Robin, I just stepped out in the shop and did a little experiment of my own that might help to clarify. Using what was a recently abandoned and not terribly informative attempt at a monochord as a beam, and clamping a dial indicator to it, I laid it across the rim of an unstrung piano. In the last treble section, where the plate is most heavily braced, and the struts and unsupported spans are shortest, I took a gage reading and set a 10lb box of tuning pins on the plate next to the dial indicator. The plate deflected about 0.0015". I then set the same box of tuning pins on the rim next to the beam and got a similar change - just over a thousandth of an inch. Being relatively stiff doesn't make either of these things infinitely stiff, and that seems to be the presumption in your approach. If not, please correct me. As it is, they will both support a measurable transverse vibration, and will produce audible sound as a result. The same applies to the soundboard, only it's far easier to induce transverse vibrations in. Ron N
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