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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.)

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The effective "end" of the pipe depends on the nature of the opening. Even the length of an "open" cylindrical tube does not coincide exactly with the physical end, but will be slightly longer, resulting in an End Correction. In flutes and whistles there is also a "correction" for the mouthpiece.

It is consistent that partially covering a hole will result in a note between the 2 extremes of totally uncovered and totally covered. See Accoustic Length of Flute.

In some cases a hole which is not at the end may be left uncovered with no effect on the pitch of the note : see Why does the note played by a flute not change in this case when the air column is interrupted?

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