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Thread: break angle and string tension

  1. #51

    Default Re: break angle and string tension

    Quote Originally Posted by Walt View Post
    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.
    That's this bit under the tailgut. The "Monteone" style cast brass tailpieces are before he started doing that, I guess.
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  3. #52
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    Default Re: break angle and string tension

    Quote Originally Posted by Marty Jacobson View Post
    That's this bit under the tailgut. The "Monteone" style cast brass tailpieces are before he started doing that, I guess.
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    I have actually seen that one before. There is supposedly one that has some sort of dovetail mechanism that allows you to raise and lower that ebony saddle under the tailgut. I have no idea how it works.

  4. #53
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    Default Re: break angle and string tension

    Based on the experiment suggested by others, the pitch in the afterlength section of the string appears to be about a half note higher than the pitch between the bridge and nut. All measurement were taken on the G course.

    The afterlength of my string is 4 3/8". It produces a very sharp Eb5 note.
    At 4 3/8" on the bridge to nut side, it produces a sharp D5 note. So roughly a half note lower.
    To produce the same very sharp Eb5 note on the bridge to nut side, I have to move all the way up to 4 1/8" from the bridge.

  5. #54
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    Default Re: break angle and string tension

    Just tried it again on another mandolin and got basically the same results. It can be tricky figuring out the exact point of contact with the tailpiece, but I think these measurements are very close.

    Afterlength: 3 15/16" and F#5 note.
    Bridge to nut at 3 15/16" is F5.
    To produce F#5 on bridge to nut side, I have to move up to 3 11/16".

    For both mandos, there's roughly a half note difference at equal lengths.

  6. #55
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    Default Re: break angle and string tension

    Marty's post #51 shows the mandolin version of John's floating violin style tailpiece that has what I know as a Saucony style adjustable tailwire. The same basic design is what he uses on the current (extremely cool) archtop guitars.

    Here is one of John's on my new Brazilian rosewood and red spruce Condino octave mandolin. You can see that it eliminates the need for an endpin and if you do your prior calculations well, approx. 1/2" of length adjustment on the underside works well. They are not commercially available, so you need the secret handshake to get one....

    I've been wanting to try a violin style ebony saddle under the tailwire combined with a traditional endpin and tailwire; maybe on the next batch of mandolins. That way, you can make an oversize taller saddle to reduce the breakover angle on the bridge. This is very common for double basses, but there I don't have to listen to a chorus of wankers complaining that it is not what they used in 1923 so it can't be useful.....
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    Default Re: break angle and string tension

    It seems to me that if there is a difference in tension anywhere on a string, the higher tension section would pull the lower tension section toward itself until they reached equilibrium of equal tension. Now if there existed a pinch or other affect making the motion impossible then unequal tension could exist.
    -Newtonamic

  9. #57
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    Default Re: break angle and string tension

    corrected in post #55

  10. #58
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    Default Re: break angle and string tension

    corrected in post #55

  11. #59
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    Default Re: break angle and string tension

    Quote Originally Posted by grandcanyonminstrel View Post
    Here is one of John's on my new Brazilian rosewood and red spruce Condino octave mandolin. You can see that it eliminates the need for an endpin and if you do your prior calculations well, approx. 1/2" of length adjustment on the underside works well. They are not commercially available, so you need the secret handshake to get one....
    That Monteleone tailpiece base is killer. I have almost set up a backyard foundry on more than one occasion to try and make that piece. The floating TP on the short scale mando I made for my daughter is the traditional endpin and ebony saddle, but it is less than refined with its uncoated steel cable for tailgut. Pics won't load right now, which may be a good thing.
    I love the idea of a floating tailpiece that allows little micro adjustments. The mandolin I'm playing the most right now is super sensitive to break angle. If I raise the bridge at all, it goes from sounding nice and open to super-tight. So even though I'd prefer a slightly higher action, I leave it low because it sounds more open. An adjustable tailpiece would really help it out.

  12. #60
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    Default Re: break angle and string tension

    Quote Originally Posted by Walt View Post
    Just tried it again on another mandolin and got basically the same results. It can be tricky figuring out the exact point of contact with the tailpiece, but I think these measurements are very close.

    Afterlength: 3 15/16" and F#5 note.
    Bridge to nut at 3 15/16" is F5.
    To produce F#5 on bridge to nut side, I have to move up to 3 11/16".

    For both mandos, there's roughly a half note difference at equal lengths.
    I just did some very approximate calculations, based on the formula
    f = sqrt(T/M) / 2L
    f is frequency
    T is tension
    M is mass per unit length
    L is length.

    Using D'Addario's quoted tension for the G string in the EJ74 set, (quoted as 24.480lbs / 11.113kg) that gives approximately 27.5 to 28 lbs in the afterlength. About 3 to 3.5 lbs extra tension.

    As others have expressed, I think the tension in all parts of the string will tend to equalise, but perhaps the wound strings will grip the bridge hard enough to allow for some inequality. On the other hand, if this is so, I'd assume that in the process of tuning up from a slack string, the tension will remain lowest in the afterlength. The difference in tension would then tend to pull the bridge forwards, towards the nut. But, if an adjustable bridge is raised while the strings are under tension, that could imbalance the tension in the opposite direction, pulling the bridge back towards the tailpiece.

  13. #61

    Default Re: break angle and string tension

    I'm struggling here.
    If my imput is 24.5 pounds of pull, regardless if the wound string grips or slips, how can I gain more pull on the other side of the bridge? I only put in 24.5 total.

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    Default Re: break angle and string tension

    After-length or even 'pre-length', the distance from nut to tuning post also affect the pitch and quality of the sound. The tension from either side of the 'string length' should be so that normal overtones result. Often a 'sticky' bridge or nut will change the tensions and the temperance / tuning becomes a problem. Freeing the hangup usually solves the problem.

    Break angle is just one of a number of factors that affect the performance of the instrument. Neck angle for instance or the break angle from nut to string posts are two others.
    Decipit exemplar vitiis imitabile

  15. #63

    Default Re: break angle and string tension

    How about something like this... you could use it with the tailgut style, or make the strings attach to the top adjustable surface. Doesn't allow you to modify afterlength on the fly, but you could adjust break angle on the fly, like Ken Parker's guitars a bit.
    Basically like a banjo or other adjustable tailpiece.

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  17. #64
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    Default Re: break angle and string tension

    Quote Originally Posted by Marty Jacobson View Post
    How about something like this... you could use it with the tailgut style, or make the strings attach to the top adjustable surface. Doesn't allow you to modify afterlength on the fly, but you could adjust break angle on the fly, like Ken Parker's guitars a bit.
    Basically like a banjo or other adjustable tailpiece.

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    Yes, that looks great! That coupled with the adjustable tailgut James mentioned would be a powerful combination. I feel like once you get the tailgut tuned in to the proper length, you wouldn't have to really adjust the afterlength very often. You have done some 3D printed tailpieces, right Marty? Would 3D printed steel be strong enough for the above configuration?
    I've also toyed with* the idea of getting a wax 3D printer and doing some lost wax casting of small parts.

    *of course by "toyed with" I really mean "I spent three hundred hours on the internet reading about it and never taking any actually steps."

  18. #65

    Default Re: break angle and string tension

    Fascinating reading gentlemen. So what do you think Nugget was after when he made this tailpiece? It creates a significant increase in after length.

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  19. #66

    Default Re: break angle and string tension

    Quote Originally Posted by Walt View Post
    You have done some 3D printed tailpieces, right Marty? Would 3D printed steel be strong enough for the above configuration?
    I've also toyed with* the idea of getting a wax 3D printer and doing some lost wax casting of small parts.
    That was Ben Pearce. You can do DMLS "3d printing" in metal. These two little parts would cost over $1000 from one of the usual suppliers. Better to have a machine shop make them up for you, 3d printed or investment cast parts are going to require dozens of hours of cleanup, while machined parts should be ready use after a little polishing.

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  21. #67

    Default Re: break angle and string tension

    Marty,
    Vega archtop guitars of the 30's & 40's came with the "Adjustone" tailpieces that functioned in the same way. Definitely related to their banjo tailpieces.
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  23. #68
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    Default Re: break angle and string tension

    I've been reading this thread and thought I'd weigh in, since my graduate training was in physics, and I teach at a major university. Several folks have written correct things, but not specified exactly what they meant, and so they wound up talking past one another, at least to some extent. To make everything as clear as possible, I tried my own hand at a making up a diagram. But first, some comments:

    1) The tension, T, as a matter of definition, is simply the force stretching the string. It is always measured along the length of the string, regardless of the direction that the string is pointing. Since the string is static (i.e., it's not moving), the tension on any one side of the string (say, to the left) is always equal to the tension on the other side (say, to the right). This is due to Newton's laws.

    2) And YES, the string tension equilibrates on either side of the bridge. In fact, if there were a bit more tension on one side of the bridge than the other, any small slippage would immediately take the string out of tune. (The very same thing is true at the nut, by the way.) The only thing that could resist full equilibration would be contact friction at the bridge slot, which is undesirable. This means that the string tension in the region between the tailpiece and bridge is exactly the same as the tension between the bridge and nut. Andrew Mowry, Marty Jacobson, and others are all 100% correct on this point. Also, the "afterlength" tension does not change with a change in the break angle. The afterlength tension is the same as the scale length tension, and this is always a fixed (invariant) quantity for a given set of strings tuned to the correct pitches. What changes as you increase the break angle is the static loading of the top. Not the string tension, in any portion of it.

    3) Most folks position their bridges so they don't "lean," that is, that they are (very nearly) perpendicular to the mandolin top at their base, and also perpendicular to the fretboard surface. I will assume this orientation in everything that follows.

    4) The break angle, a, is defined as the angular change that occurs as the strings pass over the bridge (see diagram). The complement of this angle, (180 degrees - a), is the opening angle of the string over the bridge. By symmetry, the net downbearing force exerted by the string against the bridge saddle bisects the opening angle. Check out the diagram below to see what I mean. And so, half of (180 - a) is 90 - (a/2). The downbearing force therefore makes an angle of 90-(a/2) with the string, on both sides.

    5) Because of this, the downbearing force is not quite "straight down through the bridge." In fact, it makes a small angle, equal to a/2, with it. The main force is downward-directed onto the top, but there is also a small component of force that acts on the bridge saddle towards the nut (that is, to the left in the diagram, along the fretboard direction). This force is resisted by contact friction between the mandolin top and the bridge base, acting parallel to the mandolin top and in the opposite direction. If that top contact were perfectly slippery, the bridge wouldn't be able to stay in place!

    The formula that HonketyHank offered at the very start of this thread, [F = T*sin(a)], is the correct formula for the vertical component (only) of the bridge force, acting directly "down" against the top. And the formula that Tom Haywood supplied happens to be the correct formula for the NET (total) force acting on the top [F = 2T*sin(a/2)], which includes both force components. When a is small, sin(a) is nearly equal to a (with a measured in radians, not degrees!), and we wind up with 2T*sin(a/2) ~ 2T*(a/2) = T*a. And using F = T*sin(a) also gives F ~ T*a, which is the exact same result! Both formulas give the same answer for small a. That's because the force component acting towards the nut becomes negligible at small break angles.

    For a break angle of 16 degrees, we have a = 16 deg = 0.27925268... radians. The sine of (0.27925268... radians) is 0.275637356... --- nearly the same! In fact, there is just a 1.3% difference between using the exact formula and the approximation.

    For a break angle of 16 degrees, we get F_vertical = T*sin(a) = 0.276*T, and F_total = 2*T*sin(a/2) = 0.278*T, and these two formulas only differ by about 1%. So it really doesn't matter which formula you pick, in practice. This also means that if you prefer to set up your bridge to lean 'backwards' just a little, so it bisects the string opening angle, instead of being perpendicular to the top, it won't change the downbearing force placed on the top by any meaningful amount (1% or less). However, leaning the bridge rearward in this fashion can 'zero out' the component of downbearing force that would otherwise act towards the nut, so that the bridge base doesn't need to resist it using contact friction. Regardless of what you choose to do -- lean, or don't lean -- this is a tiny effect.

    Finally, note that practically 30% (27.8%) of the total string tension on mandolin, which can range up to ~20 lbs/string, or (~20*8) = ~160 lbs in all, appears as a downbearing force with a break angle of 16 degrees. That's getting up to about 60 lbs bearing down on the top, which is a whole lot of force, in my opinion! The formulas tell us that any break angle in the range of 12-18 degrees will place a net downward force ranging from 20% to 30% of the total string tension on the top.

    You may have to click on this image to enlarge it, I'm afraid:

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  25. #69
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    Default Re: break angle and string tension

    Quote Originally Posted by sblock View Post
    i've been reading this thread and thought i'd weigh in..... This means that the string tension in the region between the tailpiece and bridge is exactly the same as the tension between the bridge and nut. ....
    thank you.
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    Default Re: break angle and string tension

    Okay, thanks, I'm glad I'm not crazy!

    Though I've mentioned it before, it's pertinent here so I'll mention it again, I have a calculator on my site that allows you to play with many of the angles and forces that come into play.

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    Default Re: break angle and string tension

    Quote Originally Posted by amowry View Post
    Okay, thanks, I'm glad I'm not crazy!

    Though I've mentioned it before, it's pertinent here so I'll mention it again, I have a calculator on my site that allows you to play with many of the angles and forces that come into play.
    No, you're not crazy! In fact, you're a darned fine luthier -- I have one of your fine A5 models, in fact, in Art Deco style.

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    Default Re: break angle and string tension

    If I understand the terrific explanation by SBLOCK, Changing the break angle effects static loading.

    So the concern would be not so much about string tension but Lbs of downward pressure. And that can be slightly modified by the break angle....right?

    And for extra credit, how does this effect the tone and / or performance of the instrument?

  30. #73
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    Default Re: break angle and string tension

    Quote Originally Posted by DougC View Post
    If I understand the terrific explanation by SBLOCK, Changing the break angle effects static loading.

    So the concern would be not so much about string tension but Lbs of downward pressure. And that can be slightly modified by the break angle....right?

    And for extra credit, how does this effect the tone and / or performance of the instrument?
    OK, I'll bite...

    Obviously, excessive downbearing pressure can cause structural collapse of an arched top. This can be rapid -- and catastrophic -- or it can be gradual (i.e., top sinkage). Sinkage can be minor, and compensated by raising the bridge saddle height, or it can be severe, leading to the loss of the top, or perhaps the entire instrument. Given the amazingly high loads we calculated earlier in the thread (up to 60 lbs!), it's easy to understand why luthiers must take great care with thickness graduations, and not go too thin to support the typical downbearing forces. However, they try to get close to the thinnest possible tops to have good efficiency (thinner wood means less damping = louder volume) and desirable tone. It's always a trade-off.

    Too little downbearing pressure can lead to a serious reduction in, or even a momentary loss of, the intimate contact between the bridge base and the arched top -- during string vibration -- leading to reduced energy transfer. This leads to both undesirable dissipation (loss of volume) and to sonic distortion (loss of tone). That is why having a good-fitting bridge is imperative, and why a certain amount of downward pressure on the bridge is required to improve the contact.

    But these represent the extremes. In addition to all that -- and perhaps most important of all -- the static loading of an arched mandolin top pre-stresses the wood. Getting pre-stressed changes the resting stiffness of the top, generally increasing it. This is because wood doesn't behave as simple elastic solid: it has a nonlinear stress-strain component. So, downbearing forces have an immediate effect on the top stiffness. Since the natural frequencies of various modes of vibration tend to depend on the (square root of) the stiffness, and inversely on the (square root of) the mass, increases in the stiffness will raise various mode frequencies and thereby directly affect the tone. As for whether the tone gets "better" or "worse," that is not possible to say on the basis of the acoustic physics alone, because good tone is strictly a value judgment. Duh. Besides, you want to have good volume along with good tone. And it can be hard to get both. But one way or another, the sonic spectrum of a mandolin will certainly change as the string break angle gets changed.

    The effect of string break angle is not so easy to test on a mandolin, but it's very easy to test on a 5-string banjo! Many/most bluegrass banjo tailpieces have adjustable angles (Presto, Kershner, Waverly, Oettenger, Prucha, Gold Tone, etc.), which lets you futz to your delight with the downbearing force, because you can change the pre-stress applied by the banjo bridge to the head by simply tightening a knob or turning a screw. It's best to tighten the head down first, because -- remember! -- the non-linear component of the pre-stress is what's important, and a slacker head behaves more like a linear elastic. With a banjo, you can explore the trade-offs between head tension and downbearing force (static pre-loading) on volume and tone. Most banjo players will tell you that the optimal adjustment for the tailpiece angle (which sets the string break angle) depends on how tight your banjo head is in the first place, how heavy your bridge is, and what kind of strings you're using. And that all makes perfect sense once you start to think about it.

    (I placed 2nd in the banjo contest in Winfield in 1978, so I've done my share of adjusting banjo tailpieces! That was a LONG time ago, geez. OK, I can practically hear those banjo jokes forming in your mando-centric brains.)

    I hope this qualifies for extra credit.
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  32. #74
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    Default Re: break angle and string tension

    Quote Originally Posted by Walt View Post
    Just tried it again on another mandolin and got basically the same results. It can be tricky figuring out the exact point of contact with the tailpiece, but I think these measurements are very close.

    Afterlength: 3 15/16" and F#5 note.
    Bridge to nut at 3 15/16" is F5.
    To produce F#5 on bridge to nut side, I have to move up to 3 11/16".

    For both mandos, there's roughly a half note difference at equal lengths.
    So....I just repeated this on a plain steel string instead of a wound string and the notes are basically the same at equal lengths. Technically, one measurement is 1/32" greater, but that could be human error. I'm having to use the sharp edge of a dobro slide to reach the note, which could account for the difference.
    So what is the deal with the wound strings being a 1/4" off? Binding in the saddle slot?

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    Default Re: break angle and string tension

    Quote Originally Posted by sblock View Post
    OK, I'll bite...

    Obviously, excessive downbearing pressure can cause structural collapse of an arched top. This can be rapid -- and catastrophic -- or it can be gradual (i.e., top sinkage). Sinkage can be minor, and compensated by raising the bridge saddle height, or it can be severe, leading to the loss of the top, or perhaps the entire instrument. Given the amazingly high loads we calculated earlier in the thread (up to 60 lbs!), it's easy to understand why luthiers must take great care with thickness graduations, and not go too thin to support the typical downbearing forces. However, they try to get close to the thinnest possible tops to have good efficiency (thinner wood means less damping = louder volume) and desirable tone. It's always a trade-off.

    Too little downbearing pressure can lead to a serious reduction in, or even a momentary loss of, the intimate contact between the bridge base and the arched top -- during string vibration -- leading to reduced energy transfer. This leads to both undesirable dissipation (loss of volume) and to sonic distortion (loss of tone). That is why having a good-fitting bridge is imperative, and why a certain amount of downward pressure on the bridge is required to improve the contact.

    But these represent the extremes. In addition to all that -- and perhaps most important of all -- the static loading of an arched mandolin top pre-stresses the wood. Getting pre-stressed changes the resting stiffness of the top, generally increasing it. This is because wood doesn't behave as simple elastic solid: it has a nonlinear stress-strain component. So, downbearing forces have an immediate effect on the top stiffness. Since the natural frequencies of various modes of vibration tend to depend on the (square root of) the stiffness, and inversely on the (square root of) the mass, increases in the stiffness will raise various mode frequencies and thereby directly affect the tone. As for whether the tone gets "better" or "worse," that is not possible to say on the basis of the acoustic physics alone, because good tone is strictly a value judgment. Duh. Besides, you want to have good volume along with good tone. And it can be hard to get both. But one way or another, the sonic spectrum of a mandolin will certainly change as the string break angle gets changed.

    The effect of string break angle is not so easy to test on a mandolin, but it's very easy to test on a 5-string banjo! Many/most bluegrass banjo tailpieces have adjustable angles (Presto, Kershner, Waverly, Oettenger, Prucha, Gold Tone, etc.), which lets you futz to your delight with the downbearing force, because you can change the pre-stress applied by the banjo bridge to the head by simply tightening a knob or turning a screw. It's best to tighten the head down first, because -- remember! -- the non-linear component of the pre-stress is what's important, and a slacker head behaves more like a linear elastic. With a banjo, you can explore the trade-offs between head tension and downbearing force (static pre-loading) on volume and tone. Most banjo players will tell you that the optimal adjustment for the tailpiece angle (which sets the string break angle) depends on how tight your banjo head is in the first place, how heavy your bridge is, and what kind of strings you're using. And that all makes perfect sense once you start to think about it.

    (I placed 2nd in the banjo contest in Winfield in 1978, so I've done my share of adjusting banjo tailpieces! That was a LONG time ago, geez. OK, I can practically hear those banjo jokes forming in your mando-centric brains.)

    I hope this qualifies for extra credit.
    I give credit where credit is due and you've gone past your credit allotment. Now I think I'm indebted for a while now....and no more Banjo jokes. This topic has come up right when I learned that my 'hot shot' violinist nephew showed me his baroque violin and said that the luthier raised the saddle and made a new bridge. It is all about finding the 'sweet spot' like they say in tennis.
    Decipit exemplar vitiis imitabile

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