Yes.
When your character is not in immediate danger or distracted, you may choose to take 10.
So as long as you're not in combat, or in other danger, you can Take-10 on any skill check unless it is explicitly stated that you cannot. There is no such explicit prohibition, so you can Take-10.
When you have plenty of time, you are faced with no threats or distractions, and the skill being attempted carries no penalties for failure, you can take 20. In other words, if you a d20 roll enough times, eventually you will get a 20. Instead of rolling 1d20 for the skill check, just calculate your result as if you had rolled a 20.
Taking 20 means you are trying until you get it right, and it assumes that you fail many times before succeeding. Taking 20 takes 20 times as long as making a single check would take (usually 2 minutes for a skill that takes 1 round or less to perform).
Assuming you have enough time, 20 rounds, and the spell will actually last that long, and the spell allows a new save every round, and you have enough rounds of Bardic Performance, and you don't mind a whole bunch of failures, you can Take-20.
This means that the victim of the spell will roll a save, using your Performance skill in place of his normal save. In the first round, you "roll" a 1. In the second round, you "roll" a 2. In the third round, you "roll" a 3. Etc. Eventually, you will "roll" high enough that he will make his save, but it could take a while.
Hint: If a 10 is high enough, just Take-10 and do it in one round. If a 10 is not high enough, you can Take-20, but it literally means that you know the victim of the spell will fail at least the first 10 saving throws for the first 10 rounds of your Take-20.
Agree with DM_Blake that you can both Take 10 (one action to start performance) or Take 20 (20 actions to start performance). With Take 20 it will take fully 20 times as long, you don't get to count up to 20 and succeed as soon as it would work.
That's arguable, especially if the victim is already suffering the effects.
Let's say an enemy is Fascinating your fighter with song. You, as a Bard, want to Countersong that. The fighter is already fascinated so if you fail, nothing else happens, he just remains fascinated.
Is that a "penalty"?
I would say no, it's not a "penalty" so the bard can Take-20 if he wants.
On the other hand, if a Banshee is wailing (one-round attack) to affect the fighter but not affect the bard, and the bard tries to interrupt that with a Countersong, there is clearly a huge "penalty" for failure, and no benefit to spending 20 rounds doing it, but the question is, can a bard even (stupidly) try to Take-20 on this effect?
I would still say the bard can Take-20 if he wants since there is no "penalty" to the bard (and the fighter "may use the bard's perform check" with "may" being the operative word, so he doesn't have to if he doesn't want to; maybe his own Fort save bonus is higher than the bard's Perform check assuming the "roll" of a 1.
But if the bard is in the area of effect and would suffer the "penalty" for failure, then he can't even try to Take-20.
Is the effect of a spell considered a penalty on a failed saving throw for purposes of taking 20?
Only if the Bard will be affected. If another would be affected, they will suffer the effects for 20 rounds, then get the bard's countersong @ Take 20.
Bizbag: I'd honestly never noticed that suggestion was subject to countersong - thank you.
Edit: Actually, I take back the part about the Bard being affected. They can try to Take 20 regardless. If suffering the negative consequences for 20 rounds (or 20 actions) prevents them from completing the Take 20, that's fine, but there are no negative consequences to attempting a countersong - the negative consequences come from the failed saving throws.
Edit: Actually, I take back the part about the Bard being affected. They can try to Take 20 regardless. If suffering the negative consequences for 20 rounds (or 20 actions) prevents them from completing the Take 20, that's fine, but there are no negative consequences to attempting a countersong - the negative consequences come from the failed saving throws.
I see it as one and the same.
The skill, Perform, usually has no consequences for failure (other than you don't make much money when you fail). But the skill DOES have consequences for failure when it is used in place of a saving throw against an effect that does cause consequences to you. Saying the Perform check has no consequences for failure, in this case, is identical to saying the Saving Throw has no consequences for failure, which clearly would not be true - because the skill check IS the saving throw.
Also I believe Take 20 would burn 20 rounds of bard performance rounds, as you assumed to do it 20 times.
Already noted:
Assuming you have enough time, 20 rounds, and the spell will actually last that long, and the spell allows a new save every round, and you have enough rounds of Bardic Performance, and you don't mind a whole bunch of failures, you can Take-20.
Although I didn't explicitly state that it burns 20 rounds of Bardic Performance, so maybe it's better to state that outright, as you did.
How does this bard qualify to take 10 or 20 at all in this situation? Someone is Fascinating your teammate. Even if they're not overtly trying to kill you, that's a Threatened situation.That's arguable, especially if the victim is already suffering the effects.
Let's say an enemy is Fascinating your fighter with song. You, as a Bard, want to Countersong that. The fighter is already fascinated so if you fail, nothing else happens, he just remains fascinated.
OK, replace "enemy" with "a pretty bard in a tavern" who is fascinating your fighter. you want to leave, but the fighter is just sitting there staring and drooling and throwing platinum coins at the beautiful bard. So you decide to Countersong so you can get your fighter friend out of there.
No enemy, no threat, just a lonely fighter and a pretty bard.
In any case, you're not affected either way, so arguably, there is no immediate threat to you. Defining a threat to your whole party as being a threat to you, or as being sufficient threat to not Take-20 is definitely one interpretation, but I interpret it differently.
For example, the PCs get split up and the whole party is in a room slowly filling with water and they're all going to drown, except the rogue who is outside the room trying to disable the trap. The rogue is in no danger of drowning and no monsters or other threats are endangering or distracting him. the trap is already sprung, there are no consequences for failing to disable it. Eventually the group inside might drown, but the water is filling slowly and the rogue believes there is time to Take-20.
Can he Take-20 on disabling the trap or not?
I say yes, he can.
"When you have plenty of time, you are faced with no threats or distractions, and the skill being attempted carries no penalties for failure..."
He has plenty of time, he is not faced with threats or distractions, and thee is no penalty for failing the Disable Device check.
So Take-20 should be allowed.
No real difference in the tavern/bard scenario, though I agree, my initial scenario where I said "enemy" probably wouldn't qualify.