Fwd: Re: [tuning-math] Re: Fried Alaska

>From: Carl Lumma <ekin@...>
>Delivered-To: mailing list tuning-math@yahoogroups.com
>Date: Mon, 16 Jun 2003 19:21:27 -0700
>Subject: Re: [tuning-math] Re: Fried Alaska
>
>>>By simplicity, don't we mean something like the Van Eck widths?
>>
>>That's tough to answer without knowing what a Van Eck width is,
>
>I found gcdb by the way, but have no idea how it works.
>
>The Van Eck width of ratio Ri is log(R(i-1))-log(R(i+1)), where
>Ri is, say, the ith ratio in a Farey series of order n.
>
>Unfortunately, I guess these widths just shrink to nothing as
>n goes to infinity. The harmonic entropy based on them, however,
>converges to a finite value.
>
>>but the rules of simplicity are these:
>>
>>(1) q and -q, 1/q, and -1/q are equally simple. In particular, 0 and
>>infinity are equally simple.
>>
>>(2) To judge how simple q is, you need to look at how simple 5/(3-2q)
>>and (3-2q)/5q are as well.
>>
>>(3) Low numerators and denominators are better than high ones;
>>bearing in mind that infinity = 1/0 counts as low.
>
>Since we have no idea what's supposed to make one brat better than
>another, I suppose this is fine.
>
>-Carl