A 50% drop would lead to the same beat frequency. But as you go higher, a higher beating frequency tends to sound better. So the 30% is a compromise between the 0% drop you'd expect when keeping the tremolo reed set self-consistent with clean internal intervals, in particular clean octaves, and between the 50% drop you'd expect when keeping the beat frequency constant.Can you explain the math?
If I understand correctly going from A440 to A880 drop the number of cents by 30%? Naively I would expect a 50% drop
What ratio stays the same?