Bansuri, as we all know, cannot be (and need not be) tuned once it is made. This is unlike many other contemporary instruments. Does this mean that the pitch of the bansuri is constant once it is made?
Actually – no. It is actually very common that the pitch of the Bansuri can change from day to day and from person to person.
There are several factors that affect the pitch. These can be categorized in two areas – environmental factors and individual factors.
Basic physics behind sound production in Bansuri will tell you that the sound is function of length and width of the air column, temperature of the air column, density of the air and humidity. While the length and width of the Bansuri get fixed while designing and making the Bansuri, the other factors change every day. It is very common to have a Bansuri play a couple of cents lower in winter compared to summer or in mountains compared to sea level. Barometric pressure also seems to make some difference.
Each player has different characteristics of blow in terms of how hard or soft the blow might be. This in itself is function of lung power as well as embouchure style (i.e. how you shape your lips). I recall in my beginner days, my teacher played the Bansuri I was playing during the lesson and he could manage to play it one full note higher because of the power of his blow (and lack of it in mine).
It also matters how much of embouchure hole you cover with your lips. More you cover the embouchure, flatter the Bansuri sound.
Additionally, even within the same register, pressure needed to get optimum sound from each hole is different. For example, air pressure needed to play Pa note (all six holes closed) will be much lower than pressure needed to play Sa note (only three holes closed). A well designed Bansuri will have linearity in increase of pressure for every higher note so that it is comfortable for the player.
So what does this all mean practically. If you are playing solo, it means that rather than tuning your tanpura to a standard note such as E and then trying to adjust the Bansuri sound, you are better of warming the Bansuri by playing it for a couple of minutes and then adjusting tanpura pitch to wherever it might be comfortable. Indian classical music is about relative pitch – once you fix Sa, all other notes get fixed relative to it. But there is no defined pitch of Sa and therefore, you can adjust it to whatever pitch might be comfortable.
If you are playing in a group or in band, you may have to adjust the pitch. This is done by adjusting the intensity of blow, adjusting how much you are covering the blowing hole and by changing the angle of blow. Often people performing in bands are known to carry multiple flutes that are a few cents apart and picking the one that plays comfortably to the band pitch.