Different vibrating tone on a belt drive with a Shimano Alfine hub
Try more tension on the belt. It will help with the skipping problem and a tighter belt will change how the belt vibrates.

For internal gear hubs Gates recommends 35 – 50 Hz
Montague Bikes - Adjusting Belt Tension with an Eccentric Bottom Bracket

Based on this article you are adjusting the belt just 2 Hz more than the minimum.
This gives you some wiggle room to experiment with. Try 40 or 45 and test for changes.

I think, perhaps, the #1 problem with the Alfine 11 is belt drive. Lots of Alfine 11 bikes come stock with Gates. Not a single belt bike I have ever worked on came in with the belt tension high enough.
Sheldon Brown - Additional comments by Aaron Goss (toward the bottom of the page)
Note: the Alfine 11 is similar to the 8