what stops them from reaching situation where they never actually catch each other and constantly jump on the same sequence, but with shifted index of the sequence array?

You use an interrupt to determine the time to change to the next frequency. However the actual frequency change is performed on the main loop. I understand interrupts are used to get a precise 'interrupt_time' of 10 ms intervals to set the next frequency.

However I think that given how it works you should be able to do the same by just storing the last millis() as a multiple of 'interrupt_time' and checking whether the next millis() multiple is greater than that. I think it works the same as the 'fired' variable in your code because millis() value is interrupt-generated anyway.

That approach would greatly simplify the code and make it more portable. Does this make sense to you?

Thanks