Department of Mathematics
J.Wilson, EMAT 6680

Lesson #12

by Jan White

This is an exploration of the length of piano strings covering one octave in the upper range of my grand piano. I entered the data in a spread sheet starting with the first string and numbering it zero (first column) and the length (second column) and continuing for one octave. I then took the ratio of the longer length divided by the next smaller length and entered this in the third column. The fourth column are the theoretical points from the function f(x)=10.4*(1.05296)^-a.

 String # Length Ratio 10.4*Ave. Ratio^-a 0 10.4 1.05050505050505 10.4 1 9.9 1.0531914893617 9.87691840145875 2 9.4 1.0561797752809 9.38014587587254 3 8.9 1.04705882352941 8.90835917401662 4 8.5 1.04938271604938 8.46030160121621 5 8.1 1.06578947368421 8.03477966989839 6 7.6 1.04109589041096 7.63065992050827 7 7.3 1.05797101449275 7.24686590232134 8 6.9 1.06153846153846 6.88237530610976 9 6.5 1.04838709677419 6.53621724102508 10 6.2 1.05084745762712 6.20746964844351 11 5.9 1.05357142857143 5.89525684588542 12 5.6

This first chart shows the measured data and that the function is probably a exponential function.

This chart shows the measured data and the function, f(x)=10.4*(1.05296)^-a, overlaid.

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