Question:
flute scale computation
I've been looking at the computations for a flute scale (tonehole positions) and I have found what appears to be an oversight. They all assume the temperature (and thus speed of sound) is constant throughout the tube.
The air inside the tube near the blowhole is going to be warmer than the air at the foot (human breath being warmer than ambient air). Thus sound is traveling faster near the blowhole, so the same tonehole distance (wavelength) corresponds to a higher frequency. That would make short tube notes (like C#) tend sharp relative to long tube notes.
Perhaps this is why many players find flutes designed for A=442 to be easier to play at A=440, than a flute designed for A=440. If neither design is temperature compensated, then the A=440 is going to go sharp for the short tube notes. The player pulls out the headjoint to compensate. But this affects short tube notes more than long tube notes because any distance you pull out is a bigger % of a shorter tonehole distance. Thus, with the A=442 flute he can pull out to flatten the short tube notes. The warmer air is only at the shorter end of the tube, and so is the effect of pulling out the headjoint, so they effectively cancel each other.
It doesn't take much temperature shift to change the pitch. 440 versus 442 is only about 0.5%. This is roughly the same as a 5*F difference in air temperature. Now consider that the air temperature difference between human breath (at the blowhole) and ambient room temperature (at the end of the flute foot) is probably around 10* - 20* F.
If this has any merit, it would mean that one manufacturer's A=440 might be another's A=442 or anything else unless they are all doing calculations to an industry standard temperature & speed of sound. By my calculations, A=440 at 69*F is the same as A=442 at 64*F.
It would also mean that a temperature compensated A=440 scale (if any such thing exists) should play something like an uncompensated A=442 (or 441, 443, etc.).

Answer:
Good thinking.
And it is worse in a clarinet, because the short tube notes are shorter still and the long notes longer still.
I found this to be a nightmare for pitch when playing pp in long passages in a really cold pit...
I could not stop to blow warm air through the instrument.
pp volume meant not much air even entered the instrument, let alone went far down the bore.
pp meant I could not adjust pitch much with embouchure gymnastics..

Answer:
Originally Posted by MRC01
The air inside the tube near the blowhole is going to be warmer than the air at the foot (human breath being warmer than ambient air). Thus sound is traveling faster near the blowhole, so the same tonehole distance (wavelength) corresponds to a higher frequency. That would make short tube notes (like C#) tend sharp relative to long tube notes.
Are you assuming that air is flowing thru the flute though to come up with that idea? The standing wave returns to the embouchure hole which is more consistent source of sound origination. Air that is blown through a small opening is small and fast and not all that warm. If you blow with a flute embouchure against your finger, the air is quite cool. There is friction caused by the standing wave at the boundary layer also which contributes to a more even warming of the tube. In this sense the longer tube notes may be cooler because the bore down there is utilized less. But I don't know if it's enough to create the scenario you describe. Playing in the third register above cut-off where the entire bore is utilized should be enough then to "warm-up a whole flute to avoid the effect.
It is possible that the effect might occur initially when a flute is cold but as friction warms the bore in a very short time, It may be more dependent on how often the bore is experiencing friction and retention of that heat as playing continues. It's my guess that the temperature difference from the friction of air vibration is an initial problem that could quickly be overcome by playing. The effect may only be transient.
Just a thought from thinking out loud...
Joe B

Answer:
Originally Posted by JButky Are you assuming that air is flowing thru the flute though to come up with that idea?
...
Nope. The only assumption is that the air at the embouchure hole is warmer than at the foot. Such a differential could persist in a steady state even after everything has warmed up and equalized. That's because the embouchure hole sees a constant stream of warm air (breath from the lungs) while the rest of the flute sees some mix of ambient air(entering through tone holes) and warm air.
This would also explain why it's not uncommon to see altos and basses tuned for A=443 - higher than what the same company would use for a soprano flute. The longer the tube, the greater the temperature differential. Now I don't know whether these companies do this intentionally because they are aware of temperature effects, or whether they just discovered experimentally that a bigger harmony flute is easier to play in tune at A=440 if they are tuned higher than a normal flute.

Answer:
Joe, you make some good points, especially the breath coming from the lips quite cool.
However the reality speaks for itself...
I pick up my cold flute (surrounding air temp 23 degrees C), and play a second octave B loudly for a minute. Then I test the temperature of the tube metal against my upper lip. The head is warm and the foot is still cold.
I repeat the experiment playing low C. The foot is a bit warmer, but still there is a significnt temperature differential between head and foot.
So I have to agree with MRC01 that this is must be a significant issue. Do designers of scaling take it into consideration?

Answer:
Originally Posted by Gordon (NZ)
So I have to agree with MRC01 that this is must be a significant issue. Do designers of scaling take it into consideration?
I don't see why they would...That scenario should only be a problem in cold temperatures. If part of the flute is cool the other half is warm, you are at best dealing with only one quarter wavelength that is affected. (flute is a half wavelength instrument and if you are seeing only half the length of the flute affected that makes only a quarter wavelength affected)
Why would manufacturers account for something like that which would be not too significant and less common?
I'd be more concerned with the interaction with static air pressure temperature differences. Isn't this also more a function of the density of the air rather than the temperature? There is dependence of air density at specific temperature. Speed of sound relies on density. Doesn't playing provide a generalized local density sufficient to overcome this phenomenon?
I haven't thought about that in a while, so I have to review the whole speed of sound in air/density facts and dynamics before I can say that with surity, but something in the back recesses of my mind reminded me of that...
Joe B

Answer:
Originally Posted by JButky I don't see why they would...That scenario should only be a problem in cold temperatures. If part of the flute is cool the other half is warm, you are at best dealing with only one quarter wavelength that is affected. (flute is a half wavelength instrument and if you are seeing only half the length of the flute affected that makes only a quarter wavelength affected)
It would depend on the note. For middle C#, most of the air to the first open tonehole would be warm, so we're talking about a half wavelength instead of a quarter. For middle Eb, the warm air section makes up a smaller portion of the wavelength, so it's probably more like a 1/4 wavelength as you suggested. So the temp differential would affect C# a lot more than it would Eb.
Originally Posted by JButky Why would manufacturers account for something like that which would be not too significant and less common?
I asked one flute designer who has been doing this for over 30 years, used to work for Powell, now has his own flute company. He has measured the temp differential in steady state and found it to be significant enough to account for it in his scale.
Originally Posted by JButky Speed of sound relies on density. Doesn't playing provide a generalized local density sufficient to overcome this phenomenon?
This is a common misperception, seems intuitive and is even suggested (incorrectly) by some physics textbooks. Speed of sound in air doesn't depend on density - depends almost entirely on temperature alone. The reason sound travels slower at high altitude is because it's cold up there.
Or to put it differently, suppose you are indoors, in a temperature controlled environment. Sound travels at the same speed in that room regardless of altitude because the temperature is the same.
I know it seems weird, but it's true. If it weren't it would be impossible for strings to tune with winds at 6,000'. Strings would be unaffected by altitude while winds would be at A=430.8 - far too low to compensate.

Answer:
Originally Posted by MRC01
This is a common misperception, seems intuitive and is even suggested (incorrectly) by some physics textbooks. Speed of sound in air doesn't depend on density - depends almost entirely on temperature alone. The reason sound travels slower at high altitude is because it's cold up there.
Regarding the 1/2 vs 1/4 wavelength...flutes operate as a 1/2 wavelength instrument (tube open at two ends) that make the distance from embouchure to open tone hole a 1/4 wave. (needs to make the round trip to create the half wavelength.) That doesn't change depending on any particular note on the flute. But I do understand what you mean by temperature differences since the area above the C# tone hole is "activated" most of the time and can experience higher temperatures.
But I think you're analysis is too simplisitic leaving many factors out. The speed of sound is a function of density and pressure and both density and pressure are functions of temperature. I don't think you can't say that internal temperature difference alone is the determining factor to justify changing the scaling.
You would need to determine, not the flute tube temperature, but the temperature of the air inside the tube. I understand that there would be some influence but it is not an absolute corelation. Temperature is shown to not be constant in an acoustic pressure wave. What that translates to in terms of adjusting scaling is therefore quite complex.
I've found some interesting reading relating this to thermodynamics of what happens when acoustic waves pass through these differences. The problems as I understand them stem from the phenomenon being only quasi static, meaning the system has different rates of temperature transfer within the system. There are some mathematical compensation differences, but I don't know if they are incorporated into current design. But I suspect they are because of the differing methods from which scaling was derived. (in other words, not solely computational...)
I think It's a great question though. I need to do more homework to get a better grasp on what's happening first. But my impression is that altering scaling to account for those differences may be moot when one considers that there is temperature variance in the standing wave itself. And there are other factors which may have a greater impact on the sytem. I don't deny that these changes are there, but they maybe within a realm of insignificance if other factors are exhibiting greater affect that surpass the difference that temperature variations present.
Too much to think about right now....I have to get back to inventory!
Joe B

Answer:
Originally Posted by JButky The speed of sound is a function of density and pressure and both density and pressure are functions of temperature. I don't think you can't say that internal temperature difference alone is the determining factor to justify changing the scaling.
The formula for speed of sound in air is usually given as:
V = 331.3 + 0.6 T
This is in meters / second and degrees C.
Basically, pressure & density affect the speed of sound in opposite directions and cancel each other out, leaving Temperature as the sole determining factor:
Originally Posted by JButky You would need to determine, not the flute tube temperature, but the temperature of the air inside the tube. I understand that there would be some influence but it is not an absolute corelation. Temperature is shown to not be constant in an acoustic pressure wave. What that translates to in terms of adjusting scaling is therefore quite complex.
Yep - exactly.
Originally Posted by JButky And there are other factors which may have a greater impact on the sytem. I don't deny that these changes are there, but they maybe within a realm of insignificance if other factors are exhibiting greater affect that surpass the difference that temperature variations present.
Possibly - but consider that wind instruments select a pitch by wavelength, so the frequency you get depends on the speed of sound. And the speed of sound varies quite a bit - more than many people realize.
For example most people would agree that a flute tuned for A=440 plays differently from A=442 -the difference may not be huge but it is noticeable. This is about a 0.45% difference in pitch, which is less than a mere 5* F difference in temperature. That is, a flute set up for A=440 plays A=442 if the air is 5* F warmer.
I'm not free to discuss exactly what temperature difference the flute designer I mentioned measured and accounts for in his design since it is proprietary but I will say the difference is more than 5* F. So we're talking about significant effects. Huge? No. But definitely noticeable.

Answer:
Somewhere at the back of my head was a notion that woodwinds were designed for a specific ambient temperature - possibly 21°C (68°F).

Answer:
Originally Posted by MRC01
This is a common misperception, seems intuitive and is even suggested (incorrectly) by some physics textbooks. Speed of sound in air doesn't depend on density - depends almost entirely on temperature alone. The reason sound travels slower at high altitude is because it's cold up there.

Or to put it differently, suppose you are indoors, in a temperature controlled environment. Sound travels at the same speed in that room regardless of altitude because the temperature is the same.

I know it seems weird, but it's true. If it weren't it would be impossible for strings to tune with winds at 6,000'. Strings would be unaffected by altitude while winds would be at A=430.8 - far too low to compensate.
From

"What is the speed of sound?
Speed of sound depends only on
the temperature of the air."

From

"The speed varies depending on atmospheric conditions; the most important factor is the . Air pressure has almost no effect on sound speed. Air pressure has no effect at all in an approximation, because pressure and density both contribute to sound velocity equally, and in an ideal gas the two effects cancel out, leaving only the effect of temperature. "

A far more technical approach that is pretty meaningless unless you up to speed with the physics, is at

It sure is counter-intuitive for me that the speed does not depend on pressure.

Perhaps it could be explained (oversimplistically? incorrectly?) thus:

There is a direct correlation between temperature and the speed of atomic particles. Represent the particles as people in a corridor. They are moving about, and bumping into each other in a random fashion. Their speed of movement represents temperature.

There are large open doors at both ends of the corridor. There is some movement of people in and out the ends of the corridor, to areas where there are more people.

A travelling wave is wave is generated in the form of a group of people pushed into the entrance at one end. Those nearby get bumped so that they have faster velocity towards the far end of the corridor. However the added directional bumping, after many bumps, becomes non-directional,i.e. contributes to the RANDOM motion. All that is contributed to the system is a higher density of people at one end of the corridor.

After a lot more bumping, this higher density evens out along the corridor. When the far end of the corridor has a higher density (of people) that the outside space, the equilibrium of movement in and out is out of balance, so more people leave the corridor. That represents the sound wave leaving the corridor.

The time taken for that pressure wave to reach the other end depends only on the speed of the random motion between bumps, i.e. temperature.

Adding more people (representing pressure) to the system does not increase this speed, so the "sound wave" does not travel faster.

Travel through a solid is quite different, because there are not those large gaps between particles that have to be travelled before the energy of a particle can be imparted to the next particle.