Pan pipes in the Andes

I ride the subway to and from class a couple times a week, and every so often there's a band playing music from the Andes.  Usually, these bands have a least one guy playing a pan pipe, which is essentially a series of tubes stuck together.  When the musician blows across the top of a particular pipe it makes a sound.  Listen to the music here, for example: http://www.youtube.com/watch?v=GIXE-5NrC3o

In any case, the other day, when I stopped to listen, I began to wonder: Do these pan pipes sound different back in the Andes?

I'm going to try and avoid any serious physics/mathematics here, but there three important things to consider.  First, that in a pipe of fixed length, the frequency of a sound wave (i.e. the particular note you hear) that resonates in that pipe depends on the speed of sound.  Second, the speed of sound depends on the density of the medium it's travelling through, which in our case is air.  Finally, the density of air changes at different altitudes.

So, since the density of air is different at different altitudes, the speed of sound is also different, and therefore the frequency a pan pipe plays will be different.  Assuming I did my math right, the ratio of frequencies at different altitudes is equal to the ratio of the speeds of sound at the different altitudes.  So, the frequency of the pipe in the Andes  is related to the frequency in the NYC subway system, by:

Although there are ways of calculating the speed of sound at different altitudes, I just looked it up in a table (you can also enter any height, and this will calculate it for you).  The average altitude in the Andes is 4,000m, so the speed of sound there is 324.6 m/s and NYC is at approximately 0m so the speed of sound there is 340.3m/s. Thus, the frequency will be shifted down (lower pitch) by around 5%.

What this means, in practice, is that most notes will sound about semitone flatter in the Andes than they do in NYC.  For example, if this is how the music sounded in the subway:

This is how it would sound in the Andes:

So, the music you hear in the subways is not really authentic; it's a semitone high pitched.