Robin, I do appreciate and enjoy reading your dissertations on string vibration. I would not attempt to discuss this with you on your level of experience with physics because you have obviously reached a level of theoretical analysis that I do not presume to have reached. On the other hand I would offer to you the "billiard ball argument". To state it categorically, duplexophobes and duplexophiliacs ( I am enchanted by your enhancement of the duplex vocabulary) are "behind the eight ball" . In this regard. If the 8 ball is touching another, say the 4 ball, and you strike the 8 ball with the cue ball straight on, the 8 ball will not move, but the 4 ball will. The energy of the cue ball is transferred through the 8 ball to the 4 ball. And so it may be possible that although the bridge pins do not move, and the toatl string length between the outer and inner bridge pins do not move, either, that the energy from the impulse of a longitudinal wave is conferred on the duplex segment of the string, and around the hitch pin, and back towards the bridge and the speaking length. But this is all "balltalk" and may be superfluous. The idea of ninths and flat fifths and major sevenths is inconsistent with the design of the duplex scale. If you are having qualms about the difference before and after tuning a duplex, may I suggest you do what I did 15 years ago. VIZ test the difference yourself with an analyzer. It does take some refocusing to fine tune your perception to the differences in tone, but the difference in sustain should be immediate. Thank you for your serious input. Dan Franklin
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