QUOTE(Jimbo @ Apr 1 2009, 04:08 PM)
increasing the bore diameter would have the same sharpening effect on the fundamental as shortening a smaller bore flute? Finger hole area/volume would be smaller in relation to bore area/volume, so I would think that simply increasing bore would sharpen the fundamental (all holes closed) and flatten all other notes.
The basic answer is the length has everything to do with it, not the diameter.
That being said, there are some "second-order effects" that have the appearance of changing the pitch by increasing the bore, and some caveats to throw in.
The finger holes are one of those second-order effects - if you increase the bore uniformly along the entire length, and leave the finger holes (and TSH) the same, then the holes will be flatter because the the ratio of the hole-to-bore diameter is smaller. As for the fundamental, the foot will be bigger, so the end correction will be slightly longer (k1), which will make the fundamental slightly flatter.
If you look closer at how the bore works on the fundamental, you find that increasing the diameter near the ends will sharpen the pitch. That's where the analogy of water flowing in a pipe "holds water" (pun intended...). That's because the ends are at acoustic flow antinodes. Lew Paxton Price talks about this in his books, and in this zone those equations work well. On the other hand, if you increase the bore diameter in the middle where the flow node is, the flow is minimal, and the pressure effects dominate instead (the flow node is also the pressure antinode). Near the pressure antinode, or in the "pressure zone" the springiness of the air is what matters. A bigger bore has a "softer" springiness in the air column, so it takes a little longer to transmit the pressure wave, so the pitch flattens.
The sharpening in the flow zones balance the flattening in the pressure zones, so if you enlarge the bore everywhere, you are only affecting the end corrections at the openings (i.e., those second-order effects). But if you are selective in where you enlarge the bore, you could make some notes to go sharp and some to go flat, depending on whether the enlargement is in a pressure zone or a flow zone for that particular note.
So, to answer your original question (assuming you only want to change the fundamental), you could try sanding just in the vicinity of the direction holes to increase the diameter in the fundamental's flow zone. But don't make the walls thinner AT THE DIRECTION HOLES because that will sharpen the pitch due to the holes. I recommend trying the following inverse experiment first:
- make a ring of paper or cork or fun foam (craft supplies) with the outside diameter the same as the inside diameter of the bore
- make the ring about an inch or so long and about 1/16 thick around the perimiter
- slide the ring up the bore to where you plan to remove material
- play all the notes on the flute and record how much they changed compared to without the ring
What this does is create a bore constriction instead of a dilation. The effect is the opposite of what would happen if you removed that much material. If you find that the fundamental flattens, but the rest of the notes hardly change, then sanding in that spot will sharpen the fundamental without disturbing the other notes. If other notes DO change in the experiment, then you can expect the same relative change in the opposite direction. It's a good way to test any planned bore perturbations before doing anything permanent. Keep in mind that 1/16 inch is a LARGE amount of material, so the effect will be amplified -- when you actually remove material you will do so very slowly and you can check your progress often.