acoustics - Do we hear sounds differently on the highest mountains?

Some searching gives that above 6,000 meter altitude the air density is less than half of that at sea level. Speed of sound is about 15-20% slower and "acoustic impedance" seems to change too.

Do humans notice these differences in sound? Does the pitch of tones change noticeable?

Answer

There more sides to this scenario that you're considering. Firstly, if we are assuming that the temperature is the same at sea level and on the high mountains, then the speed of sound doesn't actually change, as a constant temperature will take care of the air pressure-density ratio.

$$c = \sqrt{\kappa \frac{p}{\rho}}$$ Where $p$: static air pressure, $\rho$: air density and $\kappa$ the adiabatic index $c_p/c_v$.

Again the statement being: The static air pressure and the density of air are proportional at the same temperature, meaning the ratio $p/\rho$ is always constant, on a high mountain or even on sea level altitude.

So in the scenario you're describing, if $T$ is taken as constant, then the speed of sound doesn't change, but its intensity does, as the density of the air is much lower on top of mountains, rough approximation for the intensity would be

$$I \propto p v \propto \omega² c \rho$$ Where $v$ is the speed of air molecules, $\omega$ sound frequency. So one thing is for sure, you will need to shout much louder on a mountain, for people further ahead to be able to hear you.

Furthermore, if $T$ is changing, then ($p/\rho=constant$) doesn't hold anymore, so $c_{air}$ changes. There are rough approximates relating the speed of sound to $T$. In a crude manner:

$$c_{air} = 331.3 \frac{m}{s} \sqrt{1+\frac{\theta}{273.15}}$$ Where $\theta$ is the air temperature in °C. Such estimate gives e.g. $60 \frac{cm}{s}$ change of speed of sound for $1 °C$ change of temperature. Further scenarios:

At $-20°C$: $c_{air} \approx 319 \frac{m}{s}$

At $0°C$:$c_{air} \approx 331 \frac{m}{s}$

At $20°C$: $c_{air} \approx 343 \frac{m}{s}$

At $100°C$: $c_{air} \approx 387 \frac{m}{s}$

Next logical step would be to consider the change in wavelength of the sound, when $c_{air}$ changes. For this you have the general formula $c = \lambda f$

So $\lambda$ changes with $T$ as the speed of sound changes and in case of a flute e.g. the length of the vibrating air column doesn't change, so when $c_{air}$ changes due to $T$ fluctuations, then the sound frequency $f$ changes (or pitch of tone as you call it). But since we don't use flutes to speak, this doesn't concern us, so in order to conclude, in a mountain, the intensity I, speed of sound $c$ and the sound wavelength $\lambda$ change (the last two only hold for $T$ varying) but not the pitch.