I’ve seen this before! Indeed it has nothing to do with Python or the GIL.

The OS scheduler has to execute M threads on N cpu cores, while also balancing competing priorities like latency and power usage.

Because each separate process uses a naive timer, the timings will drift slowly due to imprecision and small process scheduling delays etc.

After enough drift the timers will sync up by chance (harmonics), at which point OS scheduler incentives can lead the timings to “stick” together seemingly.

This may be a bit tangential, but I find it fascinating that there seems to be a mechanical version of this phenomenon with ancient roots - lookup spontaneous synchronization of pendulums.