Nonuniform Strings

Oh, now that Dan brought up the topic of nonuniform strings, try this
experiment sometime: Wrap a grocery-store vegetable-bag "twist tie" very
tightly around the G or D string of a guitar and place it at the center of
the string, right above the octave fret.

The results are ... uhmmm... "decidedly non-string-like", I'll say.

What happens is the odd-numbered partials, which have an antinode at
that point on the (open) string drop way down in pitch, but the even
partials, which have a node at that point on the string, don't change much
at all.

You also find that the nodes of partials move toward the center of the
string. By that I mean that the third-harmonic (although it's far from
harmonic now!) nodal point you normally get by lightly touching the string
over the seventh fret, moves quite a bit toward the octave fret.
Presumably it's seeking a point where all three of the loops have equal
mass (or probably more accurately, equal torque: mass times distance from
the node).

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