Ron N asked; "Does anyone know, do the proportional relationships of the partials to the fundamental, and to each other, remain relatively constant as string tension is changed?" I had to do some research on this in my college days as I was trying to find out why some pianos sound "Tinny" and others sounded great. After taking readings with an FFT analyser, the results actually confounded my expectations. The gaps between the partials increase as the tension of the strings is raised, as well as the partials frequencies increasing BUT it is the rate of change that is crucial; the rate of acceleration actually DECREASES. When the data is plotted on a graph, the curve starts to flatten out as the tension of the strings is raised. This led me to the conclusion that the higher the tension of the strings, the lower was the proportional inharmonicity. This also gave me the impression that the curve on the graph would be a straight line just at the breaking point of the string. I shall try and dig out the data from my archives. Alan Forsyth PS. Never did find out why some pianos sound so crap!
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