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Mar9-12, 02:04 PM
P: 129
I did not realize that. I´m bit skeptical about the musical aspects, but you´re welcome.

Let me just point out a things I´ve learned about panflutes or haven´t said clearly enough.
(l: length; d: diameter)
- The correction of .82d is partly empirical in that it covers acoustic end correction and "normal" lip influence. (source: wikipedia)
- (The acoustical part is somewhere about .6d, IIRC. It applies to a free panpipe. See my link above)
- Resonance of a blown panpipe is not exactly the same frequency as resonance of a "free" pipe. (The difference does not matter much, really)
- (Your original question) l/d doesn´t matter in computing end correction if l >> d, so you´d better stay with, say, l > 5d.
- A more mathematical scaling rule (reported as observation of existing instruments in Fletcher/Rossing, The physics of musical instruments) is l ~ d2. (Solve for d, of course).

Why am I skeptical?
Good panflutists can play chromatic/all scales on a diatonic panflute by changing angle and lip covering. This also means that they are constantly checking and correcting intonation.
A microtonal panflute might appear as "cheating" compared to learning to play microtonal on a normal panflute.
Yes, there will be a problem with going "microtonal sharp". You might experiment with a small hole in the side of the pipe, a bit below the mouth. Normally covered with a finger and opened for going sharp. (Size and position will have effect on pitch, so the holes can all be the same position but different diameter, but don´t ask me to calculate this. Look at a few woodwinds to find a starting point for experiments).
And I fear it will be very difficult to play with more pipes than the traditional approach. That will partly depend on the kind of music you intend to play.

I wish you success and pleasure in designing, building and playing your novel instrument.