Was Riker's holodeck jazz trio actually playing the music we hear?

Question

This is about the production of Star Trek TNG episode "11001001".

Riker fires up a holodeck program to recreate a jazz club. On stage there are 3 musicians. At one point in the episode, he briefly picks up a trombone.

My question(s): were the actors actually musicians? Is the music we hear actually from the performance we see i.e. filmed "live"? And is Jonathan Frakes really playing that trombone?

The thinking behind my question:

Capturing and utilizing the whole performance would create a natural feel and flow to the scene - it does seem as though that is what was done, but appearances can be deceiving.

The musicians could be real musicians, even if the music we hear was recorded separately due to the difficulties of working with "live" sound

The "musicians" could simply be actors and the music was performed by someone else entirely - it's all "movie"(TV) magic.

Answer 1

In the scene where the musicians' hands are visible it is absolutely clear that they are not playing the instruments at all. The drummer's brushes don't touch the snare drum or the cymbal, the pianist does not depress the keys and in a close-up of the bassist's hand, the strings are do not vibrate after supposedly being plucked.