break angle and string tension

[O. Apitius]

I've been reading this thread and thought I'd weigh in, ........

Now that's a clear and concise description.
Thanks.

[Jeff Mando]

Don't you have to know what kind of string tension you want, before you can try to change it? I say that having played the banjo for 45 years and have never messed with that little knob on the tailpiece. Have I been missing something?

[sblock]

Don't you have to know what kind of string tension you want, before you can try to change it? I say that having played the banjo for 45 years and have never messed with that little knob on the tailpiece. Have I been missing something?

Dear Jeff Mando,

Well, perhaps missing a little? A key point of my previous posts, #68 and #73 in this thread, is that changing the string break angle does nothing at all to change the string tension. This may seem quite counter-intuitive, I freely admit, but it's absolutely true! A given open string will sound at the desired pitch (usually G, D, A or E on a mando), over a given scale length (~13-7/8" or 14" on many mandos), when the tension is brought to a particular value (often something around 20 lbs for medium gauge strings). If you increase the string break angle, you will increase the downward force acting through the bridge onto the mandolin's top, but this will have no effect on the pitch. To get the right pitch, you need to place the appropriate tension on the string, irrespective of the break angle.

In the case of a banjo tailpiece, you can "mess with that little knob" on the back, either to press down further on the strings (thereby increasing the break angle) or let them rise upwards (thereby decreasing the break angle). Of course, doing so will send the strings out of tune. (In practice, you usually detune the banjo before adjusting this knob anyway, so that really has no bearing, but you can also do it under full tension on some tailpieces.) Regardless, after adjusting the tailpiece angle, you then retune the banjo back to the correct notes. At this point, the tensions in the 5 banjo strings will be exactly the same as they were before you messed with the knob! The only difference is that you've now changed the break angle, and therefore changed the downbearing force on the banjo head.

I've actually been playing the banjo for 46 years -- just a year longer than you. It probably took me a good 10 years before I started seriously messing with the tailpiece knob, though. But, as I mentioned in post #73, there is a strong interaction between the tailpiece angle and the head tension. If you prefer a fairly slack head, then adjusting the tailpiece will likely have little effect. If you like a tight head, then the tailpiece adjustment will be much more sensitive. Give it a shot, I say! If you have an Oettinger tailpiece, or one similar to it, you can even monkey with the downbearing force of each string individually, with 5 screws, instead of just one knob. To me, that's overkill, but some folks swear by it. Anyway, you can exert a whole lot more control over the tone of a banjo, by fooling with strings, bridge, head tension, and tailpiece than you can with a mandolin. That's a stubborn fact. Banjos are like the 'hot rods' of musical instruments, made of a jumble of interchangeable parts that can be souped up.

OK, I hereby apologize to my MC colleagues for making this seem like the Banjo Cafe. I now return to writing about our favorite, the mandolin:

Note that on the mandolin, the tailpiece is NOT designed to produce any additional downbearing force, beyond that supplied by the default saddle break. If it did (by pushing down on strings), it would produce an additional torque on the endblock, which could eventually damage the instrument, or produce excessive downbearing force against the top, which might lead to top sinkage or cracking. The mando has comparatively huge amounts of string tension! Unlike the banjo, you always leave a mandolin tailpiece "in neutral", so that the strings exit the tailpiece in a straight line as they rise up from the attachment point to meet the bridge saddle, and therefore don't bend as they exit the tailpiece. The string break angle on a mandolin is therefore something fixed by the geometry of the instrument. Typically, it's 14 to 16 degrees on modern carved archtop instruments.

Because of this, the string break angle for a Nugget-style (short!) tailpiece, a Gibson- or James-style tailpiece (with the cover), or an Allen- or Monteleone-style tailpiece (solid cast metal) is always the same. Changing out your mandolin's tailpiece among these many models will do nothing to change its break angle, nor the down-bearing force exerted on the top. Not if you correctly adjust the tailpiece angle during installation to leave it "in neutral," that is -- as you should. So those of you who thought the shorter Nugget tailpiece might sound a bit different due to a different break angle, or to a greater "afterlength" of the strings behind the bridge -- not so! Any differences in tone you might detect (and there really should not be much of a difference, based on first principles) are more likely attributable to the lower mass of the tailpiece, and not much else.

[amowry]

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?

I think so. We've been assuming zero friction on the saddle (and nut), but I would guess there may be significant friction, especially with wound strings. I'v always assumed that's why when strings break while tuning up, they usually break between the tuner post and the nut.

[Tom Haywood]

I needed to confirm that the string tension is the same on both sides of the bridge because a couple of folks demonstrated to me how the string feels tighter after the bridge, indicating that it is under higher tension. I became unsure what the math would show. The approach I took was to first use a tuner to read the frequency/note of an E string on both sides of the bridge, tuned to pitch before the bridge. Then, I measured both lengths. On this particular mandolin, the lengths were 13 7/8" and approximately 6.25". Then, being lazy, I found an online calculator that included the unit weights of D'Addario strings (which are on this mandolin) in pounds per inch. With this information, I was able to input the different lengths with the same tension and the notes observed on the tuner, and see that almost exactly the same string unit weight would produce those notes. By changing the (after)length input to 6.24", the string unit weight calculated as exactly the same as I could get it - a difference of .00000004 lbs/inch. That seems to be a pretty good proof that the string tension is the same through the entire length.

[HoGo]

I wanted to add a few notes about the afterlength. Some folks take it as magic bullet but it is more complicated. We should consider that the floating tailpiece like on violins has verry different effect on tone than fixed metal tailpiece. on violin the tailpiece vibrates with the bridge. Tha mass acts as mute and actually "takes away" some energy and filters some frequencies (that's how the wolf eliminators and mutes that hang on afterlength do work) but fixed metal tailpiece (especially the heavier cas ones) doesn't vibrate or just marginally so the effect of tailpiece is minimal.
One interesting thing was posted on one of the violin forums by respected maker who used to be physicist before. He tried to change break angle of violin by adding way high tail nut to violin, up to height that resulted in almost zero break angle at bridge and the difference in tone was very small even with that drastic change.
The conclusion may be that the vibrations or "energy" gets into instrument via bridge and the tail end where the tailpiece is anchored and the total sum is very similar whether more of it comes via bridge or tailpiece.
Banjo is another animal as the "body" is so stiff (heavy cast tone ring and thick ply rim) that pretty much all energy goes via bridge into the head so the break angle adjusted by tailpiece makes huge change in tone.

[Marty Jacobson]

I needed to confirm that the string tension is the same on both sides of the bridge because a couple of folks demonstrated to me how the string feels tighter after the bridge, indicating that it is under higher tension.

It feels stiffer in the afterlength because it's shorter, probably.

[Tom Haywood]

It feels stiffer in the afterlength because it's shorter, probably.

I think maybe it feels stiffer because it takes more force to displace the shorter string even though the string tension is the same. But it also takes more force to displace the longer string when the tension is increased. So I think it is natural for us to equate a tighter feel with an increased tension, and that's where my confusion set in.