# OT Re: Phiew.... guitar intonation - hard work!

```Douglas Baldwin wrote:
> If a string could be reduced to a Platonic ideal, it might have zero
> mass, and the 12th fret would be exactly beneath the half-way point
> between the nut and the bridge.

With apologies for being pedantic.

"The speed of propagation of a wave in a string (v) is proportional to
the square root of the tension of the string (T) and inversely
proportional
to the square root of the linear mass (μ) of the string."
(where "linear mass" just means the mass per unit length of the string).

So the ideal string has to have mass, otherwise it's frequency will be
infinite.

Actually, the theory for vibration of a string, which is where our ideal
string comes from, assumes the string is infinitely thin, and hence
infinitely
flexible.

It's actually the stiffness of the string which causes it to differ from
our ideal of "12th fret at mid way".

Of course, what Douglas says about the extra tension from fretting the
string
is 100% spot on, and probably more relevant.
( lower action for better intonation )

>    The wack part of this observation is what happens when you deal with
> wound strings, because the windings add to the pitch-lowering mass of
> the string WITHOUT adding to (or subtracting from) the tension necessary
> to reach their desired pitch.

With respect, that's not the case at all. Wound strings behave the same as
unwound in terms of thickness versus tension.
However, round strings are a bit more flexible than the equivalent plain
string,
(think thick piano wire) which explains the famous pattern at the bridge.

:-) ...and shouldn't it be a Pythagorean ideal?

andy butler