> All clock signals were derived from that single quartz. That meant that also the clocks driving the raster beam were derived from that single quartz.

Yes, and that VIC clock also drives the SID sound chip. So while the same code will play a song back "in tune" (relative pitch) on both a PAL and NTSC C64, it will be tuned lower (absolute pitch) on a PAL C64. Think of it like the concert pitch difference between A = 443 Hz (Germany -- common) and A = 430 Hz (Verdi tuning a.k.a. Schiller Institute -- uncommon).

To play the same absolute pitch on both a PAL and NTSC, code could use an alternate lookup table to map a note to different SID frequency register values for PAL or NTSC. In practice, I don't think this was done, but someone can correct me. What was, sometimes, done was skipping every 6th frame of a raster vblank music playback routine on an NTSC C64 (@ 60 Hz) to match the tempo (not pitch) of the same song played on a PAL C64 (@ 50 Hz).