RE: Dare to Square

>>Does this mean that you're going to go over to squared detuning?
>
>Go over from where? I used squared error as the loss function to calculate
>optimal meantone temperaments and the quality of equal-tempered
>approximations in many posts here. When I said that the maximum error was 20
>cents, would it have made any difference to say that the maximum squared
>error is 400 cents squared? No, it would have just made me sound silly.
>
>>Are you
>>sure we should be squaring logorithmic measures of detuning?
>
>Since the amount of detuning is small, it doesn't matter (calculus again).
>But ultimately, yes, our perception of pitch intervals is logarithmic, and
>any valid model should reflect that.
>
>>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.
>
>You lost me. What are you trying to say/ask?
>


SMTPOriginator: tuning@eartha.mills.edu
From: "Paul H. Erlich"
Subject: RE: Erlich's Theory
PostedDate: 05-11-97 22:34:54
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