compensation bridges

[dwhite]

Could someone explain how compensation bridges work? I sort of understand them on a guitar but on a guitar, the slope of the compensation in uniform from low to high. I always assumed it was meant to compensate for the string thicknesses from low to high.

But a mandoling bridge has alternating notches. How does this work? I'm looking at making a bridge for my mandolin banjo. Glen has very kindly shipped me some blanks.

Thanks in advance, Dan.

[Ben Milne]

It's based on the thickness of the inner core. I believe it to be the same for guitars.

[Geoff B]

Compensation adjusts each strings scale length so that it intonates properly (plays "in tune" up the neck, 1st harmonic sounds the same as at the 12th fretted note). Because the strings have different diameters and are stretched at different tensions, they require slightly "compensated" scale lengths to make it work all right (there is a lot of theory behind this, but that's the gist of it). I'm no guitar expert, but I think the slant that you refer to on an acoustic guitar involves a certain compromise. Look at the saddles of an electric guitar, you'll see similar forward/back adjustments for each string. With the mandolin, in general, you'll have the G pair furthest back, up some for the D pair, back a little for the A pair, and the E pair furthest forward. Since you'll be making your own, try to have them span the centerline, so there isn't too much pressure forward or back. If you take a standard bridge and copy it, you can dial in any changes that need to be made, but they will get you in the ballpark in general.

[dwhite]

I think I get it. If its based on the core, the E strings should be closer to the nut, the A jumps back a bit, the D, which has a bigger overall diameter but (I'm assuming) a smaller core than the A, jumps back toward the nut and the G, with the biggest internal diameter, jumps back again. Is this correct?

[Tavy]

I think I get it. If its based on the core, the E strings should be closer to the nut, the A jumps back a bit, the D, which has a bigger overall diameter but (I'm assuming) a smaller core than the A, jumps back toward the nut and the G, with the biggest internal diameter, jumps back again. Is this correct?

Yup.

[Willie]

I for one have wondered about this for a long time...It would seem to me that some smart engineer would be able to figure out what diameter strings should be so that a bridge saddle could be cut straight across(uncompensated) and it would be a whole lot easier to make them if that was the case....There must be more to it than just that....I made a saddle un compensated and it worked just perfect on a mandolin and I sold it with it on there and will try doing it on some others that I have to see what happens....I`m too stupid to understand a lot of things that are installed on mandolins like the Gibson style tailpieces with those little hooks that are off set, I just hook my strings on the ones that are in line....I have often wondered if some things aren`t installed just to make people take notice and ask questions, I don`t see any reason for the points on the bodies either, they are solid I believe and don`t have a thing to do with the tone etc, just for looks I suppose and I guess thats why we all invest in F model mandolins....A status symbol, maybe....

[dwhite]

Thanks everybody. I wonder if all this means that different string sets from different manufacturers in different weights might require different compensation. Or, in another way, once you fine tune the compensation for a particular brand of strings, it would be best to stick with that brand.

I imagine fine tuning would be hard. You could put on one G string and one E string and get the overall angle of the bridge and then you would do your fine tuning on the D and A areas of the bridge. Is this the right approach?

[James Sanford]

When I build an instrument I compensate the bridge for the particular set of strings I use (J74's and J76's). I do this by building a straight edge bridge top to fit the posts of the bottom half of the bridge.

I then use my clip on tuner to set the 12th fret pitch as close as possible to dead on by moving the test bridge back and forth. After I have found the location for the best pitch I measure from the center of the twelfth fret to the front of the straight bridge top and note the length. (IE say 200mm).

I do the same procedure with each string in turn and note the length. For example say 195mm for the E, 198mm for the A, 199mm for the D and 200mm for the G. I then use an uncompensated new bridge top and use the shortest distance for the front of the saddle and then locate the other distances in relation to that dimension. This will give you a customized compensated saddle for the particular string set you are using. If you change string type it will have to be redone. The dimensions mentioned are meant for example only.

To be exact you must do this process or something similar. Standard compensation is a compromise which may work ok or it may not.

Hope this helps.

[DerTiefster]

The variable stiffness of strings is shown when you take a few of them and hold them in your hand and then try to point the strings at the horizon. Some will stick out a little farther than others, and the most flexible might run right down your hand like a rope. When you try to set up a fret board, you expect that a given tension in the string, the frequency of vibration will scale with length the same way for each of the strings. Otherwise you'd have to have a different fret layout for each string. The frets are laid out for some approximately correct average string.

For a perfectly flexible string (which doesn't really exist) at constant tension, the frequency f and vibrating length L scale so that f*L is constant. That's frequency times length. Double the length of the string, and you halve the frequency.

Basically, the fact that the string is tied at both ends means that if you distort the string, it "has to" roll over and start pointing at the other mooring point. The "restoring force" of the string on any piece of the string is due to the curvature that is enforced on the string at its endpoints, or boundaries.

But if you make the string stiffer, you add some restoring force. More force means more acceleration and faster response, so you can understand that the frequency would rise. So stiffer strings at some given tension have to be longer than an "ideal string" to vibrate at the ideal string's frequency. That's why the larger core diameter (stiffer) string has to be compensated. The stiffness of the string scales like the 4th power of diameter (can't recall for sure), so small changes in diameter make large changes in stiffness.

The compensation is only correct for some fret, like the 12th if you adjust for octave pitches at the 12th fret. But the lower frets will be over-compensated (pitches slightly too low because of the longer string) and the higher frets will be under-compensated. Like the even-tempered scale, it's all a compromise, but one that can sound acceptable to the ear.

My take on the issue. I tried to explain what was bothering Willie. Changing the heat treatment of the string cores will change the stiffness vs. diameter relationship, so string manufacturers don't just randomly change what they do (if they have a discriminating clientele and want to keep it that way). I hope this is understandable, and even correct. I do make mistakes, but I think this is a correct description.

[Willie]

D.T. I understand what you are saying and thanks for the explanation....That also explains why some mandolins don`t intonate correctly on all strings because the gauges aren`t the same as other makes, ex: A strings that are .015 and some are .016....I have a friend that dug into this real deep and he has come up with his own string sets, he buys single strings and uses them and says he doesn`t have any problems with intonation...I might have to try different A strings and see what I come up with...The others are right on all the way up and down the fingerboard, at present I use .016 gauge A strings, the thing that confuses me is that the A string notes sharp on the 7th fret and notes flat on the 12th fret, that boggles my mind. ....Thanks again for the data....

Willie

[DerTiefster]

Sharp at the 7th and flat at the 12th? That boggles my mind, too. One thing I forgot to suggest was just that kind of info: with electronic tuners we can measure how much sharp/flat the various frets are. A map of this across the fretboard would be informative. You might also consider expending a couple of A strings and installing them on the E course to verify that they intone the same way there. You could just move the strings over to the other slots and keep the possibility of moving them back without having to throw them away and install new ones. Comparing a map of the E vs. A string would be interesting (to me, anyway).

Don't absolutely discard the idea of changing the action height as an exploratory technique. Or so I think.

[Rick Turner]

We're starting to see two very separate issues get tangled here in this thread.

Compensation is about string stiffness, and you can't get around that well by simply changing string gauges or types. Strings sound good within a fairly narrow band of tension relative to their ultimate breaking strength. String makers try as much as possible to match tension across a set. There are lots of details like core diameter vs. wrap diameter, tension of the core during winding, tension of the wrap during winding, hex core vs. round core, alloys for core and wind, plating for core (tin vs. brass), etc. The type of wrap and how tightly it's packed on is a major factor in string stiffness; it's not just about the core.

The other issue is that most Western fretted instruments are simply never "in tune" all up and down the neck and in all keys because they're fretted according to the 12th root of two...tempered tuning...which simply allows playing acceptably out of tune in all 24 major and minor keys. Tempered tuning makes certain notes flat and others sharp, and we've just gotten used to it. Some folks are very sensitive to it; others are not. It's the old "your mileage may vary" routine.

Some of the best information on the 'net is on the D'Addario site. Check it out.