compensated bridges

[twaaang]

Does anyone understand how having the E and D strings shorter than the A and G makes sense? It seems like your choices are to have the E and D "true" and the others flat; or the A and G "true" and the others sharp. I'm presently opting for the latter, where my ear doesn't start to worry until I get above, say, the seventh fret of the E string and things get noticeably sharp.

On my older mando with a straight bridge, everything is just peachy: with a little attention to intonation when I change the strings, all four courses seem "true" all the way, both to my ear and to a tuner. Yet compensated bridges are clearly the industry standard now (just survey the offerings at Elderly).

Is it possible there's some reason to be deliberately out-of-tune a bit, perhaps to limit sympathetic-response?

Whatever the physics may be underlying this, I'd be interested to know if others perceive a problem and if so, how they "compensate for this compensation".

Apologies if there's already a thread on this, I looked and didn't spot one. -- PDW

[twaaang]

Hmmm, not a huge turnout on this one. I did see a similar thread that just appeared; one respondent referred to a demo link from FOTW which is about what I already do, so I withdraw my questions about HOW but am still interested in WHY the staggered string-lengths in the compensated bridge are deemed superior to a straight bridge with even string lengths. -- PDW

[davestem]

I think the idea is to offset the effect that the difference in diameters of the strings have on fretting intonation.

[grsnovi]

Intonation absolutes are hard to come by and I suspect that depending on your ears, your instrument and your choice of strings things will be better or worse. It sounds to me like you hear a straight bridge as being nicer than a compensated bridge? I went slightly nuts after acquiring an electric 12 string with a six saddle bridge. Picked up a Peterson Strobe Tuner and installed a 12 saddle bridge and wondered why a "straight" bone saddle in an acoustic twelve string seemed to sound just fine. Virtually all electric guitars have adjustable saddle bridges yet straight bar bridges are routinely used with fine results.

I was completely happy with the intonation on my Collings MF when I purchased it. As the strings aged and I decided they needed to be changed, I also tweaked the bridge position slightly.

I realize this doesn't "answer" your question but the whole "physics of intonation" has turned into somewhat of an obsession with me.

I'm just glad I don't have to tune pianos for a living...

[mandroid]

The shortness of mandolins string length makes A Big difference.
Think of the violin family, the right spot to put your finger on a bass viol is a range which on a violin takes in 2 or 3 scale half steps.
I offer my experience with a rigel resonator mandolin, nice instrument,well made, but out of the 1st position, open string scales, the notes sounded off pitch at the 12th fret and higher. a thin straight piece of wood atop the spider bridge works fine on a dobro guitar, with a 25" scale , less well adapted to a 14" scalein a mandolin. For me, no strobotuner was required to hear the off pitch notes.

[Lee]

Piano tuner here. It's a fascinating skill and a topic of endless discussion. Did you ever see inside a piano and look at the gracefull curve of the piano bridge and wonder why it's shaped like that? Forbes magazine did a study a few years back to determine which profession provided the highest income with the least stress. Piano tuner/technician came in #1.
Strings vibrate three ways. The first two we don't think about often but are important in other discussions; these are: Longitudinal vibration. The vibrating string is not in even tension up and down it's length when it vibrates. Pockets of lower and higher tension travel up and down the length of the string. Torsional vibration is the tendency for the string to roll; again not evenly throughout it's length. A plucked string will exhibit more torsional vibration than a hammered string, as on a piano. Lateral, or radial vibration is what we're most familiar with. This is the tendency for the vibrating string to back and forth; actually it will begin to move in 360 degrees of motion. The fundamental note of the string is the most pronounced note and occurs because the string vibrates radially over it's entire end to end length. The first harmonic occurs because the string simultaneously vibrates radialy over each half of the length of the string; the center point having no vibration at all. You've probably seen an exagerated picture of the first harmonic vibration; the string takes the shape of a sine wave. The mid-point of the string is the node point. Put your finger at the mid-point node lightly and you'll hear the first harmonic sounding one octave higher than the strings fundamental note. The string also vibrates in thirds, fourths, fifths, etc. each becoming less audible. There are several factors that influence the note of a string; the thickness, the tension, it's mass, and the strength of the material. Strings have a property called stiffness which is basically the ratio of it's thickness to it's length. Stiffness causes an effect called string inharmonicity. The amount of stiffness of the strings is more pronounced in it's first harmonic because all other factors remain the same except the string's vibrating portion is only half as long for the first harmonic as it is for the fundamental. Therefore in real life the strings first harmonic will be vibrating slightly faster, or sharper, than an octave higher than the strings fundamental. The bridge should be positioned so the 12ft fret plays one octave higher from the fundamental. But we have four groups of strings each with a different tension, material, thickness, ratio from each other. Therefore if the bridge were straight across and the 12th fret where physically perfectly half the distance from the nut to the bridge, then because of string stiffness causing inharmonicity, this might not make the 12th fret actually play the perfect octave from the fundamental that your ear likes to hear. So to keep the builder's life more simple, mandolins are most often constructed with parallel frets and the bridge is compensated to account for the string inharmonicity caused by differing amounts of string stiffness amongst the four groups of strings.

[Steven]

YIKES!!!!!!

[b.pat]

Lee,
That's "Exactly" what I was going to say

Seriously, well stated.
B.Pat

[mandroid]

funny Forbes magazine didnt mention being born Steve Forbes as being the lowest stress job,

[Chris Baird]

Lee,

#Your model is certainly true in the practical sense but an artificially excited string does not vibrate in a sine form until the very end when it is almost inaudible. #A pick or hammer creates a distrubance that propagates up and down the string length and reflects off the bridge and nut. #Those disturbances follow the complicated outline of a sawtooth wave form. #The main reason why a bridge is compensated is to account for variances in tension increase from the bend created by fretting. #Also strings do not vibrate beginning right at the nut and bridge. #There is a small bit of string that is not included in the vibrating section and that small bit varies string to string. #Many compensated bridges are not built to the degree of accuracy needed for perfect compensation and even if they were it could only be for one particular set of strings. #It is rather easy to make small adjustments with a file such that compensation will be perfect for your strings and action.

[Chris Baird]

Here is a fine site with some visuals for those wanting to know more about a vibrating string.

http://www.phys.unsw.edu.au/~jw/strings.html

[twaaang]

Whoa! What a difference a day makes! Special thanks to Lee, Gary, Chris, and Dave for time, effort and consideration on this one. Who knows how long it would have taken before it occurred to me to do some creative filing?

Thanks again, I really owe you! -- PDW