Re: Carlos scales

On Tue, 30 Mar 1999, Paul Hahn wrote:
> In a nutshell: given any random stepsize, the function computes the sums
> of the squares of the errors of the closest approximations of the
> following intervals: 3/2, 5/4, 6/5, 7/4, and 11/8. The intervals are
> not weighted, i.e. each interval in the list counts no more or less than
> any other.
>
> Viewing a graph of the function, one can see that there are valleys of
> almost exactly the same depth at alpha and beta, and therefore at
> alpha/2 and beta/2 as well. In between alpha/2 and beta/2 is an even
> deeper valley; this is gamma.

I decided to mess around with the numbers a bit myself, and I'm glad I
did: the plot that Wendy includes with her _CMJ_ article includes three
different curves/functions. They include the first three, the first
four, and all five of the target intervals listed above. The one from
which she derives alpha, beta, and gamma is actually the first, i.e. the
one which only targets 3/2, 5/4, and 6/5.

If you'd like a couple of more significant figures than she gave, here
they are:

Alpha 77.965 cents/step
Beta 63.833 cents/step
Gamma 35.099 cents/step

Sorry about misrepresenting things before.

--pH <manynote@lib-rary.wustl.edu> http://library.wustl.edu/~manynote
O
/\ "How about that? The guy can't run six balls,
-\-\-- o and they make him president."

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