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Cumulative upkeep
(At the beginning of your upkeep, put an age counter on this permanent, then sacrifice it unless you pay its upkeep cost for each age counter on it.)
: Put a music counter on target creature. If it doesn't have "At the beginning of your upkeep, destroy this creature unless you pay
for each music counter on it," it gains that ability.
If a music counter is put on a creature by some other means (Fate Transfer, for example), but that creature has never been affected by Musician’s ability, that creature won’t have the triggered ability and its controller won’t have to pay mana. The music counters will stay on that creature but won’t do anything.