Originally Posted by: hdoran
In these lessons you give one very interesting example I'd like to learn a little more about. Specifically, you note that the open A string rings out at 110 hertz and then at the octave (same string fret 12) we have a 2:1 ratio since it rings out at 220.[/quote]
Sounds like you are referring to this lesson:

http://www.guitartricks.com/lesson.php?input=13698&s_id=835

The E note on the 7th fret is the 5th of the scale and is 165 hertz. The reason I use the metaphor "as far from home base as you can get" is because it is halfway between the pitches of A above and below. The octaves of A are "home base". If you go any farther up or down you are closer to an A. So, the next thing to do is split the A & E in half.

A - 110Hz
C# - 138Hz
E - 165Hz

Halfway between the root & fifth is the major third. :) The more you study this topic, the more you grasp the basic principle of a continuum on which simple ratios forming consonance & more complex ratios forming dissonance. Music is often a process of starting on consonance, building dissonances (adding drama & tension) aiming toward consonances (resolving & releasing tension).
[QUOTE=hdoran]What I'm curious to learn more about is the other strings and the mathematical relationship between all frets.
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Does such a resource exist?