Westerners are constantly confused about the tuning of Indian instruments. Interestingly enough the source of this confusion is more cultural than musical.
In the West, there is a basic principle of standardisation. One can take virtually any instrument and refer to any string and declare down to the very number of vibrations per second what the tuning is going to be. Presumably this cultural predisposition is a result of the symphonic tradition (i.e., the only way that you can have 50-100 musicians playing together is if there is standardisation).
We must not forget that when we stand apart from the Western tradition, we find that such standardisation is an aberration. It is not a part of most of the world's musical traditions.
The Indian approach to tuning musical instruments is basically similar to that of the guitarist who adopts open tunings. In this fashion, a guitarist may adopt any tuning that is appropriate to the particular piece he/she is going to play.
Even though standard tunings for Indian instruments are rare, standard approaches to tuning are the norm. Let us look at these approaches.
Key - An unmodified instrument will play from one pitch only. If you have to change the key, you will have to either retune the instrument, change the playing string, or change the entire instrument. Indian musical instruments are not designed to change keys in the middle of the piece (although the people in the film industry have developed workarounds).
Mode - Many Indian stringed instruments such as sitar, sarod and sarangi, have a number of sympathetic strings and/or drone strings. These will be tuned according to the rag that is being played. Since the number of strings generally exceed the number of notes in the rag, this leads to different approaches to their tuning. As a general rule, as long as you adhere to the notes of the rag almost any approach to tuning these strings will work.
Bansuri - Bansuris are of a fixed tuning. One must have a selection of different bansuris so that you can select the appropriate flute for your particular application. For six-hole bansuris, the lowest note of the flute is generally chosen so that it corresponds to Pa. For filmi and light music, it is not unusual to select a flute such that the lowest note corresponds to Sa. The situation will be different when dealing with seven-hole bansuris.
Dotar (simple two stringed variety) - In South Asia, the particular folk music cultures may vary every hundred miles. Therefore it is impossible to make blanket statements about a dotar's tuning. However at least one of the strings will correspond to the tonic.
Gopichand - The gopichand is usually tuned to the tonic
Harmoniums are of a fixed pitch. Any change of pitch must be done by a tedious process of scrapping microscopic amounts of metal off of the reeds. However within the fixed tuning of the harmonium, it is based upon a tempered scale. Therefore any key can correspond to Sa according to our requirements.
Mridangam - The sides are generally tuned to either Sa or Pa
Pakhawaj - The sides are generally tuned to either Sa or Pa
Pungi - The pungi also known as the bin, is often considered to be more of a noisemaker than a musical instrument. Therefore it is often left in a semi-musical state. However, if a more precise tuning is required, it is sometimes tuned by partially occluding holes with wax.
Sur-Peti (acoustic) - The sur peti has a number of stops. The design and number of stops varies considerably. Some sur petis are designed to cover only a few steps while others are designed to cover an entire octave. The proper selection of stops varies according to the design.
Sur-Peti (electronic) - Electronic sur petis and electronic tanpuras vary considerably in design and features. Refer to the user's manual for proper tuning.
Surmandal - The surmandal will be tuned according to the key and mode (that) of the rag
Tabla - The right hand drum is generally tuned to either Sa or Pa. Opinion is divided as to whether to tune the left side or not. The majority of musicians say that it is not necessary to be tuned, due to the constant modulations of the bayan.
Tabla Tarang - Each tabla of the tabla tarang is tuned the note of the rag. But remember, the open "Tun" stroke is generally a full tone higher than the other strokes of the tabla. Therefore you would not tune it as you normally would tune a tabla, but generally a full tone lower than your normal inclination would be.
Tanpura - The thick heavy outer string is tuned to Sa. The medium outer string on the opposite side is a fifth up (Pa), and the two lighter gauge strings in the middle are set to Sa, but an octave higher than the thick heavy Sa string. In situations where the Pancham is not present, the Pa string is usually tuned down to Ma.