Kenneth and Andrew Hsu

Ths Hsus sought to establish scaling relations

f = c⋅i-D

between the frequency f of the interval i between successive notes of a musical composition.

For each interval i they plotted Log(f) vs Log(i) and sought a linear trend in the graph.

For most compositions, the range of intervals is small, certainly 0 ≤ i ≤ 20.

Moreover, within this data lie some expected deviations.

For example, the diminished fifth (i = 6) generally is regarded as dissonant and so appears with lower frequency.

Within this range, they obtained reasonably linear plots for compostions of Bach and Mozart, less so for Stockhausen.

Here is their plot for BWV 772 of Bach.

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