Fwd: [tuning-math] harmonic entropy (was: Re: Fried Alaska)

>From: "wallyesterpaulrus" <wallyesterpaulrus@...>
>Delivered-To: mailing list tuning-math@yahoogroups.com
>Date: Tue, 17 Jun 2003 18:48:31 -0000
>Subject: [tuning-math] harmonic entropy (was: Re: Fried Alaska)
>
//
>> No; how do you sum over row infinity of the Farey sequence?
>
>first of all, carl and i both had errors. carl's definition was wrong
>because the width goes from mediant to mediant. my probability
>definition was wrong because i only included the height term but
>forgot to multiply by the aforementioned width to get the area under
>the curve!
>
>now, row infinity? it's the farey, or mann, or tenney series of order
>n. n and s are the two parameters of the harmonic entropy function,
>plus you get to choose farey/mann/tenney/etc., and you get to choose
>bell/Vos.

>From: "wallyesterpaulrus" <wallyesterpaulrus@...>
>Delivered-To: mailing list tuning-math@yahoogroups.com
>Date: Tue, 17 Jun 2003 20:23:13 -0000
>Subject: [tuning-math] harmonic entropy (was: Re: Fried Alaska)
>
//
>
>>> Does harmonic entropy seem to converge to a continuous function
>>> as n goes to infinity?
>>
>> as n goes to infinity, the "shape" seems to converge, but it gets
>> taller and flatter. if we had some suitable way to correct for the
>> tallness and flatness as a function of n, we might be able to
>> define a function which indeed converges to a limit as n goes to
>> infinity. this is my hope, as i communicated to you some time ago.
>
>i actually made some inroads into acheiving this, but without any
>sort of mathematical insight or proof. i recommend you spend some
>time looking over the harmonic entropy archives, they are quite short
>compared to those of other lists. and let's continue the discussion
>there, shall we?