Re: Bob responds to Bob again

Hi Dan!

>
> > So a two-term index always coincides with a Fibonacci series built on
> > that index where the two terms are converted into adjacent fractions
> > (think Yasser and Kornerup combined).
> >
> > So here's the familiar [2,5] diatonic index:
> >
> > 1 3 4 7 11 18 29
> > -, -, -, --, --, --, --, ..., oo
> > 2 5 7 12 19 31 50
> >
> > And here's the [2,5] index:
> >
> > 3 1 4 5 9 14 23
> > -, -, -, -, --, --, --, ..., oo
> > 5 2 7 9 16 25 41
> >
>
> And just when I thought I understood... I feel like there must be a
> typo here. This seems to be producing the [2,7] flavor of 9.2.
>

And then he said "Aha!" The typo was that the second should have been
[5,2].

So now, psuedocode that represents my psuedo understanding is

given [q,r]

if (q > r)

q-r 1 q-r+1
--- --- ----- etc... fibonacci style
q r q+r

else

1 r-q
--- --- etc
r q

GREAT! But what does it represent? It doesn't seem to give the complete
list of generators? Or am I still missing something?

fer instance...

[3,4] (what I would call 7.3 BaaBaBa)

1 1 2 3 5 8 13
- - - -- -- -- --
3 4 7 11 18 29 47

seems to be running a path of [3,4] that doesn't include 9/31.

Bob Valentine

Hi Robert V.,

<<The typo was that the second should have been [5,2].>>

Right, sorry about that!

<<seems to be running a path of [3,4] that doesn't include 9/31.>>

That's because it only represents the Fibonacci sequence, or the
golden generator branch... but if you were to seed the Stern-Brocot
tree with the same adjacent fractions you'll get the 9/31.

--Dan Stearns