RE: RE: Quantitative harmonic entropy

Paul Erlich wrote,

>>I said _otherwise_! We already know that 1/sqrt(n*d) is cool. But what
>>about for triads, as Graham was asking? What if the measure was the
>>totient of the smallest number in the ratio? It wouldn't _necessarily_
>>work.
>
>That's the leap of faith I was talking about. What's the totient of the
>smaller number in the ratio?

I don't remember you ever asking for a leap of faith... I suppose that
phrase would make an good search... Anywho, I believe the so-called
totient function is sometimes called Euler's function. It gives the number
of new members in consecutive orders of the Farey series, and was suggested
as a possible complexity measure early in the complexity thread (by Kraig?).
It makes a bad complexity measure, though; I used it in the example above
because its value is all over the place.

-Carl