This is one of those arcane subjects . . . My understanding and observation would be this:
The speaking length of the string is between the nut and the bridge. Aside from two favorite tricks of some (picking the length between the nut and the key for that ring-ding effect, or pushing down on that same length as some sort of vibrato), the length between the nut and the key, and in the case of two piece bridge/tailpiece axes like Alembics or Warwicks, is not involved in playing. Having said that, the bigger a breakover angle (where the strings angle down and away from the plane of the fingerboard at one or both (headstock and the angle between the bridge and the tailpiece)ends supposedly imparts more 'downforce' onto the nut and bridge saddles, ostensibly for more sustain via higher loading of those parts.
In my experience, I've never noticed less tone/sustain on a Fender-style neck (head parallel to the strings, shallow down angle) on the E-string, and it's key is very close to the nut and typically doesn't pass through a string tree like the other strings. I've never heard any difference in a 'stings through the back' bass either.
This sometimes (or even usually) is brought up vis-a-vis sustain. I'd say, again from my experience, on a loud stage, EVERYTHING sustains just because it's so loud. Going direct, through phones with no amp, you find that there are basses that record well and basses that are better left for live work . . . but it usually has not much to do with sustain.
The one physics lesson I would like to see: Tuning is tension. You pull a string up to a given lbs/ft, and you're tuned to the right open note. I'd be interested to see if the down angle promotes this as a mechanical advantage/multiplier, which would account for the difference in 'tension' we seem to feel from one type of bass to another. Throw in scale length, types of core wires/windings in strings, etc., there's a lot going on here !
J o e y
