Assuming you have a simple scale, my answer is 9.

First divide the coins into 3 piles of 9.

Measure 2 piles at a time until you find the pair that is equal in mass. This can take up to 3 tries, but if you were lucky you could get it on the first try.

Put the piles of coins with equal mass to the side.

Repeat the process this time with 3 piles of 3 coins, maximum 3 measurements.

Repeat the process this time with the 3 remaining coins, find the two that are equal, the remaining coin has a different mass.

If you are a very luck person you coulp potentially only have to make 4 meaurements, 3 to rule out equal pairs and 1 to compare the final coin to the rest.

9 is the most you would have to do the efficient way, and at any point you can observe is the unequal pile has more or less mass.

Six is the minimum for exact weight of finding the coin

1. Divide 27 into 3 piles of 9 coins each.

Weigh two piles against each other.

If weight is same, the third pile has the coin of different weight.

2. If weight is different, take one pile off the weighing machine and put the other pile of 9 coins.

Again weigh against each other.

If weights are same, then the pile you took off has the coin. If not, then the pile on the machine has the coin

So in 1 or 2 weighings you got the pile of 9 coins.

3. Similarly, divide the 9 coins into 3 piles of 3 coins each

Weigh two piles against each other.

If weight is same, the third pile has the coin of different weight.

4. If weight is different, take one pile off the weighing machine and put the other pile of 3 coins.

Again weigh against each other.

If weights are same, then the pile you took off has the coin. If not, then the pile on the machine has the coin

So in 3 or 4 weighings you got the pile of 3 coins.

5. Similarly, divide the 3 coins into 3 piles of 1 coin each

Weigh two piles against each other.

If weight is same, the third pile has the coin of different weight.

6. If weight is different, take one pile off the weighing machine and put the other pile of 1 coins.

Again weigh against each other.

If weights are same, then the pile you took off has the coin. If not, then the pile on the machine has the coin

So in 5 or 6 weighings you got the coin with different weight.