I am traveling with an Indian Musical instrument known as a Tabla Set. Will Etihad Airways allow me to carry it on board as hand baggage?
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Etihad Airways require to check your musical instrument, from Etihad's policy:
Musical instruments must be transported as checked baggage only.
So it all comes down to the size and wight of Tabla Set. If you can fit it in a proper bag and are less then 7kg, you are good to go.
Each item must not exceed dimensions of 115 cm (40x50x25).
You can always buy additional seat, if the instrument is very expensive and too bulky for the over head compartment.
Airlines do allow exceptions sometimes. Although, even if you have such case or example, there is no guarantees that it will happen again. So you should follow their rules on the website or be prepare to check you luggage in case of refusal.