a bud which terminates a stem

Having had a bit of a chance to go over the links that Paul Erlich put
up in his "metal mining and Pell-icans" post last week, I think I've
decided (for my own doings anyway) to try and narrow all this down to
three generalized constants -- A "Golden", an "Equal", and a "Silver"
derived from the following three series respectively:

1/1, 1/2, 2/3, 3/5, 5/8, ...

1/1.5, 1.5/3.25, 3.25/6.375, 6.375/12.8125, 12.8125/25.59375, ...

1/2, 2/5, 5/12, 12/29, 29/70, ...

The general umbrella term I've been thinking about using to prefix
these constants, generators, scales, and related conditions and ideas
is "Apical": roughly meaning 'a bud which terminates a stem'...

By using these Apical constants -- Phi, 2, and sqrt(2) -- to weight a
given Ls index, it is my hope that a unique threefold measure of the
resulting scale's character will emerge.

Any comments and/or ideas?

--Dan Stearns