The time scale is set by the orbital period of the innermost stable circular orbit (ISCO https://en.wikipedia.org/wiki/Innermost_stable_circular_orbit https://e

The time scale is set by the orbital period of the innermost stable circular orbit (ISCO https://en.wikipedia.org/wiki/Innermost_stable_circular_orbit https://en.wikipedia.org/wiki/Innermost_stable_circular_orbi...). That period depends on the spin of both the black hole and the accretion disk, but the possible orbital periods range from 4 to 54 minutes for our galaxy's supermassive black hole. The period is proportional to the black hole mass, so for a really big black hole like the one in M87, the period is weeks long. That's part of the reason why the EHT imaged the M87 black hole, but has not produced a Sgr A* image - it takes many hours for the EHT to gather the data to produce an image, and Sgr A* is not stable on that time scale. It's like taking a long exposure of a foot race. But M87's black hole can't change much in a few hours.