Travelling from the US, I am allowed to carry 2 pieces of luggage. I am checking a guitar as one. The guitar case is 12 cm over the maximum dimensions. I was told they cannot tell me until I arrive at the airport how much it will cost. Anybody have any info on this? I don’t want to be surprised with a huge fee.
Given that this is a flight from the US, the guitar must treated as a standard bag, even if it is over the allow size for such a bag! This is true regardless of whether you choose to carry it on board, or put it in your checked baggage.
This was made law as a part of the "FAA Modernization and Reform Act of 2012" - you can find the details of the rule directly from the US Government here. The US Department of Transportation has since clarified some of the statements in this rule in a further document that should be read in conjunction with the above.
Given that you are flying a non-US airline it is possible they will not be fully aware of this law, so it would be worth carrying a printout of the details just in case you have any problems.
The Rule cited by @Doc above requires certificated carriers (I assume all passenger-carrying carriers in the US are certificated, including Turkish Air) to accept musical instruments as carry-on baggage, even when larger than the airline's normal carry-on limits, provided the instrument can be accommodated in the in-cabin storage of the aircraft.
If it cannot be so accommodated, the instrument must go in the hold. Under some circumstances, the airline may charge for hold instruments. The second cited source (the Federal Register, which contains the actual text of the Rule) says:
...we conclude that carriers may impose the same checked-baggage charges that apply to other checked baggage of that size and weight. If a musical instrument exceeds the size or weight limits in the carrier’s free baggage allowance but does not exceed the size or weight limits of Section 403, the carrier may assess the same over- size and over-weight charges that are applicable to other checked baggage that is over-size or over-weight.
This means that if the checked instrument goes in the hold and does not exceed the limits imposed by Section 403, the airline can charge for it, in the same manner it'd charge for other over-size or over-weight luggage.
Section 403 appears in 49 U.S.C. Section 41724, the final sub-section of which is:
(3) Large instruments as checked baggage.
An air carrier shall transport as baggage a musical instrument that is the property of a passenger traveling in air transportation that may not be carried in the aircraft cabin if:
(A) the sum of the length, width, and height measured in inches of the outside linear dimensions of the instrument (including the case) does not exceed 150 inches or the applicable size restrictions for the aircraft;
(B) the weight of the instrument does not exceed 165 pounds or the applicable weight restrictions for the aircraft; and
(C) the instrument can be stowed in accordance with the requirements for carriage of carry-on baggage or cargo established by the Administrator.
Thus, depending upon the size of the instrument in question, it may be carried in the cabin as a carry-on, or carried as hold cargo; in the latter situation, if the instrument exceeds the airline's hold baggage size and weight limits, but is less than 165 pounds (or the applicable weight restriction for the specific aircraft) or exceeds 150 inches (or the applicable size restriction for the specific aircraft), then the airline can charge for the instrument's carriage.