break angle and string tension

[Marty Jacobson]

Technically, break angle will increase the total string tension. The vibrating length tension will remain the same of course but the "afterlength" tension will increase with a steeper break angle.

You're right, by "string tension" I was talking about the tension in the primary vibrating length of the string, which is a result of scale length, unit mass of the string, and desired pitch.

[Phil Goodson]

Why would the afterlength tension change because of the break angle? Unless there's a great amount of friction in the saddle slot, that shouldn't happen.
And what difference does the afterlength make in any of this given a constant break angle???

[Marty Jacobson]

It does happen because the angled afterlength has to deal with the primary string tension, plus the tension applied by "climbing" the bridge in a shorter distance. So if you have one rope at 30 degrees and another at 60 degrees with the same weight spread between both ropes, you'll end up with approx 75% additional tension in the 60 degree rope.

Afterlength contributes to tone in that there is a lot of harmonic content that can be present there... not always a good thing if it gets out of control, but definitely an inherent part of mandolin (and violin, archtop guitar, etc.) tone which you'd miss if it weren't there.

[Phil Goodson]

It does happen because the angled afterlength has to deal with the primary string tension, plus the tension applied by "climbing" the bridge in a shorter distance. So if you have one rope at 30 degrees and another at 60 degrees with the same weight spread between both ropes, you'll end up with approx 75% additional tension in the 60 degree rope.

Afterlength contributes to tone in that there is a lot of harmonic content that can be present there... not always a good thing if it gets out of control, but definitely an inherent part of mandolin (and violin, archtop guitar, etc.) tone which you'd miss if it weren't there.

I can see that the % contribution to the down-force on the top is greater because of the difference in angles (maybe), but I can't see that the actual string tensions above and below the bridge are different. If so, why doesn't the string slide across the saddle groove to equalize the tensions??

If the angle increases the tension, you'd think that ALL guitar strings would break after the sharp downward angle into the pin holes before getting up to standard pitch.
I'm gonna need some more proof before I buy this.

[Br1ck]

Guys, plees don talk sketch subjeks, my brane don't work they good.

[Phil Goodson]

Guys, plees don talk sketch subjeks, my brane don't work they good.

Just try not to think about it.

[O. Apitius]

It's simple physics. I don't understand it myself but........

[Phil Goodson]

Irrelevant.
Force vectors and string tensions are not the same thing.The illustration does not show a saddle supporting a tense string.

If this is a valid proof, I'd like to hear from one who understands it and can explain why 2 different parts of a continuous and unrestrained string have different tensions.

[Earl]

I won't call myself an expert, but I agree with you Phil. It must be that others are somehow seeing the problem differently than you & I do. I'm not prepared to say that anyone is wrong, but we must be talking about different things. Sure vectors can be resolved into components, but that (I agree) has no bearing on the tension in the after-length. (IMHO)

[Marty Jacobson]

Irrelevant.
Force vectors and string tensions are not the same thing.The illustration does not show a saddle supporting a tense string.

If this is a valid proof, I'd like to hear from one who understands it and can explain why 2 different parts of a continuous and unrestrained string have different tensions.

I agree that it makes more intuitive sense that the tension anywhere on a string, strung to pitch, will be the same. I definitely can't give an authoritative answer, but I'll ask some folks for a clearer explanation.
Even without no knowledge of physics (which I don't claim), it's pretty easy to do an experiment on this - pick the string, and then the afterlength, measure the pitches. See if the pitches correspond equally to their lengths.

[O. Apitius]

I don't claim any more than my grade 10 education when it comes to physics and I am not here to argue. I do find this question interesting and relevant information for a builders of instruments with floating bridges.

I recall (vaguely) reading an article by Roger Siminoff in a Frets magazine back in the late 70s/ealy 80s. In this article, Mr Siminoff constructed a jig that could measure the downward force on a bridge as well as the tension of the vibrating length of the string and the tension of the after length. As I recall, the results were that as the bridge was raised the downward force increased as well as the tension on the after length. The tension of the vibrating length was of course kept constant to keep the string at proper pitch.

This makes sense to me because one rule of physics that I remember is that 'you can't get nothin' for free'. So if the downward force increases with bridge height as I think we all agree, then it seems to me that the extra force has to come from somewhere and an increase in the after length tension would account for this.

The graphic below seems to confirm this as the values for T1 and T2 are different with the shorter length having a higher tension.

[Tom Haywood]

I think it is a very interesting question and am enjoying the discussion.

I observe that as you raise the bridge the string tension increases on the entire length because the pitch goes up on both segments of the wire. You have to tune back down to concert pitch. My question is whether the pitch on the after-length segment isn't simply the same tension as the longer segment, just at a much shorter length. On the other hand, although the wire slides across the saddle, I like the idea that it is somewhat fixed by the saddle due to bending/crimping and friction. This sure gets complicated quick.

[Phil Goodson]

Oliver, I think that your equations differ from what I am saying IN PART because the downward rope in your drawing is fixed onto the other parts of the rope and cannot slide. A mandolin string DOES slide over a saddle when you move it. That's why the tensions can (and do [imo]) equalize unless the string is pinched in the saddle groove. We talk about this occurrence more often with the nut.

I think that if the bottom rope in your drawing simply had a slick hook on the upper end hanging on the rope, the lower rope and weight would SLIDE to the left until the tension was the same in both rope segments above.

I think we're just talking about two different things.

James, you brought up the afterlength. What were you alluding to??

[Marty Jacobson]

Sorry for my crappy sketches, just thinking through this... gotta be careful because a lot of what makes intuitive sense is oversimplified, and sometimes the examples we remember from class are oversimplified. But anyway, I think the two-rope diagram is oversimplifying the system.
Sliding isn't part of this, it's a simple statics question, everything is at equilibrium.

It's correct in that we don't get anything for free, and that there are X and Y components of the forces.



But what we've left out is that the downward force on the bridge is opposed by an equal and opposite normal force (at least... if we followed the specs and didn't carve our cedar tops to Loar specs, haha)



So the vertical component of the force is there, it just doesn't have to be handled by the string. It cancels out, and the tension in the string is the same on both sides of the bridge.

(At least in this version of reality which I'm choosing to live in, and may have just wished into existence through my own ignorance.)

[amowry]

Interesting.

I've always assumed the tension would be the same on both sides of the bridge, assuming zero friction in the saddle slots, or time for the tension to equalize. Like Phil, I think if the 10kg were hanging from a pulley that could slide across the supporting rope, T1 and T2 would be the same.

However, I see that it's a somewhat different system on a mandolin, because the bridge is in a fixed position. I think some of it has to do with how much the string can stretch, which makes it complicated...

[O. Apitius]

Yes Marty, I've been thinking about this and wondering where the extra downward force comes from and as you have shown, the "extra" force is not extra at all. It's just that more of the force gets directed downward and less laterally. For years I have thought of it as having the tension divided up unevenly on either side of the bridge. I got that idea from the article by Roger Siminoff that I mentioned earlier. It's possible that I either remembered it wrong or that the string was pinched at the bridge in Roger's test rig. So until someone with a real thorough knowledge of the subject proves otherwise, I will change my view on this. Thanks all.

[amowry]

Here's what I don't quite get: If you have a rope hanging on a pulley, there's never any mechanical advantage, no matter what the angles of the ropes as they exit the pulley, or the length of the ropes on each side of the pulley are, correct? In other words pulling with 10 lbs on one end of the rope always pulls the other end with 10 lbs. Why isn't that the same on a mandolin bridge, again assuming zero friction?

[Cobalt]

How about this? Pluck one of the strings between the tailpiece and the bridge, assuming it rings with a clear rather than muffled tone. Now finger the main part of the string at one of the upper frets to give approximately the same pitch. Now measure the two vibrating lengths, fret to bridge, bridge to tailpiece. We know the pitch is the same (we chose the fret that way). If the two lengths are the same we know the tension in both portions is also the same. If the lengths are different, the one with the shorter length must be under lower tension (and vice versa).

[j. condino]

"James, you brought up the afterlength. What were you alluding to??"

Thanks for asking.

I spent a $#!tload of time in engineering school, but I find more practical use from 400 years of the violin building.

In the violin world, all the way up the scale to the double bass (which I am heavily involved with), the tailpiece and afterlength are known to be a very important element in the overall sound, feel, tension and setup. The attaching "tailgut / tailwire" are adjustable, the mass of the tailpiece is critical, and the afterlength is almost universally understood to have a profound effect on the overall balance of the instrument. A seemingly unbalance instrument can be brought into great focus and power by manipulating this. Body sizes and geometry tend to be much more standardized than the mandolin. Most people try to have the afterlength tuned to either an octave and a fourth or an octave and a fifth; approx. 1/6 of the working string length. It can make a huge difference.

Adjustable breakover angle tailpieces like on some banjos and late model Jimmy D'Aquisto guitars also offer up a lot of possibilities.

In our nerdy mandolin world, there tends to be a fair bit of nonstandard body geometry, neck lengths, body joints, bridge to f hole orientation, et cetera, but then most folks just bolt on a generic metal tailpiece and accept that everything is fine...

There are times when it works quite well, but I'm of the impression that we could do a whole lot better towards tuning the fittings to produce consistently better balanced instruments.

Anyone who enjoys this somewhat analytic approach to instrument building really should attend the Oberlin acoustic physics and violin building summer workshops where you get to hang with some of the most brilliant minds in the world who not only talk about this, they spend the whole week building and scientifically analyzing the results. I cannot say enough good things about it. I spent a whole week sitting side by side with Nugget while we nerded out on everyone else's work AND I brought in instruments and materials of my own to study. It had a profound effect on my building- as in everything before, and now everything I do post Oberlin. They are more powerful, easier to dial in the voice I am after, and they are very consistent- something I struggled with before....and the setup kicks a$$!

[Phil Goodson]

James,
Have you been able, with your own graduations and system of mandolin building, to determine a "best afterlength" for your mandolins? Or is there so much difference between instruments that the best afterlength will have to be determined for each individual instrument?
How much difference is there in "best afterlength" among various randomly selected instruments? Are we talking about 1/8 inch or 2 inches???
Thanks for your comments.

[j. condino]

Phil: Statesville is pretty close; stop by for a visit sometime.

1/8" can make all the difference on certain instruments. The closer you get to that fine line between blowing the doors off everyone in the room and the whole instrument collapsing, the more difference can be heard. An overbuilt beast with 1/2" thick top and 200 coats of polly finish will have little impact when you make subtle changes. Everything seems to be a case by case outcome, that is why I've worked so hard to have a modular building process that allows me to fine tune many aspects of a build in real time while playing. Lets also not forget the player- a half deaf old geezer will (or not!) hear very different things from a 18 year old with true perfect picth!

[Tom Haywood]

I've just got back from the from the violin/cello/bass store where I got a good explanation about this string tension and after-length stuff. It raised the question that James just implied, which is why aren't we as mandolin builders more focused on the after-length? I'm about to do some experimenting.

Responding to James' first comment in this thread, I deleted my after-length comments from my earlier posts, because I assumed Hank had a fairly accurate break-over angle and there was no need to discuss calculation of the angle. I believe that what Steve was getting at is that the numbers are generally far less important than most of the other considerations, and I wholeheartedly agree with that. But in designing string instruments, I spend quite a lot of time calculating the geometry that will hopefully produce the sound I want to hear and allow the instrument to hold together. Break-over angle and down-force are a big part of that.

Thanks to James' input and Marty's bringing up the string tension aspect, I now see that after-length is much more than just a measurement for calculating the break angle.

[Phil Goodson]

Phil: Statesville is pretty close; stop by for a visit sometime.

1/8" can make all the difference on certain instruments. The closer you get to that fine line between blowing the doors off everyone in the room and the whole instrument collapsing, the more difference can be heard. An overbuilt beast with 1/2" thick top and 200 coats of polly finish will have little impact when you make subtle changes. Everything seems to be a case by case outcome, that is why I've worked so hard to have a modular building process that allows me to fine tune many aspects of a build in real time while playing. Lets also not forget the player- a half deaf old geezer will (or not!) hear very different things from a 18 year old with true perfect picth!

One more question & I'll stop: Do you have to build a different length tailpiece each time? Or can you clamp something heavy (sort of like one of those Weber harmonic suppressors) on the strings near the TP to do the final tuning?

I'd love to visit one of these days. Thanks,

[darylcrisp]

"James, you brought up the afterlength. What were you alluding to??"

Thanks for asking.

I spent a $#!tload of time in engineering school, but I find more practical use from 400 years of the violin building.

In the violin world, all the way up the scale to the double bass (which I am heavily involved with), the tailpiece and afterlength are known to be a very important element in the overall sound, feel, tension and setup. The attaching "tailgut / tailwire" are adjustable, the mass of the tailpiece is critical, and the afterlength is almost universally understood to have a profound effect on the overall balance of the instrument. A seemingly unbalance instrument can be brought into great focus and power by manipulating this. Body sizes and geometry tend to be much more standardized than the mandolin. Most people try to have the afterlength tuned to either an octave and a fourth or an octave and a fifth; approx. 1/6 of the working string length. It can make a huge difference.

Adjustable breakover angle tailpieces like on some banjos and late model Jimmy D'Aquisto guitars also offer up a lot of possibilities.

In our nerdy mandolin world, there tends to be a fair bit of nonstandard body geometry, neck lengths, body joints, bridge to f hole orientation, et cetera, but then most folks just bolt on a generic metal tailpiece and accept that everything is fine...

There are times when it works quite well, but I'm of the impression that we could do a whole lot better towards tuning the fittings to produce consistently better balanced instruments.

Anyone who enjoys this somewhat analytic approach to instrument building really should attend the Oberlin acoustic physics and violin building summer workshops where you get to hang with some of the most brilliant minds in the world who not only talk about this, they spend the whole week building and scientifically analyzing the results. I cannot say enough good things about it. I spent a whole week sitting side by side with Nugget while we nerded out on everyone else's work AND I brought in instruments and materials of my own to study. It had a profound effect on my building- as in everything before, and now everything I do post Oberlin. They are more powerful, easier to dial in the voice I am after, and they are very consistent- something I struggled with before....and the setup kicks a$$!

has anyone made/used an adjustable angle tailpiece on a mandolin?
I have a banjo I replaced a solid piece(no knot) with an adjustable angle and it made a positive difference.

d

[Walt]

has anyone made/used an adjustable angle tailpiece on a mandolin?
I have a banjo I replaced a solid piece(no knot) with an adjustable angle and it made a positive difference.

d

I have heard that Monteleone had a mechanism on some of his floating tailpieces that allowed the tailpiece to be raised/lowered from the body changing the break angle. I have never been able to find a picture, though. The same thing could be accomplished with a floating tailpiece and interchangeable tailpiece saddles of different heights. A lot of folks have noted that the high mando string tension wouldn’t work well with a banjo-style adjustable tailpiece.