Jan, you are correct, I had it backwards and that throws my whole argument off. I found a couple of things online that support your idea.
"Sounds can be heard clearer on a cold night-
The speed at which sound travels through a medium depends on the elastic properties and density of that medium.
In general the more dense the medium, the greater the speed
As the temperature increases so does the speed
The fact that the speed of sound in a gas increases with temperature sometimes causes refraction
On a warm day the air near the ground is warmer than the air higher up and sounds travel faster near the ground
This causes it to be refracted upwards
At night the air near the ground is cooler and the sound is refracted down and appears to travel better over the ground."
"Warming up wind instruments. As a saxophone warms up, you need to pull the mouthpiece out to keep it in tune. Thing is, this doesn't seem right to me. As a sax gets warmer, I should think it would expand, making the tube bigger and longer, forcing a player to compensate by pushing the mouthpiece in to shorten it up.
Metals expand by about .001% to .002% per °C. And in any case, the metal itself doesn't warm up much. So the change in the dimensions of the instrument are negligible.
Two things happen when the instrument warms up. First, the air inside becomes warmer. The speed of sound in air is proportional to the square root of the absolute temperature. Normal temperatures in a sax are roughly 300 K, so this effect is worth about 0.17% per °C (K is for Kelvin, the units for absolute temperature. A temp difference of 1°C and 1K are the same, so you convert to K simply by adding 273 K to the temp in °C.)
The other important thing is that the air in the instrument becomes humid: your breath is nearly saturated at 37°C and when it cools in the instrument, water condenses on the metal providing a water reservoir to keep the air nearly saturated in the instrument. The speed of sound is is inversely proportional to the square root of the average molecular mass of the air. Water molecules are lighter than nitrogen or oxygen, so humid air is less dense than dry air, all else equal. (Yes, I know that non-scientists talk about humid air being 'heavy', but I think that by this they mean that one sweats less effectively in humid air.) From normal values of humidity to saturated can increase the speed of sound by 0.1 to 0.2%.
So it's easy to have 1% or even 2% or more increase in speed of sound, and therefore in playing frequency. A semitone is only 6%, so this is a lot."