RE: [tuning] Distribution variant

Pierre wrote,

>Farey series or related series are particular Stern-Brocot subtrees which
>differ by a contingent way of limiting values.

Agreed! I've tried many other ways, and would love to try more.

>Mediant property has nothing
>to do with restriction modalities but only with fact of being Stern-Brocot
>subtrees.

Yes, Pierre, mediants seem to be the right thing to use no matter whether
Farey or an alternative series is used. Please enlighten me -- this is why I
contacted you in the first place!

>Besides, with calculation depending of distance between ratios,
>jump to subsequent series results in few abrupt change in places.

Can you clarify? Do you mean changes in the distance between mediants?

>For the sake of coherence it could be useful for particular calculation to
>use series of N-first [strata/layers/levels??] of Stern-Brocot tree.

hmm...

>What
>is expecting ?

> - well-distributed changes from a series to the next

You mean changes in the distance between mediants?

>As you know probably, by citation of Alex Bogomolny, I have soon
>demonstrated that Arithmetic Sum of simplicities on each layer is equal to
>1. This is equivalent to Harmonic Sum of complexities defined as 2^sonance
>or ab, in the case of reduced a/b. I recall what is Harmonic Sum :

> HS (a, b, c ...) = 1/(1/a + 1/b + 1/c ...)

>If we attribute to each reduced ratio a/b of N-first layers series a weight
>equal to Nab then Harmonic Sum of those weights is equal to 1. I don't need
>to demonstrate that since it's almost an evidence.

PIERRE:
*********************
Can this be used to our advantage if we use a layer of the Stern-Brocot tree
to calculate harmonic entropy???
*********************

>New fitted weights are defined at limits and vary only by factor N/N-1 when
>jumping to N.

Sounds promising . . . I guess I need to calculate these things myself and
look at them . . .

>I did'nt read sufficiently on entropy theory to know if relevant as
>starting series. It seems only, at first glance, that it would be
>independant of subsequent physiological (and other) hypothesis by which
>smoothing and upper limitation of distribution could be obtained.

Yes! Yes! Yes!

I'm gonna try using it for harmonic entropy instead of Farey series and see
what comes out . . .

>Besides, in the same
>spirit, I recall that "lot of mathematics" is not synonymous with "most
>scientific".

That applies to dualism as well as everything else . . .