We talk about temperaments here but that applies to the way sounds and notes mix and mingle together and I don't think it applies to tuning. Yes it is important in music if you want an ethereal sound for say a suspense thriller soundtrack where you want that perfect sound for to set the mood.
I was speaking about something that cello, viola, and violin players do. They tune the open notes of their instruments in perfect fifths against (I believe) their A strings which are tuned to concert pitch. Since they have no frets they can adjust the finger position of each note as needed to play against fixed pitch instruments when that is required. Three of their open notes will be a bit off compared to a piano, for example, however and I assume that they avoid open notes when that would be a problem. A fretless bass could be tuned in perfect fifths and fingered accordingly when even tempered notes are needed. But you cannot bend the notes on a fretted bass or at least you can only bend them up, so in my opinion a fretted bass should be tuned to even tempered notes using an electronic tuner rather than in perfect fifths as a cellist would. A fretted bass tuned against an electronic tuner will give you the same notes, good or bad, as any other even tempered instrument. Tune the open strings to perfect fifths and all the fretted notes will be neither even tempered nor just and I cannot see that as being a useful sate of affairs in many circumstances.
Ken
very hard to eq that out.