Re: Luthier question: Intonating via thinning braces

Sorry I was out of town when this came up.

Top motion can effect the pitch of specific partials of certain notes.
I talked about this in my article on strings last year in
'Guitarmaker' magazine. For those who don't have it, here's how it
works (physics alert!).

Start by thinking about pushing a kid on a swing. If you push the
swing once it moves away from you as you push; in the direction of the
force. If you push more often, it at a rate that is below it's natural
frequency, the result will be the same: the force and the motion will
be 'in phase'. If you try to push the swing more times per minute than
it naturally 'wants' to go, you will have to start pushing on it as it
is coming toward you, so the force and the motion go 'out of phase'.
The same thing happens when the string is pushing on the top: if the
pitch of the string is below a resonant pitch of the top, the force
and the motion will be 'in phase', and so on.

Let's assume for the moment that the string is just vibrating in it's
fundamental mode, with no overtones (no, you can't get it to do that
by plucking, but we've got to start someplace). If the string is
vibrating 'up and down' relative to the plane of the top, then it will
be pulling 'up' on the top when the string is above it's resting
position, and moving downward, and pulling 'down' when it's below. If
the top is capable of moving at the pitch of the string, this means
that the top of the saddle is NOT stationary as the string vibrates;
it's moving up and down too. If it's not moving then you won't hear
anything and you're trying to play 'Layenda' on a Les Paul.

Let's suppose that the string in question is the G string, and the top
has it's 'main tap tone' at G#. In this vibration mode the whole lower
bout of the top is moving in and out like a loudspeaker, and the
bridge moves up and down a relatively large amount. Since the string
is pushing below the top's resonant pitch, the motion is in phase with
the force: when the string is above center moving downward and pulling
up on the top, the bridge is moving upward. If you think about it,
this means that the stationary point, that defines the length of the
string, is actually not at the top of the saddle; it's a little way up
the string toward the nut.

The string 'thinks' it's _shorter_ than it really is! Even weirder,
it has this crazy notion_only_ for the fundamental vibration of that
particular pitch! As far as the overtones are concerned, the saddle is
the stationary end of the string. Even better; when you play the A
note, the saddle top and the string force go out of phase, and the
string thinks its _longer_ than it is. And, best of all, if that top
pitch really is exactly G#, the string doesn't know WHAT to think
about it's length at that pitch!

In practice, of course, you'd only really see a major effect from this
if the 'main top' pitch is between two frets, say G and G#, and very
strong. Then the fundamental of the G would go sharp, and that of the
G# flat. And, yes, I've seen this in measurements of real strings on
actual guitars: it's not fiction.

If your tuner is 'hearing' the fundamental of the string as you tune
up (and a lot of them seem to), what this means is that you'll end up
putting a little less tension on the G string than you 'ought' to,
since the top will be kicking the pitch up a hair. The open string
will sound OK, but the fretted notes, and particularly the G#, will
sound flat.

This effect depends strongly on how tightly defined the top pitch is,
and exactly where it is relative to fretted or open notes. Small
changes in the bracing can effect both of these things, and that's
probably what Blackshear is doing when he rubs the braces; the salt is
a mild abrasive for one thing. The 'main top' pitch is the most likely
to cause problems, but there are others that could well have effects
at other pitches. For example, the 'main air' pitch, about an octave
lower, also pushes on the top quite strongly, and can cause problems
on the low E string.

Alan Carruth / Luthier
.

Relevant Pages

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