Dare to Square

>>The harmonic entropy curve, like the Plomp-Levelt roughness curve for tones
>>with harmonic partials, has local minima at small-integer ratios. It is
>>standard in physics (and justified by calculus) to approximate any local
>>minimum with a parabola. Therefore, near a just ratio, the change in
>>dissonance is proportional to the squared detuning.

Does this mean that you're going to go over to squared detuning? Are you
sure we should be squaring logorithmic measures of detuning?

Parabolas aside, my original warning regarding cent-detuning was that you
can bump into other low-number ratios without knowing it. We got into this
19/16 thing because I said that 16 cents flat of a 6/5 we have old 300, and
18 cents flat we have 19/16. By cents-detuning, the 19/16 is worse than the
300 cent interval. By cents detuning squared it'd still be worse.

Even if you don't agree there's a difference between 300 and 19/16, it
doesn't make the 19/16 worse than the 300. But there must be more-better
examples. Maybe: the 12TET minor 7th is 18 cents flat of a 9/5, and 22
cents south of the 9/5 we have 16/9.

|-----------------------------------------|
| Carl Lumma |
| http://users.nni.com/source_of_goodness |
|-----------------------------------------|


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