Calkin-Wilf Tree

Gene posted something interesting on Igs' new forum here:

http://xenharmonic.freeforums.net/index.cgi?board=math&action=display&thread=22

So our mission, if we choose to accept it, is to find a way that this
sequence, which enumerates the rationals, is musically useful.

After a lengthy deliberation, by which I mean I only had a minute or two to
look at it, it seems to me that the Nextrat() function spits out the terms
in the Calkin-Wilf tree

http://en.wikipedia.org/wiki/Calkin%E2%80%93Wilf_tree

Look under "breadth-first traversal". This looks like the same sequence
that Gene's nextrat function yields.

So, anyone got any bright ideas about how the Calkin-Wilf tree might be in
some way musical?

(I'm reposting this here because I think that, while I support Igs' idea to
start a new forum, serious math discussion is simply best left on
tuning-math.)

-Mike

--- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> So, anyone got any bright ideas about how the Calkin-Wilf tree might be in
> some way musical?

While you are at it, you could figure out the use of the fusc function:

fusc(0) = 0; fusc(1) = 1; fusc(2n) = fusc(n); fusc(2n+1) = fusc(n+1) + fusc(n); which leads to fusc(n)/fusc(n+1) as the Calkin-Wilf enumeration of the rationals.