I have a piece that is set at dotted quarter=72 in 6/8 time. What would this be in bpm? And does 6/8 change anything?
What would this be in bpm?
It would be 72 bpm. The fact that the metronome setting is given for the dotted quarter note indicates that each dotted quarter note is one beat. Besides, 216 bpm is far too fast to be practical.
And does 6/8 change anything?
Aside from the meter, no. For example, if the metronome mark were the same in a 3/8 or 9/8 or 12/8 piece, you would still be playing 72 bpm. The number of measures per minute would change, of course, since the number of beats per measure would change.
The time signature 6/8 is compound duple. There are 2 beats in a bar, and these are dotted crotchets (dotted quarter notes). These beats are subdivided into three pulses that are quavers (eighth notes).
So if the tempo is given as a dotted crotchet = 72, this means there are 72 beats per minute, and (3x72=) 216 pulses per minute. You would set a metronome to 72 (adagio) because this will click on the beats. And you would count as 1-trip-let 2-trip-let :| or something similar emphasising the beats (numbers) only.
The two existing answers are correct and helpful. I just want to add, in case this wasn't clear to you:
In general, in a 6/8 meter, you can either think of the eighth notes as the beat, in which case there will be six of them in a measure; or you can think of the dotted quarter as the beat, in which case there will be two of them in the measure.
(Actually, if the tempo is super, super fast, a conductor might just give one beat per measure!)
What's special about a 6/8 meter: There is an inherent ambiguity -- shall I think of this, or conduct this, with six beats in the measure, or with two beats in the measure? I think it's best to be flexible about this, and realize that there is a duality. As you are playing, it may sometimes feel like two groups of three beats in a measure, and sometimes like two beats per measure. Which one fits the music the best may change from one section of the piece to another, and it's good to train yourself to be able to make the change without changing the metronome marking.
Dotted crotchet =72bpm. That equates to two clicks per bar, each click meaning three quavers. If you set the metronome to three times that - 216bpm, it would be six clicks per bar - one for each quaver, were there six played in a particular bar.
HOWEVER - a lot of metronomes, especially mechanical ones, won't quite reach that. And it's manic! So set for 72bpm and recognise two clicks per bar. The 6/8 won't affect the tempo to play at. That's catered for in the 'dotted quaver = 72bpm.'.
In 6/8 the beat is a dotted quarter. So dotted quarter=72 IS 72 beats per minute. If you mistakenly thought 'beat' (as in b.p.m) always meant 'quarter note', that should be sufficient answer.
But perhaps this question refers to a very basic sequencer program that DOES think that, one that only counts tempo in quarter notes? Dotted-quarter=72 equates mathematically to 8th=216 (3X72) or quarter=108 (half of 216).
Consider very carefully whether this information is of any practical use though! I doubt you'd find a metronome clicking every 2/3 of the musical beat very helpful.