| Compensating to correct the intonation: Part I
Here is a typical Martin belly bridge. Much copied, we've all seen this
bridge, or minor variants of it.
Years of listening to clients and other players bemoaning how Martins (in
particular, but not exclusively, since so many other makers copy Martin)
intonate sharp as the low E is fretted up the neck made clear that the
saddle was simply in the wrong place. It needed to be moved back a) so
the vibrating string was longer and b) so the fretted notes came closer
to what they should be.
The bridge has a "footprint" on the top, and so it can't be moved, and
most of the time, fortunately, the high E is fairly correct, so here then
is the simplest cure: put the saddle where it belongs.
To do this you fill the slot with ebony (or rosewood, as appropriate)
and cut a new one. The point of contact for the high E is usually left
precisely where it was, but the point of contact for the low E ends up
farther back.
There's a problem with this however: sometimes the bridgepins are in the
way of where the saddle needs to go - there is not enough room for the
desired change. This image, above, looks fine, but in reality it's trouble
because there's really not much room for the low E string to go up and
bend over the saddle from the string ramp in the bridgepin hole. If the
saddle is low, it can sometimes work. But more often than not, it's a compromise.
And sometimes the entire saddle needs to be not only angled back farther,
but the point of contact for the high E has to go back a bit as
well. See the blue saddle above. Now the bridgepins are really in
the way.
Here's another look at the basic factory bridge. The yellow line is
for a reference on the location of the bridge pin holes. (It also shows
how the belly bridge evolved from the earlier pyramid and 1x6 configuration).
Now have a look at the image below. The footprint of the bridge remains
the same, but the bridgepins and the saddle are both moved - reference
the yellow line in the two sketches, above and below. Now there's room
for the ideal saddle angle and for string approach from the bridgepin holes
because the bridgepins are moved back. The only way to accomplish this
is to start over:
-
remove the old bridge
-
new bridgeplate - includes filling the original holes in the spruce top
as well
-
new bridge from scratch
Real bridges look a little different than these sketches of course,
particularly Martin bridges, which have the saddle and the bridgepin holes
even closer than these sketches indicate. And the saddle angles in my sketches
here are somewhat exaggerated to illustrate the point.
Simply listening makes it clear that saddle angles on conventional commercial
guitars tend to be able to play in tune only when the action is fairly
low and the strings are light. In other words, under these presumed conditions,
the deflection of the string is relatively low in actual play, the string
is not stretched so as to raise its pitch as much, and therefore less compensation
is necessary. Alas, not all guitarists want their guitars set up this way.
In my opinion, installing a wider saddle, with the concomitant added
mass, to simply be able to extend the vibrating length of the lower strings
to accomplish better intonation is a mistake. For the sake of tonal clarity,
I think a conventional 3/32" bone saddle has the ideal mass, and when the
spread for the high and low strings is correct, there's plenty of room
to finesse the intonation of the B string. Read on.
Compensating to correct the intonation: Part II
Here we dial in the individual strings of a typical steel string guitar.
The simple angle back is a basic compensation for string gauge and the
raising of pitch that occurs when stretching the string down to the fingerboard
during playing. Most manufacturers put a simple crown down the center of
the top of the saddle, and that is what you get.
This is different:
The hard red line indicates the adjusted high point on the fully compensated
saddle. This is the point of contact that defines one end of the vibrating
stringlength.
Pale green is back-slope and potentially a bearing surface for the string.
Note that the B and the low E have a bit of meat under them behind the
final point of contact. This is essential. The pink surface is drop-off
in front.
The green arrows and dots indicate the ideal point where the
octave of the high E would be, based on a strict measurement of the distance
from the nut to the center of the 12th fret times 2. In other words,
even the high E is compensated as well.
Here's another way the saddle is often shaped: same points of contact,
same result, different look.
Either way it might be accomplished, this scheme is really just a series
of two lines: one for the two plain strings (or on rare occasions, three),
and another for the wound strings. With a normal set of strings that have
rational gauging and composition, and which are tuned to standard tuning,
this works. There are special tunings and gauges that will require a different
scheme than this.
Compensating to correct the intonation: Part III
Getting the right bearing surface on the top of the saddle is essential.
Most high Es need to leave the saddle at the point farthest forward
if they want to be in tune, as in the second illustration up from here.
Rounding or sloping in front of that simply sets that ultimate point of
contact a bit too far back, boogering the intonation, unless it really
needs to be farther back, as shown in the illustration just above, for
example.
Rounding in back (between the bridgepin and the ideal point of contact
on the top of the saddle) is essential for the wound strings, as they need
to ramp up to that final contact point without the windings catching on
anything. Rounding in back is helpful for all strings, because you really
want them to slide up onto the bone and have a firm point of contact on
a bunch of material, not just an edge. (the same goes for nut slots, which
I'll address elsewhere someday).
Here's a typical profile for a high E string:
Notice how the string comes up from the bridgepin and slides onto a
smooth curved surface. OK, this is slightly idealized, but the principal
is clear: the elliptical shape leaves the string firmly in contact with
the bone to a precise point of contact that will remain in full contact
(so it's slightly less than parallel to the plane of the vibrating string)
when the string is vibrating.
Not this! No flat surfaces and sharp edges! At the upper
point the string will vibrate and dig itself a notch. At the bottom arrow,
it'll hang up on an edge, especially if it's a wound string. This is a
recipe for inaccurate tuning. The notch will also cause string breakage.
And it won't sound as good, because the saddle to string contact isn't
solid.
Here's a typical profile for a low A:
The arrow shows the point of contact. For the same reason the high E
has a ramp, the low one needs one too. Therefore the back edge of the saddle
must not be a blade edge. If it is, it won't last, and it may break strings.
A broader surface to bear the string will sound better too.
The starting shape of a saddle under a wound E should have a bearing
surface with a radius that's greater than the windings of the string, at
the very least. You usually don't have much to work with, but you at least
need this much. If you make it more of a blade edge, the string will tear
through the bone and make a notch.
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