What's going on in a tin whistle when I produce a note between two regular notes by partially covering a hole?
I have a tin whistle nominally in the key of D. I can play an E (671 Hz) by leaving the bottom hole uncovered and I can play an F# (752 Hz) by leaving the bottom two holes uncovered. If I partially cover the second last hole I can get various pitches between E and F# (714-730 Hz).
So how does half covering a hole change the pitch? My naive understanding is that the distance from the mouthpiece to the nearest open hole determines the wavelength of the standing wave and thus the frequency. Half covering a hole doesn't change this distance so clearly there's something else going on. What is it?
(I've noticed that the lowest two holes on soprano recorders are usually double holes to facilitate this technique of half covering a hole.)