on engine design dynamics (street vs race; rpm range; bore and stroke; induction and exhaust design, etc), and vary from roughly 25% to 40% (but mostly close to 25%).

The principle behind the rule is that the "curtain area" (imaginary wall area rising from the port circumference up to the valve) should be at least as large as the cross-sectional area of the port in order to avoid flow restrictions. See picture.

How to calculate the ratio. The following example is based on a tonehole with diameter (d) = 30mm, pad height (h) = 7mm (center height, avg height), radius (r), and pi = 3.14:

1) The formula for the "curtain area" is: d * pi * h;
e.g., 30mm * 3.14 * 7mm = 660mm sq

2) The formula for cross-sectional area of a hole is: pi * r^2;
e.g., 3.14 * 15^2 = 707mm

3) Solve for height where curtain area equals hole area: h * hole area / curtain area;
e.g., 7 * 707 / 660 = 7.5mm

When the "curtain area" matches "hole area", the ratio of valve height to hole diameter is 0.25 (or 25%). Let's call this the "25% Rule". :)

So, The saxophone world's 30% rule seems flawed in methodology and value:

1) Since pad cups tilt open, pad height measured from the high point of pad does not provide a consistent "curtain area" measurement because key cups vary in their tilt; instead, one should measure the center height of the pad (i.e., average height).
2) the 30% figure itself does not appear to be a meaningful value in theory or practice.

That said, nothing here tells us what key pad height is ideal for any given key on a given sax. But I think the "25% Rule" provides a reasoned starting point in key pad height regulation.
 

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Good observation. The guidelines for the curtain area you discuss here provide dimensions for efficient flow of fuel/air mixture or exhaust gases. Saxophone tonehole/pad mechanisms provide a way to "cut off" a vibrating column of air. It's two different things, but the objective is to find a rule for correct pad height that can be applied easily.

We manipulate key heights to affect pitch and tone quality. Manufacturers know that they can change these two things by changing the size of the tonehole as well as by changing its location. Another factor that affects these two variables is whether there is a closed tonehole below the open key under consideration. That's why the different tone holes in the same stack (left hand group or right hand group) are different sizes, even though the key heights MEASURED AT THE CENTER OF THE TONEHOLE are all the same height in the group.

Another variable is the shape of the resonator. Is it domed, protruding nearer to the tonehole and behaving like a slightly lower key? This can actually affect pitch as well as tone qualitv, whether the key is closed or open. A protruding resonator actually changes the effective bore of the instrument in a closed key.

So now the discussion has gotten more complicated, and I've probably lost a few readers at this point. To simplify, as each separate variable is considered, it makes practical keyheight rules more complicated, and to make things even worse, the variables (tone hole size, key height, resonator shape) INTERACT(!), and we get a real rat's nest.

So the easiest way to determine proper key heights bcomes EMPIRICAL OBSERVATION (trial and error, LOL), and the preferences of the player as to tone quality are important. I tend to ask, "Do you want a darker or brighter sound?" rather than "Do you want high or low keys?"

In my experience, the smaller the saxophone, the greater the effect of key heights. Sometimes it is impossible to predict the best key height before a setup is completed. Once I had 2 Mark VI sopranos on my bench for complete overhauls. I set them up for best possible intonation using the same mouthpiece. One horn ended up with lower keys than the other one.. Had Selmer changed the dimensions of their Mark VI sopranos? I don't know. Yes, the sax with lower keys sounded darker.
 

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Wow! That is an interesting way to look at it. My understanding based upon woodwind acoustics is much simpler and has to do with the "end correction" of each soundwave as it arrives at the first opening. The "end correction" is the distance traveled past the opening before the wave is reflected back to the mouthpiece. On a saxophone the wavelength of each tone is the distance traveled down and back which is twice the sounding length of the tube. On cylindrical woodwinds the "end correction" at the open end of the pipe is .6 times the radius or .3 times the diameter. On conical woodwinds it is more difficult to calculate, but the value for cylindrical woodwinds is often used as a close "substitute". On a saxophone the diameter of each tonehole roughly corresponds to the diameter of the tube at that location. A tonehole opening that is approximately 30% of the diameter of the tonehole permits an unrestricted end correction giving the note a full clear tone. "Approximate" is the operative word when making these calculations. The best method is to open a key to its full opening and then slowly close it while playing until the quality of the note starts to be affected.
 

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Wow! That is an interesting way to look at it. My understanding based upon woodwind acoustics is much simpler and has to do with the "end correction" of each soundwave as it arrives at the first opening. The "end correction" is the distance traveled past the opening before the wave is reflected back to the mouthpiece. On a saxophone the wavelength of each tone is the distance traveled down and back which is twice the sounding length of the tube. On cylindrical woodwinds the "end correction" at the open end of the pipe is .6 times the radius or .3 times the diameter. On conical woodwinds it is more difficult to calculate, but the value for cylindrical woodwinds is often used as a close "substitute". On a saxophone the diameter of each tonehole roughly corresponds to the diameter of the tube at that location. A tonehole opening that is approximately 30% of the diameter of the tonehole permits an unrestricted end correction giving the note a full clear tone. "Approximate" is the operative word when making these calculations. The best method is to open a key to its full opening and then slowly close it while playing until the quality of the note starts to be affected.
The problem is, on a saxophone, the diameter of the toneholes is NOT roughly the diameter of the tube at that point. Not even close. You don't even need measuring devices to see the difference. Another way to increase the "curtain area" discussed above is to make tone holes larger. There has been a gradual trend by manufacturers in this direction, but of course it cannot be done by repair techs, and hole diameter increases in the last 100 years have been slight, and confined mostly to palm keys.

The only manufacturer who has incorporated significantly larger toneholes has been Benedikt Eppelsheim. His designs have resulted in bass and contrabass saxes with excellent intonation despite very low, comfortable keyheights. Why? Because he has increased the "curtain area" without raising keys.
 

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... So, the saxophone world's 30% rule seems flawed in methodology and value .... But I think the "25% Rule" provides a reasoned starting point in key pad height regulation.
I don't think the 30% guide is that bad.

1. The curtain calculation for a poppet valve assumes the valve lifts vertically. My gut feeling from my study of fluid dynamics is that the flow is not linearly proportional to the opening, so the theory would have to be modified for pads hinging form the side.
2. I quite big factor is the degree of turbulence. The design for controlling turbulence for a typical poppet valve is rather different to the situation for a sax.
3. The nature of the resonator is likely to have some effect on the turbulence, as the slope of the pad.
4. Also possibly related to turbulence... A typical poppet valve is typically concerned with fluid flow in one direction. For a sax the reality is not flow in one direction but air quickly oscillating in and out of the hole. so the situation is not really the same.
5. And last -well probably not last actually but that is all I can think of for the present - but not least: For most keys it is quite difficult to measure the "average " opening. It is far easier to measure the opening where it is greatest.

So with all this playing a part, and the 30% only being a guide, I think 30% probably does quite well.
 

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Gordon, I agree. 30% seems to work pretty well. Personally, I prefer a brighter sound, so 30% would be better than 25%. Also, on old American bass saxes, on which tonehole diameter is a bit smaller compared to bore diameter, the horn pays better with keys as high as possible in my experience, especially in terms of pitch. Unfortunately, moving big keys on big horns a greater distance can border on inconvenience. For some players, high keys are an inconvenience even on baritone and tenor saxes.
The fact that sax keys open at an angle might prove to be an advantage. I don't know. However that is unlikely to change soon in any saxophone design
 

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Discussion Starter #7
I don't think the 30% guide is that bad.
It was perhaps indelicate of me to phrase it that way. What I meant was that the 25% rule defines a meaningful mathematical value; we can say what it is. In contrast, the 30% rule is more a rule of thumb. Which might be more convenient to use (worth testing). Perhaps, in the end, we could just as well use an arbitrary 34.5% rule---if, in practice, the values are all used as a reference point to be deviated from significantly, anyway.
 

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It was perhaps indelicate of me to phrase it that way. What I meant was that the 25% rule defines a meaningful mathematical value; we can say what it is. In contrast, the 30% rule is more a rule of thumb. Which might be more convenient to use (worth testing). Perhaps, in the end, we could just as well use an arbitrary 34.5% rule---if, in practice, the values are all used as a reference point to be deviated from significantly, anyway.
I am curious as to whether "air flow" as used in terms of automotive exhaust is the same as the movement back and forth of air molecules in a sound wave. One of the common misconceptions in saxophone acoustics is that air moves or "flows" through the instrument. The body of air inside the instrument is for the most part stationary and the oscillation of the air molecules at the frequency of the sound or "waves" travel back and forth within that stationary column of air. The analogy commonly given is the movement of waves in the ocean. The water itself does not travel from one location to the next. The waves in the water do.
 

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The problem is, on a saxophone, the diameter of the toneholes is NOT roughly the diameter of the tube at that point. Not even close. You don't even need measuring devices to see the difference. Another way to increase the "curtain area" discussed above is to make tone holes larger. There has been a gradual trend by manufacturers in this direction, but of course it cannot be done by repair techs, and hole diameter increases in the last 100 years have been slight, and confined mostly to palm keys.

The only manufacturer who has incorporated significantly larger toneholes has been Benedikt Eppelsheim. His designs have resulted in bass and contrabass saxes with excellent intonation despite very low, comfortable keyheights. Why? Because he has increased the "curtain area" without raising keys.
Point taken. I need to change my thinking in this regard. :) It is however accurate to say that the diameter of the toneholes, generally speaking, increase as the diameter of the bore increases. M Postma has some data on his website that illustrates the relationships between bore diameter and tonehole diameter at that location. Diameters, Keyheights, and Ratios. I measured the tonehole diameters on a YAS-23 and compared 30% of that value to Yamaha's recommended key heights. The results are shown in the graph below.

View attachment 241074
 

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High speed, high volume air flow through auto poppets has essentially
ZERO relationship with standing waves in saxes. Really.

And it is simple to find the "average " opening. Just some math...

But it is simpler still to agree to measure at e.g. the outer edge of the tone hole for convenience. The corrected chart (% of tone hole size rather than difference) is more useful. If you want to assess the accuracy of a 30% Rule or similar.

The many compromises in saxophone construction make any such simple rule a rough approximation at best...
 

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Discussion Starter #11
The body of air inside the instrument is for the most part stationary and the oscillation of the air molecules at the frequency of the sound or "waves" travel back and forth within that stationary column of air.
Not questioning the existence of waves and oscillations---I don't know precisely how air travels through a saxophone---but some air must travel through. After all, we repeatedly expend our lungs into the instrument while playing.
 

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Discussion Starter #12
High speed, high volume air flow through auto poppets has essentially
ZERO relationship with standing waves in saxes. Really.
I agree. And the 25% value is not even applied to automobile engines, consistently. In practical application, the 25% rule (for engines or saxes) may be just a point of reference; but it's a meaningful, well-defined one.
 

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Not questioning the existence of waves and oscillations---I don't know precisely how air travels through a saxophone---but some air must travel through. After all, we repeatedly expend our lungs into the instrument while playing.
Some air does travel through the saxophone but it is a relatively small amount. The small aperture between the tip of the reed and the mouthpiece restricts the air flow as does the oscillation of the reed which at louder levels actually closes off the opening during a portion of each cycle. The difference between the air the player blows and the air flow that goes into the instrument can be demonstrated by first blowing an air stream at the palm of your hand the way you "blow" into the saxophone and then playing on the mouthpiece and neck and feeling the air flow that comes out the open end. The air flow one feels at the end of the neck decreases by the time it travels through the body tube and out the bell.
 

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Discussion Starter #15
When I blow onto my palm the way I blow into the saxophone, I feel a relatively more focused and higher pressure airflow. When I blow into the mouthpiece and neck, I feel a less focused and lower pressure airflow (i.e., seemingly less airflow). Just as you suggested. But I ascribe the lower pressure airflow to the much larger opening of the end of the saxophone neck compared to the mouth opening mimicking a normal embouchure. So, I'm still left assuming that each lung-full of air expended into the saxophone goes through the saxophone.
 

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Try blowing into the small end of the neck without the mouthpiece. There will be substantially more air flow felt at the large end. The vibrating reed acts as a valve that controls the volume and flow of air that goes into the saxophone. The Reed Controls the Air Flow
 

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.... So, I'm still left assuming that each lung-full of air expended into the saxophone goes through the saxophone.
Of course. But the speed of that air travelling down the bore of such a large diameter body is so small as to be irrelevant to any acoustic consideration.

By contrast, the air speed due to induced oscillation is far, far greated, so boundary (with the body) effects and turbulence (especially around tonoe holes) become considerations.

Probably the main consideration associated with the slow air travel down the sax is that in a cold environment the air inside the top of the sax is warm and that inside the bottom is cold. That interferes with the scaling design of the sax. (PItch is related to air temperature)
I found that really pronounced when playing a long pp clarinet passage in a very cold pit. Being pp there would be almost no air travel along the bore, especially on clarinet, which is so air-efficient.
The scaling of a clarinet is a bit dodgy at the best of times, buty this made it extremely difficult to keep in tune.
 
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