[timmer]

Even though I think we're heading into hocus-pocus land here I may have grokked out what is happening.

Scale length is determined by the saddle to nut length. This means the rest of the string beyond the saddle "should" have no effect.

BUT

Since the string is round, and only the bottom part of the string touches the saddle, I can envision a sound component traveling the rest of the length and either adding to, detracting, or having no effect on overall sound.

Since sound travels through denser material easier, the rest of the string may act like an amp with the right string length (beyond the saddle) and materials used.

I can almost envision a formula for that as well, but having slept through more than my share of antenna theory classes it's not coming to me at the moment.