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loudness of complex tones
There is a large literature by harvey fletcher and munson
on exactly this question. Read first the fletcher and munson
1933, and then look at fletcher's 1953 book. In fact he even
comments on the question you ask about. Look at
''the dependence of the loudness of a complex sound
upon the energy in the various frequency regions of the sound"
by Fletcher and Steinberg, Phys Rev, vol 24, pp306-317, sept, 1924.
In the paper "Loudness, pitch and the timbeto the intensity, ...." JASA vol 6,
#2, oct 1934, page 59-69,
on page 63, col 2, top he says:
"Practically all the loudness of the tones from the paino strings
of low pitch is due to the higher overtones."
He also has a model that gives this result.