mystery of bridge shapes

[Mandoak]

Why is it that the top edge (that touches the strings) on mandolin bridges are are not a straight line (1st and thirid pair forward and 2nd and fourth are back)?

If it is necessary for intonation or sound or anything, then how come some ofther mandolin bridges have a straight edge?

[sunburst]

The stair-step bridge tops are done to improve intonation, the straight-across bridge tops are done because it's easier.

[Mandoak]

Thanks for your reply sunburst but I still don't get it.
If it is necessay to have the steps then the ones without it would not have correct intonation. And if the one without it still have it (while being easy) then why bother?
(I have been sanding and grinding a stuburn piece of bone for last three hours hence the question).

[sunburst]

...then why bother?

A good question, and one I ask fairly often, especially on those relatively rare occasions when I'm in a "big box" store seeing the "merchandise" that is there in such profusion.

It can get a little complicated trying to explain all about string gauges, how different size strings stretch different amounts and so go sharp to varying degrees when fretted and how "compensation" at the bridge top is one way to help get things closer to 'in tune', but that is at the heart of the situation. In the end, we play slightly out of tune on fretted instrument in spite of our best efforts to improve intonation, so in a sense the question could just as easily be applied to 'compensated' bridges... "why bother?"

[Schlegel]

They don't have correct intonation straight, but easier is cheaper and that's why it was done. You'd be amazed at the horrible intonation people apparently put up with on cheapos a hundred years ago.

[Dave Cohen]

With "classical" string sets such as the T/I, straight bridge saddles give better intonation than a Gibson-type 'compensated' bridge saddle.

http://www.Cohenmando.com

[Michael Lewis]

Probably because the T/I strings are very flexible and therefore require less compensation than the heavier and stiffer steel cores of the strings we use mostly. That is like the difference between classical guitars with nylon or gut strings compared to most steel string guitars.

[Dave Cohen]

Michael, it more likely has to do with the fact that the T/I sets have wound A strings, hence different core wire sizes. I did find that angling the saddle a bit helped intonation. It was the staggering that you see on Gibson-type bridges that was not necessary. The T/I strings and others of that type are not so much more flexible per unit diameter than are heavier PB wound strings intended for bluegrass & etc. All metal strings are "stiff" compared to an idealized completely harmonic string.

http://www.Cohenmando.com

[Dale Ludewig]

Perhaps I have this in a book on a shelf, but I've wanted to ask this for some time: What is the relationship between the core and and winding and how does it affect all that goes on with a string? Is the winding basically along for the ride? I would imagine (!) that different manufacturing processes affect how the winding and the core interact. So basic, but..........?

[sunburst]

The string acts as a spring. Once set in motion (plucked) it oscillates until friction slows and stops it. Two main things affect the frequency of a string's oscillation; tension and mass. Windings add mass without increasing tension, so the frequency at a given tension is lowered. In short, with wound strings we can have lower notes at higher tension, so the lower strings don't feel sloppy or flabby as they would if they were not wound, unless the unwound strings were really big.

[Tom Wright]

...Windings add mass without increasing tension, so the frequency at a given tension is lowered...

The mass/tension relationship is not different, but the stiffness is very different. A stiffer string acts as if its fixed points are somewhere a little in front of the actual bridge or fret, so it will play sharp. A wound string acts as flexibly as its slender core, with the winding not stiffening it more than slightly. Guitar players have the choice of plain or wound G strings, and they behave very differently at similar tension.

[sunburst]

The mass/tension relationship is not different...

It is different. Think of it this way;
We have a plain, unwound string at a given tension. It will produce some specific note. Now suppose we add windings to that string and don't change the tension. The pitch will be lower because we have added mass and kept the tension the same. We have not changed the stiffness.
There is a difference in stiffness as the core wire size changes, but adding windings doesn't change stiffness. There is a stiffness difference between a wound G and an unwound G because the core wire is quite a bit larger in the unwound G. (We don't call it a core wire because it is not wound, but the principle is the same.)

[DerTiefster]

In the simplest terms I can think to offer, a perfectly flexible string has a very simple relationship between frequency of oscillation, string free length, and mass per unit length. But you can't take a perfectly flexible string and point it at anyone. It just lies there, limp, on your hand, dangling if long enough. No oscillation at all if you pluck it, because there isn't anything to pluck. It will make a great pendulum, though.

A stiff string will point at your intended target, at least a little, and will oscillate if you pluck at it because of the bending resistance its body provides at your hand and along the string. When you string up an instrument with stiff strings, you get the frequency of the ideal string modifled by the stiffness effects. The string tension provides a "restoring force" trying to put the string into its minimum-energy "straight between nut and bridge" orientation. The string stiffness provides another (small) component of this force, and that makes the frequency go up just slightly. That is why you have to lengthen the bridge spacing for stiff strings to get (as John Hamlett points out, somewhat closer to) proper intonation.

The ideal string frequency scales like 1/length, so half the length gives twice the frequency. But the stiffness component scales more strongly than just 1/length. Cut the length by half and you get higher than twice the frequency. So you have the octave with a sting free length just a bit more than half of the open length. The octave fret is fixed in position, so you lengthen the total string a little. That makes the open note go down, so you raise the tension just a bit, and then open and 12th fret work. But everything else is juat a bit off because the scalings don't work exactly and you can't change the fret spacing independently for each string.

[Stephen Perry]

Little things make a substantial difference. See, for example, stretch tuning http://en.wikipedia.org/wiki/Stretched_tuning

Stiffer strings don't quite really start their clean vibration at the stopped ends (fret and saddle). Extra length accommodates this.

I think when I tune by ear I may be adding a stretch, too. I can do a moderately OK job by ear of stretch tuning a piano, so I may do this without really thinking about it.

Violins are so much easier. Actually, I build a little "compensation" into bridge cuts, but that's because of some geometric features.

[Willie Poole]

With all of this knowledge it seems that back when engineers would have changed the string gauges so that a straight across bridge saddle could stll be used....I have posted that before and got some radical answers that are way over my head, but I have made bridge saddles that were straight and they sounded pretty good but no where near as close as the compensated ones...

This is the place to get an education on string gauges I suppose....Great information....

Willie

[Stephen Perry]

Intonation is a whole other front. Saddle only. Saddle & nut. Frets offset. Enough to drive one nuts.