Author: John Peacock
Date: 2017-04-18 13:58
Burt: sorry to keep on, but some of your statements are wrong, or at least misleading.
> The pitch drops with increase in air density.
> Lowering the temperature is one way to increase the air density.
> Reducing the air pressure will decrease the density
This statement suggests that you think the pitch must rise if you reduce the pressure, thus decreasing the density of air. But to repeat, provided you achieve this reduction in pressure without altering the temperature, it will have no effect. The density can (and does) go up and down with atmospheric pressure, but we only care about the temperature - density in itself doesn't matter at all.
And even ambient temperature doesn't matter all that much. Everyone exhales air at 36C, and I presume that the air column inside a clarinet attains a temperature that is dictated more by this supply of hot air than by what's happening outside. It's easy to see that this must be the case, e.g. by considering ambient temperatures of 20C and 30C, which are easily within the range of normal playing conditions. As you rightly say elsewhere, the frequency scales as the square root of temperature in Kelvin, so that would be a frequency difference of 3/10 of a semitone. The only way way can play in tune in practice is if there is a high degree of similarity in the temperature of the air inside our instruments.
Finally, on the CO2 issue, Google tells me that exhaled air contains typically 4% CO2. CO2 weighs 1.5 times as much as the mean molecular mass of air, so that boosts the mean molecular mass by 2%, yielding a 1% reduction in the speed of sound in CO2-enriched air, i.e. 20% of a semitone. Probably any real-world effect is smaller than that, since I expect the air in our lungs always has a fair proportion of CO2, even when a fresh breath is mixed in. But even if the proportion of CO2 was (say) 4% at the end of a long phrase and 3% straight after a breath, that would shift pitch by 5% of a semitone - a detectable change.
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The Clarinet BBoard
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