Compensating Bridges?

Compensating Bridges?

Can anyone explain the idea behind the compensating bridges you see on mandolins and other instruments, where the E and D strings (in the case of mandolins) sit on the bridge slightly closer to the nut? With only an overall bridge height adjustment.
I used to think this was just on cheaper instruments, but I’ve seen these bridges recently on very expensive instruments.
I was always led to believe that the less tension on a string, then the more the string length needs to be lengthened to compensate for the increase in tension as the string is fretted. These staggered, but fixed length compensating bridges don’t fit in with that concept though.

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On a guitar it is actually the "saddle" in the bridge, the ivory or bone (usually) part in the bridge slot. I think on a madolin it may be the entire bridge? Anyway, It compensates for the downward movement to the string onto the guitar fretboard, so as you move up the neck it compensates the string so it is not sharp or flat when playing up the neck.

The bigger problem I am trying to solve down the line with compensation on guitar is to figure out a way all of us Dropped D or DADGAD players can lower our Low E string to the D, without it going sharp when we hit the G chord up on the fifth fret, and beyond. It will take some experimenting, which I don’t have the time for, and being just still a pretty beginner builder (only struggling through my fourth guitar right now) I am not ready. Don’t even know how possible it is, I have asked my teacher and he had no answer….but there must be one?

I use light guage strings, so there is more distortion than in a medium or heavy string. I have tried using a medium low E, but don’t really like it. Pressing to the fingerboard without a death grip helps… OK this is not your original question!

Hope the above makes sense.

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Iris, your question isn’t the same one but it certainly is an interesting one. Let us know if you ever solve that one.
It was suggested to me that the best way to tune the DropD 6th string was to play the 12th fret harmonics on the 4-6th strings and tune the 6th as far down as you can go until it just begins to sound flat. Then take it back up a fraction. In other words tune it as low as the ear will tolerate without sounding bad. This compromise makes it more in tune on the 5th fret upwards.
Again not really relevant to either question.

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To the original question: "led to believe that the less tension on a string, then the more the string length needs to be lengthened to compensate for the increase in tension as the string is fretted".
This is almost true, and it *does* explain it. First you must be clear that it’s not so much the force in the string as the "force per unit of cross-sectional area". For reasonable comfort - and for reasonably consistent sound - the tension (in the sense of the actual force) in all four courses wants to be, if not identical, at least in the same ball-park from one string to another. The top strings therefore, having about the same total force but being much thinner, are much higher on the scale of "force per unit of cross-sectional area", or tensile stress.
If you are with me so far, here comes part 2:
As a first approximation we would expect the bridge to be twice as far from the nut as the twelfth fret, giving us half the length for twice the frequency, i.e. a one-octave difference. However, as someone else pointed out, pushing the string down to the fret lengthens it a teensy bit, so increasing the tension. To compensate, the bridge is moved back a little, away from the nut and the frets. You then have a smidgeon more than half the length left vibrating when you are fretting at fret 12, and in an ideal world the frequency would be exactly double that of the open string.
Part 3:
Because a graph of stress against strain is not a straight line but a curve (can you take this bit on trust?) the effect is stronger on the thicker strings (as you say - less tension, more compensation) than on the thin strings. The thin ones have so much tensile stress that they are going over the "knee" of the graph, and their tension, though bigger, does not rise as fast when the string is stretched as it does on the less stressed strings which are still on what is called the "elastic" part of the curve.
Finally:
The thicker strings, with less tension-per-unit-area, need more compensation; the bridge wants to be moved back further from the nut on those low strings than it does on the thin ones. And I think that is just what you see.

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A really fun time is getting decent intonation on an electric 12-string with 6 saddles. :(

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Good essay, Morph. I would just add that a good electronic tuner is very helpful in setting the compensation. It can go where the ear can’t.

I play in dropped D a good bit and I have to compromise a tiny bit to get the fifth fret G (almost) in tune. If I kept a guitar in dropped D or DADGAD all the time, I’d probably push the saddle compensation back a little on the low D string. If there’s room left on the saddle edge, that is.

A fretted instrument is a web of compromises.

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"A fretted instrument is a web of compromises."

That’s so true Bob - intonation really drives me to distractions sometimes. I always tune the guitar, then immediately proceed to de-tune it to get the best compromise for my style of playing. When in standard and drop D, one of the things I do, is to flatten the B and A strings, as well as the drop D, just ever so slightly.

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Thanks for the replies. I was already ok (ish) with understanding the general principal of why strings need compensating, albeit at maybe a less in-depth level.

Maybe I didn’t explain very well the main point I was trying to make, and the sole reason for the post. Or maybe I didn’t spot the answer amongst MT’s complex reply. 🙂

Before posting I looked for a photo to link to, but failed. Though I’ve just found one here:
http://www.folkofthewood.com/Images5/gtgm70bridge.jpg

So why the need for shorter E and D strings, and not the A?

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I didn’t explore that far - I was just fascinated to know these things existed. They look like they’d be a nightmare to play.

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The skinnier the string the more chance for distortion. But…. with that low E on guitar, tuned down to D, it gets a little too slack to intone properly. I don’t know, Donough, if a different saddle is the answer, but perhaps a different type of string. Perhaps a slightly compensated nut, or a zero fret that stops short of the Low E string? It would likely take ruining many saddles, nuts, and fretboards to correct it from a construction angle.

Maybe I can email a few string makers down the line about the problem and sets for dropped D playing or DADGAD could be made dead on. I just have zero time to even think about it right now. The best answer I have found is to press only as hard as you need to, to not buzz. A death grip will also shove the string a little this way or that, increasing poor intonation.

Funny, no one seems to notice it but us, LOL… or have I now opened us up to more guitar bashing, where people are going to super-focus on it!

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Re guitar intonation. I find each guitar has its own tuning idiosyncracies.
On my main guitar I generally tune the bottom E string slightly flat as the saddle is not compensated quite enough (it can be difficult to have a fully compensated saddle across six strings if you’ve only got 3.5mm of saddle to play with). Slightly flat to my ear is far better than slightly sharp, which makes my teeth fall out. and anyway, a slightly flat fretted note can be brought up to pitch by pressing slightly harder.
When playing in DADGAD I generally have the 2nd string tuned ever so slightly flat as well. Likewise in open G.

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Tigermoth, you have to look at the strings as being of two different types - wound and unwound. The principle described in replies here still applies - fatter strings need more compensation - but you have to compare wound with wound and unwound with unwound.

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Bob’s right. That’s why on a guitar saddle the ridge zips from the back to the front between the B and G strings (or should).

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Hi Bob,
Yes but surely the D strings are fatter and slacker than the A strings, therefore needing more compensation, i.e. further back, not forward?

You’ve guessed, I still don’t get it. Or rather looking at the link I posted:
http://www.folkofthewood.com/Images5/gtgm70bridge.jpg it’s just the D strings I don’t get.

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The physical characteristics of a wound string (tensile strength, elasticity, etc.) are different from the characteristics of an unwound string of the same thickness. Call it the X factor. If the extra length needed for an unwound string is 3 millimeters, the extra length needed for a wound string of the same thickness would be X times 3 millimeters. For reasons that aren’t intuitively obvious, X happens to be less than 1.0. Does that make sense?

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Donald K…what about when playing in D though… I opt to go for an in tune open D on the low string. I play it more than the G note on the 5th fret as a rule. I press as lightly as possible.

I did find in building some of my own that of course as low an action as possible helps a whole lot, the V or U shape made by pressing down is a hair less severe.

I have never yet met a guitar with 100% perfect intonation, and if I did, it would undoubtedly need constant adjustment to weather conditions. It’s one reason I started buidling, aside from having a bad case of GAS that was no longer satisfied by what others made, even the best, because they were not tailor made (ha ha TAYLOR made, pardon Pun!) to my precise way of playing, or have a neck that just fits my hand right etc… but I like to be able to trouble shoot and maintain anything I have.

I even put together my band saw and drill press, rather than asking for help (I know this stuff is child’s play for you guys, but the "girls" of my era were not allowed to play with these things, get dirty, greasy etc. so they are a little intimidating) so I know how to maintain them and understand how they tick. Same for a guitar. I didn’t want to run to a shop for any minor adjustments. Total guitar repair is down the line too, it’s a whole different ball game than building.

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Another answer to the original question would be to quote what a friend of mine called "end effect ". Basically, each string has to bend or vibrate from its two fulcrums, the bridge ( saddle on a guitar, of course, Iris ) and the nut or the fret you have held it down to. The thicker the metal, the longer the length at each end that is effectively dead, that is not really vibrating because it’s not that flexible. For the covered strings it is the core wire that is the defining factor in these allowances, hence the apparent kink in the bridge on mandolin and similar instruments with two pairs of wire, and two pairs of covered strings.
You will observe that spanish/classical/gut or nylon-strung guitars have no compensation at all, as the strings are pretty well totally flexible.
Incidentally I don’t believe all this nonsense about pairs of octave strings going out of tune with each other as you go up the fingerboard. Certainly not on my ‘zouk. I reckon the manufacturers have finally sussed out the correct guages. Maybe 35 years ago on an old 12-string you might have problems, with only a vaguely accurate bridge, but not today.
PS. thanks for that link, Iris, I knew the electric wiring stuff, but there’s a lot of other useful information there I shall be referring to in future.
PPS Don’t they sell sets of strings specifically for DADGAD now ?

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Bob,
Aha! Right, I got you.

So that makes sense that the unwound A strings would be shifted back towards the tail. But applying that theory I still can’t make any sense of the D strings being so far forward, particularly in relation to the G strings. Any angle of the entire bridge closer to the tail at the G string end would only increase that difference.

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BTW…. thanks to everyone for clarifying the "why" of it all. Honestly, the last guitar got a comp. saddle, and then I showed it to another luthier who said, get that stupid thing off there. To be honest, I did change it to a straight one to see what happened, but in the usual angled saddle slot, and it still plays fine… I don’t hear a difference… but I attribute that to the fact that maybe my action is so rediculously low, that another player (say a choppy strummer) would buzz all over the place. It’s as low as it can possibly go without buzzing for the way I play.

It’s just how I like my guitars, lower than they should be. I get very good volume however, in spite of being a fingerstyle player. Likely the fact that it gets pressed down less, fraction of an inch wise, makes the difference in intonation perhaps and keeps it right with the harmonics. at 12th fret

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I think some of that extra comp for the G strings is probably because the action is usually a little higher on that side, aggravating the intonation problem. Also, I doubt if the change in compensation length for a very skinny string all the way up to a big fat string follows a linear relationship. Some factors, like the "end effect" that Pete mentioned, might be negligible up to some thickness and then seriously come into play with thicker strings. There are probably other factors we haven’t thought about. The mathematical physics of these instruments is mind boggling.

There’s also a different kind of end effect that can impact intonation as well as clarity and loudness. If the angle of the string behind the bridge (saddle, on guitar) isn’t steep enough, that end of the string won’t be stable enough to vibrate properly over its full length. Energy can be lost and subtle distortion introduced.

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Like said above, every guitar is different. I always tune my bottom E a little flat, because when I do so, the third fret G is right on. I would rather have a slightly flat bottom note on an Eminor chord than a slightly sharp G at the bottom of a G major chord, don’t ask me why, but to my ear that compromise works better. And my B string is always fussy, and while my electronic tuner works pretty well for everything else, I sometimes tune that string by ear to get it right.
Of course, I just put on new strings to prepare for St Patrick’s Day, after having let them get too dead. No matter what the pitch, I suddenly feel like my guitar has suddenly become a banjo!

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Iris - another suggestion; I haven’t tried looking for it today, but I remember somewhere reading an article by Stephen Delft, it might have been in one of those guitar magazines in which case it’s maybe not internet accessible, but it was about compensated NUTS.
It was illustrated by a close-up photo of a guitar nut with various layers of shims glued to the front edge ( fingerboard edge ) of the nut to sweeten the intonation of individual strings. It looked most bizarre, but apparently, for those of particular acuteness of pitch, it does the job. Obviously you have to stick to the same gauge of strings or the effect is ruined. Delft was using electronic guitar tuners long before they were easily accesible, so he did know what he was talking about.

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To get back to the original question - ( again ! ) - I just checked on Red Henry’s instruction for making his mandolin bridges, and he recommends compensating on the A and G strings about 3/32nds of an inch back from the front edge of the bridge. Obviously, as well as this, the whole bridge will be slightly angled across the soundboard. This seems to work on my ‘zouk as well, even with its octave stringing on the bottom two pairs.

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It has been answered up to a point, but in a further attempt to clarify:
"So why the need for shorter E and D strings, and not the A?"
To avoid confusion, be clear that there are two quite different small increases in lenth that we are talking about - one is the "long term" increase in sounding length obtained by moving the bridge points, the other is the "instantaneous" increment in the string length caused by fretting the string, so that it is no longer a straight line but a very flat V-shape. We could call these the bridge increment and the fretting increment respectively.
Also remember it’s not the E and D strings that are shortened so much as the A and G that are lengthened *more than* the other two - all of them are at least a bit longer than the simple "twice the distance from the nut to the second fret".
Next remember that the amount of increase you need in the sounding length (the "bridge increment") depends on how much extra tension you get as a result of pushing the string down to the fret - that’s what has to be compensated for.
Thirdly, bear in mind that the proportional increase in tension (and therefore the pitch change) varies with the force per unit area in the core of the string. As you stretch the string more and more, at first the tension rises in proportion to the stretch - each millimetre wound on to the peg causes the same increase in tension. If things were that simple, all the strings would need the same bridge increment, and it would just be perpendicular to the strings - you wouldn’t normally even notice it was there.
But they are not that simple. As you stretch more, the material starts to give way - the tension does not rise as much with each millimetre of stretch. Go too far, and it will collapse altogether of course! This can be plotted on a graph that rises at first as a straight line, then curves to become flatter. Strings that are stretched like this will therefore not show as big a rise in pitch in response to the fretting increment, and will therefore not need such a big bridge increment to compensate. And as it happens wire instrument strings are generally tensioned in the region of the "knee" of the curve in that graph.
That is why as you go from the E to the A you move from a string that is high on the graph, just above the patella, so to speak, to one that is closer to the "shin". They have similar total tensions, but the E has therefore much more tension per unit area. On the flatter part of the stress/strain graph, it needs less compensation. The same is true as you go from the D to the G.
As you move from the A to the D however (and I think this is where your puzzle lies) you move to a totally different structure. The D is wound - a lot of its weight comes from the winding, and this does not contribute to the tension. The tension is supported by the *core*, which is much thinner than the string as a whole - the bridge picture you found suggests that the core of the D is comparable to that of the E, thinner than the A.
In short (I’m tempted to delete everything I’ve written and focus on this, but hey…) the reason for the increase in compensation length as you go from A to D is because it depends on the properties of the taut core of the string, not the string as a whole.
By the way, I have a strong hunch that G Pete’s clever "end effect" idea does not play a big part. The thing with gut-strung guitars is that the increase in tension from a small fretting increment in length is just very much smaller than on steel-strung instruments, as you can tell from all the winding you do to tune one up.
I hope it helps a bit, after all that…

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This is fascinating. I used to play a bazouki (8 strings, 4 pairs, bottom two pairs octaves). The thing was designed and built for really thin strings and over a couple of years I gradually increased the gauges of the strings until I was happy with the sound. Consequently it required some major rebuilding. I got a very talented guy to put a bass guitar truss rod in the neck and build me a compensating bridge. When he’d finished the bridge and showed it to me I was astonished. It was all over the place with the most beautiful carving. I just remember looking at it with disbelief, but then playing it and it working right up beyond the 20th fret. Genius.

Poor old bazouki has long since died due to the increased tension.

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This subject is surrounded by many misconceptions, for example, the concept that plastic deformation (beyond the elastic limit on the stress/strain curve) plays a part. The only time that the string encounters any plastic deformation is when it is initially strung and tuned to pitch. Plastic strain causes the familiar relaxation of the string that occurs for some time afterward. Once the string reaches its equilibrium strained state, hysteresis in the stress/strain curve ensures that it will never again plastically deform, unless it is stressed beyond the new, higher, elastic limit. Thus, the nonlinear nature of the curve is not a factor in the need for saddle or nut compensation.

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I love that. I used to be an engneer as well as a bazouki player

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Scott C writes that:
"..misconceptions, for example, the concept that plastic deformation (beyond the elastic limit on the stress/strain curve) plays a part."
I don’t know whether anybody thinks that plastic deformation plays a part, but if they do, I would have to agree that it is unlikely. It is not what I was suggesting.

He also writes:
"Thus, the nonlinear nature of the curve is not a factor in the need for saddle or nut compensation."
If the curve were not non-linear, all the strings would need the same compensation and the bridge would be straight across.
I am intrigued by your use of the word "Thus". The fact that the curve is non-linear is not the same as whether plastic deformation is involved or not. The stress/strain curve for materials of this type reaches a non-linear region significantly before any plastic deformation occurs. That is the region in which these strings usually operate.
I must confess to being uncertain as to what, if anything, hysteresis has to do with this. The curve can be non-linear with or without significant hysteresis.
I can imagine no reason for the bridge not being a straight line across the strings other than the non-linear shape of the curve. Scott, you have not in fact offered any other explanation for the value of a compensating bridge, only an assertion that the nonlinearity is not a factor. Have you got one? That would be interesting.

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Another factor is the diameter of the string. If you assume the action across all strings is the same - measured from the bottom edge to the fret - you still have to press a thinner string further than a fatter one - measured from the centre of the string unfretted to fretted. I used to have 20 and a 56 tuned to A as my bottom pair. The tension was about equal, but the 20 had to travel a lot further. The difference on the bridge was about 3mm

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Morphonymic Tootler,
Thanks for all the effort in explaining the above, even if some of it made sort of a ‘whoosh’ sound as it passed over my head. I do feel a little more at ease though about these bridges now.

With the aid of dictionary.com, I’m enjoying the discussion. 🙂

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Oh, and thanks to Bob and everyone else who chipped in.

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By George, I think Michael might have hit upon what just *might* be the most significant difference between wound and unwound compensation. The core of the wound string doesn’t have to travel as far as the unwound string to touch the fret. I’ll admit I never considered that.

Now I have to stop thinking about this stuff or I’ll have nightmares about partial differential equations and Bessel functions.

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Sometimes the math works. I played last night and kept testing my harmonic, then press to the 12th fret, dead on, no comp. saddle… action lowered to near buzz, OK for fingerstylist!

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It’s not a "bazouki" , Michael.
Are you confusing it with a weapon of war ?
That would be the Great Pipes, then.
I just checked your biog to be sure that you’re not the guy in the music-shop at Tally-Ho Corner, he thinks it’s a bazouki too.

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Back from a day’s travel and perhaps this thread has died by now, but just to provide a response:

I went back and reread your original post Tootler, to see if I’d misinterpreted your meaning, and perhaps I have, but you refer to the S-E curve "flattening out", which occurs when you’ve exceeded the proportional limit and plastic strain is occurring. For steels used in strings, the amount of nonlinearity to the left of the yield point is insignificant in terms of its contribution to the pitch change that occurs during fretting.

All strings require compensation for the reasons that have been mentioned in this thread. The amount of string lengthening required is a function of scale length, string diameter, string material (Young’s modulus), whether the string is wound or not, height above the fingerboard. All of these things determine how much the P/A stress in the string will increase when it’s fretted, and thus how much sharp the note will go. Even after the saddle is compensated as well as possible, you still don’t quite get correct note frequencies all along the fingerboard because now the unfretted string length has been changed, and it’s necessary to compensate the nut as well. See here for a good description:

http://www.doolinguitars.com/intonation/intonation4.html

The reason you don’t have a straight line of compensation is not because of shape of the S-E curve, but because each string has a different set of geometrical, physical, and mechanical properties and has a different tensile load applied to bring it to pitch.

Maybe I’m saying the same thing you are…

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Thanks for the wonderful link Scott! Now I can really drive my teacher nuts… pardon the pun!

I am working on my fourth guitar now, this time alone, but when it comes to nut/saddle time I will take this issue up with him. Can’t have too much perfection!

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I think "nut compensation" is a bit misleading. The crux of the nut matter is simply that, until recently, luthiers misunderstood or overlooked some subtle details and misplaced the nut by a fraction of a millimeter. If all the luthiers would just make that adjustment, a lot of the intonation problems would go away. If you actually apply some kind of compensation for individual strings at the nut, the effect goes away as soon as you put on a capo.

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I played a comp. saddle guitar last night and it was no better or worse than the one the night before without it. I have a lot to understand and learn about building, but am enjoying it nonetheless. So much is so subtle! The main important thing that affects everything is the neck set. If that’s off, no compensating bridges or saddles on anything are going to make the intonation right. A neck reset is a pretty expensive repair, so best to get it perfect in the beginning.

Luckily there is a luthier who lives around the bend from me… two or three houses away and it’s over a mile… still close enough. He doesn’t have his shop at the house but will by next year and he figures, I think, that I at least know enough to be a help on most steps and not a hinderance. So Next year I intend to hang around and help, and learn much more about all this.

His opinions are different on many things than my teacher, and I know yet another two who are even more different in the way they build. My teacher gave me a comp. saddle, the guy around the corner says get rid of the stupid thing, set the neck perfectly, another says, not any real difference…haven’t asked the fourth guy, I am afraid to!! They’ve all been building for decades and turn out great guitars. Go figure.

And Bob…. ugh….capos. The alleged "non-distorting" ones, forget it. The best is the old screw on type. I have one I got in 1963 when I started to play. You can control the tightness and the "string squish factor" better. They take a bit longer to put on though. Even the old rubber band type you have a few different notches to use. I try and avoid them altogether. Have you built anything, you seem to know a lot about building.

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No, I don’t build, but I have several luthier friends so I know how to talk like I know something. 🙂

I somehow lost my own 1963 Jim Dunlop capo. I have some adjustable Victor capoes that I can set almost on top of the fret to minimize the string bending. Planet Waves also has a new capo that’s even better. Both are easy to adjust.

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Do you find old strings intone more poorly or exagerate the problem? I sure do.

I don’t know what brand my old capo is, will have to look, bit it seems to have no name. It helped the tuning issues last last though. Still not perfect. I want everything perfect! Good luck!

I hope to have #4 guitar done…all but the finish, by end of April. I will pick a few luthier’s brains when it comes to saddle and nut compensation…. my fear is four different answers which is definitely what will happen. I will just pick the person whose guitars are the most dead on in the intonation department and go with their ideas.

Guitars take so long to build, and my mind is always 25 steps ahead of "real time" with other ideas and projects… I am already thinking of the next one, wish I could just pop them out and still have them be good. At some point, I will try for two week breaks in work and life to just plow through and build one. A double O is my next dream, and then a folding or removeable neck one for travel. First have to get through this one…. and fix the major stupid screw up. Not a big deal I am told, very fixable!

Building is so full of little but very critical subtleties (sp?) and it will take years of little mistakes to get to stride with building, but it is so much fun. I had a chance to learn it when I was 17 years old, and started work on one, and now wish I had stuck with it, but did other very satisfying work instead. Not too late to start….took the "age test" online and got that I will live to 109! It’s onlt half over according to this, LOL!

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Iris, In my mind, the principal outcome of having built an instrument is that you’ve discovered a whole bunch of things you can improve on the next one. I’ve been pretty happy playing my own mandolin, fiddle, and guitar, but the more I play them, the more I think of things I’ll change on the next go-around. I’m like you, I don’t have the luxury to work straight through each project, so it takes a while to finish, especially the intensive carving projects like F-style mandolins and fiddles.

My current project is a bass marimbula, which is all done save for finishing out the final lacquer coat. That was an interesting project, it’s so big it’s more like building a boat than an instrument.

I’ve also found there are parts of the job I really enjoy and parts that I despise. I love to design, build, and do the inlay work, but I HATE doing the varnish and lacquer work, so I get through the building part fairly quickly then the instrument sits for a while until I work up a head of steam to start spraying. My latest guitar is at that point now, all done and ready to stain. It’s curly maple and I can’t decide whether to leave it blonde or darken it.

I’m lucky that I work at a place where I have easy access to pretty sophisticated real time frequency analyzers, so tap tuning and tone bar shaping are a breeze.

Ten or twelve more years until retirement, and then I can really apply myself!

Back on the subject of saddle compensation: I have a really nice octave mandolin and it’s HUGELY compensated. There must be nearly a half inch difference in scale length between the G and E strings. Comes of having relatively low string tension and a long scale.