The most important factor for producing a note in tune is possessing an accurate aural perception of that note. Once this is present, intonation is developed by practising to match the note we produce with this standard. (In Carnatic music, of course, we do not have an "absolute note" -- they are all relative to the chosen reference SaDja.) Thus, for perfect intonation, a keen sense of hearing is absolutely essential.
When performing in large halls, musicians hear their own instruments only very faintly. And there isn't enough echo either.* So, intonation becomes a big challenge. Now, an accompanying Carnatic artiste has a tougher problem -- he needs to be able to hear the main performer as well. Furthermore, an instrument that is initially tuned perfectly to the taMbUrA, may go out of tune during the course of the concert; and the musician needs to be able to detect when this happens and correct it based on the taMbUrA that is droning some distace away on the platform. (And, to repeat, "I can't hear no nothing!")
Usually, to enable the performers to hear themselves, a speaker system (called a monitor or "fold-back") that is directed towards the platform is provided. However, I have never seen one in a Carnatic concert. In addition, few concert venues are actually auditoria built with necessary acoustics for a music performance. Many are just open spaces with asbestos roofing (Ayodhya Mandapam, YGP Auditorium, etc.).
Given all these hurdles, I am amazed how our musicians perform with perfect intonation. They are practically performing deaf.
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* An extreme case would be a recording studio, whose walls are built to expressly prevent any echoes. This is why (as we have seen in movies scenes featuring a studio recording) the artistes are supplied with headphones.
Update (20 Dec): I have found a related Wikipedia entry -- Foldback. Excerpts:
The provision of foldback (or monitor) speakers is essential to performers, because without a foldback system, the sound they would hear from front of house would be the reverberated reflections from the rear wall of the venue. The naturally-reflected sound is delayed and distorted.
... On stages with poor or absent foldback mixes, vocalists may end up singing off-tune or out of time with the band.
Update 2 (26 January): A post from an excellent blog (by Ramnarayan) I stumbed upon says:
Young vocalist Savita Narasimhan clarifies that the musician on the stage rarely asks for the volume to be turned up for the listeners. He or she is actually asking for help with the feedback (or fallback) so essential for the performer on stage. “Often the vocalist cannot hear the percussionist or violinist and vice versa. The musician’s request to increase the volume of the monitor is misunderstood and the technician increases the volume for the audience.”