[Paul Erlich:] >> I think Partch was right that an interval's allowance >> for mistuning, as regards the interval's ability to be >> recognized as the just ratio, is inversely proportional >> to the ODD limit. 81/64, if recognizable at all (I don't >> think so), has an EXTREMELY small allowance for >> mistuning.
[Carl Lumma:] > Ah. Well, that works. Thing is, "sensitivity to mistuning" > can mean so many things. I'm just now seeing how > you're using it here, and I can't say that it is in any way > incorrect.
> There is a type of "sensitivity to mistuning" that does not > obey the inverse to odd limit rule. For this type of > sensitivity, it seems that the 3/2 is much more sensitive > than the 7/4. Further, it seems to matter to this type of > sensitivity wether an interval is mis-tuned sharp or flat.
I think we're touching on something quite important here. It seems to me that these two different types of mistuning sensitivity may relate directly to thinking in terms of equal temperament or ratios. (This is possibly incorrect, though.)
The fact that a 3/2 is simultaneous more and less sensitive to mistuning also seems to have something to do with the fact that, because 3 is the next-strongest prime quality after the octave (2), it can be both absorbed into the strength of 2, in which case mistuning is not much of a problem, or can stand out as a powerful new identity, in which case mistuning will be very obvious.
I have said before that a basis of my theories is that we will always try to "break down" any complex situation into its most easily understood components. If periodic frequency vibrations can be understood in terms of how they divide into 2s and 3s, this is a very easy comparison for our brains to make, thus even a small deviation will stand out very noticeably. The case is much more complex for, say, an accurately-tuned 7/4. It would not be as easy to notice a deviation from a ratio with 7 as a factor, simply because 7 is a much more complex comparison to make than 2, 3, or even 5, and each higher prime is correspondingly more complex.
Joseph L. Monzo monz@juno.com
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