Yes, according to Einstein, the effects of gravity are "equivalent" to acceleration.
So it's not only high rates of motion that cause time to slow down, but also strong gravitational fields.

A windowless elevator accelerating through empty space in the absence of gravity (left) is indistinguishable from one at rest in the presence of gravity (right).
https://www.cfa.harvard.edu/~ejchaisson/cosmic_evolution/docs/fr_1/fr_1_part1.html
The music would be different on the two elevators.