Technically the blanket licences here in the UK from PRS (performance) or MCPS (recording) do not include the right to make an adaptation or alteration of the work.

Consequently if the change is enough to amount to an arrangement or adaptation then, technically, the permission of the copyright holder or relevant representative is necessary.

I learned the above in the 80s when a client of mine recorded a video version of Britten's "Young Person's Guide to the Orchestra" after getting a standard MCPS permission - but changed the order of the movements to make it easier for the narrator to walk from section to section of the orchestra. I was instructed after the dirty deed was done and made public. A screaming hissyfit from a certain person at the Britten estate followed with many insults about the lack of artistic taste of my clients! Expensive for client: no way out.

The same would technically apply to changes in words melody and harmony (or counterpoint or countermelody).

It has been accepted by the courts that a rhythm can amount to enough of a musical work to make the originator of the rhythm a co-owner or part owner of copyright. What has not yet been tested is whether this is true of mere changes of tempo and if so at what point.

In the real world I suspect most people forget it.