But aren't the knowledge to use instruments is needed first?
I've seen Urist in taverns simulating x instruments.
But that does not mean my Civ knows how to make x instruments.
I've not gone the extra mile to check if I have x instrument available, and temple for deity that Urists worships yet.
Worth a !science! check.
I do wonder if furniture built instruments are needed instead of hand held item instruments.
I tracked music skills in several forts until I got the gist of it and grew bored with the record keeping. Dwarves don't need skill to simulate, play or dance, but someone needs to have skill in a piece (music or dance) to get things started. Hence arts spread like virus'. If you look at a job while a dwarf is simulating, playing, dancing, or singing, you can learn where the piece originates and all of the instruments required. If the piece originates from your civ, all of the instruments will be from your civ and you'll be able to build them.
I'm about 90% on the above speculation. I recorded about two dozen pieces over about a half-dozen forts. In all cases either the above was true or the piece originated in a different civ and I was unable to build any of the instruments. In the example below the form is The Satin of Sweetness, from The Chestnut Kingdoms and requires a singer and a Shato. In this fort there were several different songs in the form of the Satin of Sweetness, but all required a singer and Shato. Once I crafted a Shato, they stopped "simulating Shato" and started "playing Shato". More Shatos did nothing.
Whether the instrument is built or hand held is a property of the instrument only, and so shouldn't make any difference if dwarves are preforming in a temple. Though there may be a connection to temple music forms and built instruments, dwarves would still be able to Simulate the instrument even if it weren't there. But since all of my recordings came from Inn performances, I don't honestly know what differences there are.