RE: Paul Erlich's "tonalness" algorithm

Thanks to Brian for a fine summary of the historical developments in the
theory of pitch perception. I certainly agree that the issue is complex and
that we are very far from understanding the complexities of the ear-brain
system. However, this from Brian himself:

>Among the three popular pitch theories only
>the optimum processor theory [Goldstein's]
>is able to account for most of the data
>[in] a quantitative sense.

It is no coincidence that I chose to highlight, and cite results from,
Goldstein's work, and only mentioned Terhardt and Wightmann due to some
overall similarities between their theories. Goldstein's theory can be
viewed as a first approximation to the problem, to which corrections will no
doubt be added by more sophisticated theories. In trying to understand Van
Eck's work, I carefully studied Goldstein's paper and found that the form of
Goldstein's theory was strongly suggested by the data, and was not merely a
preconceived construct to which the data was fitted. This impressed me
enough to inspire a reconstruction and correction of Van Eck's procedure,
which is the "algorithm" I posted. It seems a simple enough construct to
merit consideration, especially where no reasonable alternatives are
apparant. Far too many writers on tuning, etc. interpret chords cavalierly
and end up unknowingly contradicting themselves. A first step is to
recognize that any SWNR interval will tolerate some mistuning. A second step
is to attempt a consistent description of how an arbitrary interval will be
heard. This is what I have done, and although refinements are no doubt
possible, much useful information can be gleaned from this model.


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