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Old vs New

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?
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?
WIth the "ratio" I meant the percentage of the deviation at A440 that you go down for each note you go up.
The drop in tremolo is 30% after one octave and not 50% because subjectively our brain expects the number of "beats" per second that you hear to go up a bit as the frequency of the notes gets higher. If the tremolo goes down to 50% in one octave, where the frequency doubles, then the number of beats you hear stays the same, and if the number of cents tremolo stays the same then the number of beats doubles. When the number of beats at A5 is the same as A4 we hear that as having less tremolo at A5 and when the number of beats at A5 doubles we hear that as too much tremolo. The tremolo going down by 30% is a compromise that results in our hearing observing that the "amount" of tremolo stays roughly the same.
 
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