Hello to all those on the list. First, I'm not a piano tech nor a professional musician, rather a fumble fingered amatuer who loves the instruments and enjoys both the music and the art/science of making instruments perform their best. I've enjoyed immensely browsing through the archives and truly appreciate your community of experts. An earlier thread, one of many that branched from the historical tuning discussions, identified the phenonmenon of double or triple strings sounding lower than a single string. No one jumped in to explain, so thought I'd try. May be old hat to Del or other experts in scale design, so if this is baby talk, please excuse. The drop in pitch or frequency is real. There's a nice set of coupled partial diferential equations that describe the behavior, but the simple explaination is that each of the individual strings "sees" a small fraction of the other string's mass through the coupling coefficient. Each string in the coupled set vibrates as if it were slightly more massive, so a shift down in pitch. As an extreme case, think of all the strings of a double or triple glued together (really strong coupling!). The frequency would drop by 1/(sqroot 2) ro 1/(sqroot 3). In a piano, the coupling is rather weak, mostly through the air, bridge and soundboard so the pitch shift is small. Each piano, probably each note may have differences in the coupling so the shift may sometimes be too small to notice. Hope this satisfies the cat's curiousity. Rich Stewart
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