Musical notes are pretty well defined sound frequencies. The medium which carries that sound wave is irrelevant. You can even get yourself a pair of bone conduction headphones, which would work for listening to music even if you were in a vacuum - since ultimately what matters is the sound wave hitting your ear bones, thr air is just the most common way for it to happen.
Of course, the sound that non-electrical instruments make is indeed dependent on the atmosphere in which they are played, assuming the same motions etc. You could probably make a violin produce the exact same sounds that it does on Earth playing it on Mars, but you'd have to play it differently than you do here. But even this doesn't apply to electrical instruments - Jimi Hendrix would sound the same if he could somehow play on the surface of Mars.
Of course, the sound that non-electrical instruments make is indeed dependent on the atmosphere in which they are played, assuming the same motions etc. You could probably make a violin produce the exact same sounds that it does on Earth playing it on Mars, but you'd have to play it differently than you do here. But even this doesn't apply to electrical instruments - Jimi Hendrix would sound the same if he could somehow play on the surface of Mars.