You seem to keep missing my humor. The following was me having some fun:
“Use quasi-isometry criterion to make the face of the valves polyhedral in shape, so they impinge on the ellipsoidal shape of the valve tunnel using a congruent, interlocking, but quick-release seal. Simply use procrustes analysis to ensure the rhombial subshapes do not prevent affine transformation of the air flow.”
Maybe I should have put a smiley face in there.
In response to your thoughts:
You said, “I see two major shortcomings to pads-before-reeds: 1. I believe that pads-before-reeds makes the reeds more distant from the musicians lips, hence less control over the reeds. Using the harmonica as an idol design for bending, in the harmonica the reeds are VERY close to the musician lips. So I believe that you’ll lose control rather than gaining more of it.”
Yes, I noted in a post just few days ago how close the lips of a harmonica player are to the reeds and that this gives them great control over expressiveness. I do believe they bend notes by changing the angle of the air flow over the reeds. On the melodicas I play, in particular the HM-32 with an 8-inch tube, the highest reed is about 26 inches away from my mouth. The lowest reed is about 41 inches away from my mouth. Seems hard to believe, but I just completed the measurements. These long distances result from this model having a long channel that runs the entire length of the melodica before the air even enters into the reed chamber.
So moving the reeds a couple of more inches from the players mouth should have no appreciable effect.
Outside of pressure control, I don’t think any melodica design allows the player to influence how the air strikes the reed. The reeds are just too far away from the mouth. On a 37-key Yamaha, I just don’t think you can control how (except for pressure or valve manipulation) the air flows around a reed. The high note reeds must be at least 20 inches away from your mouth on a Yamaha 37-key melodica when using a mouthpiece.
In regards to your comment: “2. An air-tight chamber is something that no one would give up on. Pads-before-reeds require an air chamber with moving parts in it, as you need the levers connected to the keyboards to be sealed in a way that air will flow only into the correct reed (via its dedicated tunnel).”
Yes, you must have missed my follow-up post that said: “I think I see another technological hurdle with my design idea. To seal the valve chamber, the linkage between each key and valve would have to be sealed as it enters the valve chamber. That is a lot of seals and complexity and could prevent good key movement. But wait! Make the key and valve independent. “Connect” them by way of a rubber diaphragm.”
In regards to your comment: “Moreover, such mechanism will probably result in a pad that blocks air from going into a small chamber (the reed’s tunnel), which is way harder than using pads for blocking air from going out of the chamber (which is generally implemented).”
I don’t see the problem here. That is exactly how it is implemented on a harmonica: small inlet hole.
“Sound wise, I don’t think that you gain any benefit from pads-before-reeds. In reeds-before-pads, the sound is mostly extracted from the open pad, which is very close to the reed. In good designs, sound runs roughly 1cm from the reed to the pad, and then goes out condensed so is can be manipulated (if you wish to). In pads-before-reeds, you can make the distance to the reed smaller before manipulation, but it’s not condensed therefore may be harder to manipulate.”
I don’t quite understand what you are saying here. I see a huge advantage–again like a harp–in having the reeds being exposed to the air for further manipulation any way you like. When the reeds are inside the melodica, you are stuck with the sound generated by the design of the melodica. There is little opportunity to modulate the sound unless you have a HM-26/27/32. When the reeds are exposed on the outside of the melodica, you have unlimited opportunity to work with them.