source file: m1422.txt
Date: Wed, 20 May 1998 11:27:41 -0700

Subject: It's Daytime Now

From: Carl Lumma <clumma@nni.com>

>I'm agreeing that you misunderstood. Three to the something is a power
>of three, while something to the three is a third power.

Of course this is correct.  I see now that you meant base 3's in your
original post.

>>I agree that we only want one way to approximate something in an equal
>>tuning, as long as we're using equal tuning to approximate.  But I do not
>>agree that the 1% rule determines which things are one.
>
>Which things are one?

I admit this is unclear.  Here's the orginal post by Erlich...

>No, certainly not alike. But I guess I should have said something in the
>paper about how in 12-tone equal temperament there is one and only one
>way of approximating any consonant ratio, and that is a property that
>adds a degree of simplicity that musicians may not be happy to give up.

I was trying to say that I do agree we only want one way of approximating a
given consonant ratio, but that I'm not convinced that two approximations
within the 1% rule are necessarily confounded in their approximating that
ratio.

My guess would be that the chance of two approximations getting confounded
with eachother varies inversely to the accuracy of the tuning's
approximations at the limit it's being used [by the composer].  This would
explain why, in all but the most carefully used circumstances, pithces in a
just tuning cannot be used to approximate things, as I thought they might
some time ago.

Level 2 and higher consistency is the best measure I can think of for when
a tuning's approximations are likely to get confounded with eachother.

Carl