Doppler puzzle

[John Delmore]

Hi Mark:
You're not all wet --perhaps just a little damp!!  

It's not your speed that changes if you measure different pitches--it's the
size of the cents around that pitch.  So, if you're working with a
difference in cents from a certain frequency, you'll get a different result.
If the question had been phrased in Hz, you wouldn't have this problem.

For example:

A440+10 cents = 442.5489 Hz, a difference of 2.5489 Hz
A440-10 cents = 437.4658 Hz, a difference of 2.5342 Hz
A220+10 cents = 221.2744 Hz, a difference of 1.2744 Hz
And A220-10 cents = 218.7329 Hz, a difference of 1.2671 Hz.

(I hope I got these right, I'm using the "2^1/1200:1" definition that I
learned thanks to this discussion)

I'm working on the general formula to determine "cents difference" from a
pitch for any frequency, but that's a little more math than I have time for
right now...it involves the dreaded logarithmus naturalis, I think.

I hope these minutia aren't too far afield...they're a lot more "on-topic"
than "that other thread"...

John