Entropy in action

I'm trying to dig into the specific formulation of Paul Erlich's
Harmonic Entropy, and have been complaining to him off-list that the
web page on Monzo's site doesn't have an exact definition of the
Farley Series. Paul says it does; what's going on???

Turns out there are TWO similar but also very different pages on
Monzo's voluminous web labyrinth:

http://www.ixpres.com/interval/td/entropy.htm

http://www.ixpres.com/interval/td/erlich/entropy.htm

Beware! The first of these, where I had been going, is "small",
lacking much of the explanatory commentary of the second.

Monz, do I have a vague recollection of you explaining all this a few
months ago? It'd be nice to link from the "small" page to the "large"
one, for those of us who are trying to cut through the "entropy fog".

JdL

>I'm trying to dig into the specific formulation of Paul Erlich's
>Harmonic Entropy, and have been complaining to him off-list that the
>web page on Monzo's site doesn't have an exact definition of the
>Farley Series. Paul says it does; what's going on???

I assume you've found by now the definition of an order-n Farey series.
Here's LISP that will generate all "proper" (with numerator larger than
denominator) Farey fractions of a given order...

(define farey
(lambda (cap)
(seeded_farey 1 1 cap)))

(define seeded_farey
(lambda (num den cap)
(cond
[(equal? den cap) '()]
[(equal? num cap) (cons (cons num (cons den '()))
(seeded_farey (+ den 2) (+ den 1) cap))]
[else (cons (cons num (cons den '()))
(seeded_farey (+ num 1) den cap))])))

>Does this really make tuning sense? That is, is it more important to
>tune 4/3 close to true than 5/4, yet LESS important to tune 8/3 close
>to true than 5/2?

I agree with Paul that it does. Octave equivalence is a very imperfect
generalization. For basing octave-equivalent tunings on harmonic entropy,
I'm quite satisfied with using just the first octave of Farey series,
although it sounds like Paul might have something slightly better up his
sleeve.

-Carl

> [John A. deLaubenfels]
> http://www.egroups.com/message/tuning/12343
>
> Turns out there are TWO similar but also very different pages on
> Monzo's voluminous web labyrinth:
>
> http://www.ixpres.com/interval/td/entropy.htm
>
> http://www.ixpres.com/interval/td/erlich/entropy.htm
>
> Beware! The first of these, where I had been going, is "small",
> lacking much of the explanatory commentary of the second.
>
> Monz, do I have a vague recollection of you explaining all this
> a few months ago? It'd be nice to link from the "small" page to
> the "large" one, for those of us who are trying to cut through
> the "entropy fog".

Done. Thanks for the suggestion.

If it makes any of you confused people out there feel any better,
even I don't understand *everything* Paul's doing here. I struggle
to glean what I can as the fog gets thicker and thicker...

-monz
http://www.ixpres.com/interval/monzo/homepage.html

--- In tuning@egroups.com, " Monz" <MONZ@J...> wrote:

http://www.egroups.com/message/tuning/12377

> If it makes any of you confused people out there feel any better,
> even I don't understand *everything* Paul's doing here. I struggle
> to glean what I can as the fog gets thicker and thicker...
>
This is just wonderful to hear, Joe! Misery loves company, and now I
am thoroughly miserable... It's just great! My day has been
made...Thanks for the comment...

Joetoo
___________ ____ __ __
Joseph Pehrson