Erlich's Theory

>To recap some of my earlier postings and e-mails to J. Kukula:
>
>I do believe that the place and periodicity mechanisms are both at play.
>I also believe that Plomp's model gives a fine account of the
>place-related component of dissonance, which I like to call roughness.
>Combination tones complicate the matter but with a knowledge of the
>amplitudes and frequencies of all combination tone components, Plomp's
>algorithm can be still applied. But a phenomenon called "virtual pitch"
>or "fundamental tracking" is central to Parncutt's treatment of
>dissonance and does represent, I believe, an additional factor besides
>critical band roughness. This phenomenon is clearly distinct from the
>combination tone phenomenon, but it may have a lot to do with
>periodicity mechanisms. There is a very strong propensity for the ear to
>try to fit what it hears into one or a small number of harmonic series,
>and the fundamentals of these series, even if not physically present,
>are either heard outright, or provide a more subtle sense of overall
>pitch known to musicians as the "root". As a component of consonance,
>the ease with which the ear/brain system can resolve the fundamental is
>known as "tonalness." I have proposed a concept called "relative
>harmonic entropy" to model this component of dissonance. The harmonic
>entropy is based on the concept that the critical band represents a
>certain degree of uncertainty in the perception of pitch, and for any
>"true" interval, the auditory system will perceive a range of intervals
>spanning a number of simple-integer ratios. Simple-integer ratios come
>into the picture because if the heard tones are to be understood as
>harmonic overtones of some missing fundamental or root, they must form a
>simple-integer ratio with one another. The range is a sort of
>probability distribution, and a certain amount of probability is
>associated with each of the simple-integer ratios.
>
/...snip.../
>
>It's amazing I get any work done around here . . .


But your work around here is very much appreciated. It is due to my
attending High School that my background in math is poor and/or
non-existent. High School physics had a similar effect on my understanding
of acoustics, and I have had no prior exposure to the Plomp work outside of
this digest since issue 1190 or so.

However, I think I get the gyst of this. I will have to go over it some
more to be sure. It seems that if you wrote a short book to explain this
and other things about acoustics to the average musician, you'd be doing a
service to mankind.

So correct me if I'm wrong, but doesn't this tend to support that measuring
the cent detuning of Just intervals does not messure change in dissonance?
Wouldn't it also tend to support that a 2 cent detuning of the 19/16 could
produce "a first-order qualitative difference"?

Carl


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From: mr88cet@texas.net (Gary Morrison)
Subject: 88CET Ear Training Tape Article
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