Gary Morrison and Defining "Just" Intonation and "Consonance"

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Gary Morrison wrote,

>Speaking for my own experience, I don't perceive there to be any sort
>of absolute cutoff point either (beyond thus and so ratio). Again
>speaking in generalities, as the ratio becomes more complex, it becomes
>more difficult to attribute an audibly intuitive meaning to.

Agreed. The most complex ratio that one can tune by ear, and therefore
say that in some sense nearby intervals are approximating, will depend
on timbre, loudness, register, and duration. Slightly simpler ratios
will simultaneously be a target of approximation and themselves
approximate simpler ratios.

>Also, simpler ratios seem to claim more space around them than more
>complex ones. By that I mean that anything within something on the
>order of 75c of a simple ratio like an octave seems to be perceived as
>an approximation of an octave. But the "claim zone" as I've called it
>in the past, of a more complex ratio, such as 5:4 is much narrower.
>400c (13c sharp) clearly seems to be an approximation of 5:4, but you
>don't have to go much sharper than that before it starts sounding more
>like a flat 9:7.

I wholehearteldy agree. This is related to something Partch called
"Observation One", and central to my own theories. In TDs 848 and
851-852 I posted a largely original derivation (based on the appendix of
Van Eck's _J. S. Bach's Critique of Pure Music_) to the effect that, if
one compares intervals holding the pitch of the upper note constant, the
width of the "claim zone" of a ratio is inversely proportional to the
denominator of the ratio.

>Paul H. Erlich wrote:
>> essentially state that the simplest ratios will be most easily
>> perceived, but beyond a certain point (about 17/13 or 19/13 in
various
>> members' experience) the exact ratio (if there is one) ceases to be
>> relevant and the degree of approximation to simpler ratios is the
only
>> important factor.

So, Gary, I think we are basically in agreement. Is there something in
the above that you particularly objected to?

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