String Tension and Compliance

[Turnaround]

Some time ago I did a study on string tension to try to prove or disprove the claims being made about various schemes to improve string tension on basses. Conventional wisdom says that any increase in tension on a given string will raise its frequency of vibration, raising its pitch. We know that since we increase tension on a string by turning the tuner so that it stretches the string more. And it is largely understood that increasing the mass of a string (heavier gauge) will require more tension to bring it to pitch than a similar string of lighter gauge. And we also know that if we increase the scale length of the string, we will need to increase the tension on it to bring it to the same pitch. The science of this is all well-known.

A number of years ago a "fix" to increase string tension surfaced, particularly for floppy B strings. It advocated placing a spacer at the end of the string, between the ball end and the anchor point on the string. Another scheme suggested that the B string tuner should be closer to the end of the headstock to improve its tension. These arguments suggested that since the overall length of the string was increased it would require more tension to bring the string to pitch. Unfortunately, these schemes were based on a faulty understanding of the physics involved. The vibrating length of the string remained the same and in order for it to vibrate at a given frequency (pitch) it had to have a specific tension regardless of what was happening beyond the vibrating length. But in spite of the fact that the tension could not be changed by such additional string length beyond the vibrating length, a number of players said they could feel a difference. To them, regardless of the actual tension, the perceived tension increased. Arguments ensued with skeptics suggesting that the perception of increased tension was a figment of the players' imaginations.

The phenomenon of increased tension was addressed by luthier Liutaio Mottola several years ago in an article titled "Lutherie Myth/Science: Human Perception of String Tension and Compliance in Stringed Musical Instruments". In it he made the distinction between string tension and stiffness. He named a number of factors that contributed to the stiffness of the string and called those collective factors "compliance". Compliance is the term he would then use to describe the "perceived tension" of a string, one having less perceived tension as having more compliance. He referenced some work in this area that had been done years before by Master archtop guitar maker Bob Benedetto. In the same article Mottola noted that there were no comprehensive studies that looked into the extent to which humans can distinguish differences in compliance.

To shed further light on the subject I decided to run a series of test to illustrate what happens when the overall string length is increased while leaving the vibrating length the same. I would extend the length of the string between the nut and the tuner, and between the saddle and the anchor point of the string. To test "compliance" I would measure how much force it took to deflect the string a measured amount while changing the "afterlengths". I define afterlength to mean that section of the string at either end beyond the vibrating part of the string. The test rig consisted of a hardwood board with a nut affixed to one end, a bridge affixed 34" away from the nut (scale length). At the nut end I affixed two tuning machines, one 1 inch away from the nut, another 6 inches further. At the bridge end I created two anchor points for the ball end of the string - one at 1 inch form the saddle, and the second 6 inches further from the saddle. At the centre point of the vibrating length of the string (the 17" mark), I mounted a dial gauge that would accurately measure the amount of deflection of the string.

Using this rig, compliance could be measured by suspending a weight from the centre point of the string and measure the deflection of the string on the dial gauge. The more deflection there was for a given suspended weight, the more compliant the string was. Or conversely the amount of force required to deflect the string a given amount could be determined.

Compliance in such a test would be defined in terms of two elements: the amount of deflection that occurs as the string is plucked (floppiness), and the amount of force it takes to press the string to the fret (stiffness). This would be the perceived tension of the string. The tests would illustrate what happens to compliance as the string afterlengths are changed.

I started by installing a string from the inner anchor points, the tuner closest to the nut and the ball end of the string at the closest point to the saddle. I tuned the string to pitch - I was using a D string, so I tuned to D. Later I would repeat the test with an A, E and B string but the outcomes were the same. With the string at pitch I suspended a 250 gram weight at the centre of the string and measured the amount of deflection. Then I restrung using the outermost tuner and ball end location, retuned to pitch and suspended the same weight mid-string. I measured the amount of deflection. It was different. So I then repeated the test with the string on the outer mounting points but changed the weight until I achieved the same amount of string deflection as in the first test. So I had data that reflected two ways of looking at string compliance - one that measured how much a string deflected for a given force, and how much force it took to deflect the string a given amount.

The Results:
1. The longer afterlength resulted in a further string deflection with the same force applied.
2. The longer afterlength required less force to be applied to deflect the string a given amount

Conclusion:
Added afterlength makes the string more compliant, which should result in less perceived tension.

It makes sense that the string would be more compliant with added afterlength. Part of the string's compliance has to do with its stretchiness. The more overall length there is to the string, the more string there is to stretch. If a 12" string will stretch 1" under a certain tension, it follows that at 24" length will stretch twice as much - there's twice as much string to stretch. Adding afterlength to a string adds stretchable length to the string, making it more compliant, or less tense.

Getting back to the question of whether a spacer behind the bridge would increase the string tension, it has proven to be false. And this test shows that that spacer would actually increase compliance, making the string more "floppy", not less. Any explanation for a difference in "perceived tension" is yet to be uncovered.

 

[Gsnorgathon]

Doin' yeoman's work here, Turnaround! Thanks for all the details.

 

[Turnaround]

An interesting corollary...

A question was raised about whether there was truth in the claim that extending the string length past the nut makes it easier to bend strings. It follows from the study of compliance where it was demonstrated that the amount of stretch in a string increased as the overall length increased. But the answer to the bending question is a bit surprising - it's both yes and no.

The "yes" part is easy to understand. If you increase the overall length of the string, there is more length to stretch. If you look at this characteristic another way you can see that it will take less force to bend a string the same distance as the overall length of the string is extended, since there is more overall stretch. But the downside is that you will have to bend the string further to bring it up to the same pitch. If you had to bend a string 10mm to raise its pitch one semitone, you might need to bend it 20mm to bring it up a semitone when you increase the overall string length by moving the tuner further from the nut.

But here's the surprising part - in order to bend the string up a semitone with the extended afterlength, not only will you need to bend it further, it will actually take more force than the same string with a shorter afterlength. I was not expecting that, but that's what I discovered using the compliance test rig. I strung up the rig with a string running to the nearest tuner to the nut and tuned it to A. I then suspended a weight on the centre of the string (a water bottle), and added a bit of water at a time thus bending the string a bit more each time until the string sounded Asharp (one semitone up). Then I weighed the water bottle. I moved the string to the outer tuner, adding 6 inches to the afterlength, and repeated the procedure. Here are the results:

Short Afterlength
Amount of deflection of string from A to A#: .576"
Weight to deflect string from A to A#: 993 grams

Long Afterlength
Amount of deflection of string from A to A#: .684"
Weight to deflect string from A to A#: 1185 grams

So, when I added more afterlength I had to bend the string further AND apply more force to raise it a semitone. So bending the string was easier if we are looking to bend the string a certain distance, but is actually harder if we want to bend it to a certain pitch.

I don't really understand why it would take more force to raise the pitch with the longer afterlength, but I am told by an engineer that it has to do with force vectors, and he pointed me to a physics problem of walker on a tightrope and talked about a free-body diagram showing all of the horizontal and vertical components of the forces involved. I'm afraid he lost me. But I can't argue with what I found using the test rig, even if I can't really explain it.

 

[HaphAsSard]

Any explanation for a difference in "perceived tension" is yet to be uncovered.

Now we have an answer, grounded in hard evidence, regarding actual tension and compliance with different afterlengths, I still find the question of the reasons for the sometimes reported, perceived increase in tension with a longer afterlength intriguing. Why is it so? Why do players occasionally report impressions that run not just...sideways to, but contrary to the aforementioned evidence? And why did (/does?) Fodera place their B-string tuner beyond the other two in the upper row in some models (/specimens)?

As was mentioned in the original thread, @Bruce Johnson has a theory on what longer afterlengths bring to the table, namely a slight difference in the tone of the attack (what he calls a stronger "snap"), as expounded in these posts:
love of Ampeg and other Scroll Basses, Part 2
Did They Ever Make A Shortscale That...
(the latter reproduced here
Does a reverse headstock add tension? )

I ain't no physicist nor a luthier (nor that good or experienced a player, for that matter); however, I was wondering about whether there be any difference as to the pitch envelope of a note upon the attack, scale being equal, with different amounts of afterlength.
Is it possible that a string with a shorter than standard scale, but still quite long total stretched length (and a healthy amount of travel upon nut and bridge) has a more stable oscillation between sharp, flat and Goldilocks pitch at the start of a note, with a less evident (=either reduced in Hertz, and/or shorter in duration) "sproing", so to speak, reminiscent of what happens on a longer scale? Could this possibly be the specific correlate of high-tension feel that long-scale players re-encounter on a shortie-plus, and not on a shortie without significant extras?

With the appropriate recording hardware and software (which I don't have), the pertinent quantities could be measured. Just thinking e-loud.

 

[Turnaround]

And why did (/does?) Fodera place their B-string tuner beyond the other two in the upper row in some models (/specimens)?

One of the principle reasons that manufacturers adopt certain design ideas is that it makes economic sense to do so. For a while, and even now, there was a surge in the popularity of string-through-body basses riding on the idea that it increased sustain, or improved tone. If you were a maker of basses competing in a limited market, it would be a good idea to start producing string-thru basses as well or lose market share. The smart ones do it both ways - it makes the ones who feel there is an advantage happy while allowing those who feel it's just hype to chose a different model.
In Fodera's case, I suspect that Fodera made the Imperial model with the extended B-string afterlength at the request of the person it was originally being custom-built for - Lincoln Schlieffer.

 

[HaphAsSard]

One of the principle reasons that manufacturers adopt certain design ideas is that it makes economic sense to do so. For a while, and even now, there was a surge in the popularity of string-through-body basses riding on the idea that it increased sustain, or improved tone. If you were a maker of basses competing in a limited market, it would be a good idea to start producing string-thru basses as well or lose market share. The smart ones do it both ways - it makes the ones who feel there is an advantage happy while allowing those who feel it's just hype to chose a different model.
In Fodera's case, I suspect that Fodera made the Imperial model with the extended B-string afterlength at the request of the person it was originally being custom-built for - Lincoln Schlieffer.

As implied in my lack of knowledge of their models, I'm not really hip to, nor am I especially interested in, all things Fodera. I now regret mentioning them at all, since that was the only part of my post that seems to have attracted your attention.
Sure, one answer to my (more general, not Fodera-related) question - why do some players believe in getting more tension out of a longer nut to tuner string path, since actual tension is the same and stiffness is actually reduced? - might be: it only takes one influential visionario* and many other people will follow, repeating the tale until it enters the perceived wisdom, the folklore.
Could there be a little more to it though? What if they recognise something not inherent to tension, scientific or perceived, but something else peripherally related, which they misattribute it to the former?


* [in my own, the Fodera brothers' and R.M. Mottola's ancestral language, the word can at times mean "one who sees things that aren't there yet", but it usually means that, minus the "yet"...]

 

[Turnaround]

- why do some players believe in getting more tension out of a longer nut to tuner string path, since actual tension is the same and stiffness is actually reduced?

THat's a good question. Are they imagining it? Is there another reason we haven't uncovered yet?

 

[HaphAsSard]

THat's a good question. Are they imagining it? Is there another reason we haven't uncovered yet?

In my post #4 above I suggested a possible explanation (differing post-attack pitch contours across different total string lengths, scale length and tuning pitch being equal), and one or two parameters (pitch excursion; time before steady-state pitch sets in) to look at.
(I concede it would take a robotic hand, or something functionally equivalent, to ensure a consistent attack; besides, there may be further complicating factors, such as a potentially different behaviour of overtones vs. the fundamental.)

 

[Zooberwerx]

Some time ago I did a study on string tension to try to prove or disprove the claims being made about various schemes to improve string tension on basses. Conventional wisdom says that any increase in tension on a given string will raise its frequency of vibration, raising its pitch. We know that since we increase tension on a string by turning the tuner so that it stretches the string more. And it is largely understood that increasing the mass of a string (heavier gauge) will require more tension to bring it to pitch than a similar string of lighter gauge. And we also know that if we increase the scale length of the string, we will need to increase the tension on it to bring it to the same pitch. The science of this is all well-known.

A number of years ago a "fix" to increase string tension surfaced, particularly for floppy B strings. It advocated placing a spacer at the end of the string, between the ball end and the anchor point on the string. Another scheme suggested that the B string tuner should be closer to the end of the headstock to improve its tension. These arguments suggested that since the overall length of the string was increased it would require more tension to bring the string to pitch. Unfortunately, these schemes were based on a faulty understanding of the physics involved. The vibrating length of the string remained the same and in order for it to vibrate at a given frequency (pitch) it had to have a specific tension regardless of what was happening beyond the vibrating length. But in spite of the fact that the tension could not be changed by such additional string length beyond the vibrating length, a number of players said they could feel a difference. To them, regardless of the actual tension, the perceived tension increased. Arguments ensued with skeptics suggesting that the perception of increased tension was a figment of the players' imaginations.

The phenomenon of increased tension was addressed by luthier Liutaio Mottola several years ago in an article titled "Lutherie Myth/Science: Human Perception of String Tension and Compliance in Stringed Musical Instruments". In it he made the distinction between string tension and stiffness. He named a number of factors that contributed to the stiffness of the string and called those collective factors "compliance". Compliance is the term he would then use to describe the "perceived tension" of a string, one having less perceived tension as having more compliance. He referenced some work in this area that had been done years before by Master archtop guitar maker Bob Benedetto. In the same article Mottola noted that there were no comprehensive studies that looked into the extent to which humans can distinguish differences in compliance.

To shed further light on the subject I decided to run a series of test to illustrate what happens when the overall string length is increased while leaving the vibrating length the same. I would extend the length of the string between the nut and the tuner, and between the saddle and the anchor point of the string. To test "compliance" I would measure how much force it took to deflect the string a measured amount while changing the "afterlengths". I define afterlength to mean that section of the string at either end beyond the vibrating part of the string. The test rig consisted of a hardwood board with a nut affixed to one end, a bridge affixed 34" away from the nut (scale length). At the nut end I affixed two tuning machines, one 1 inch away from the nut, another 6 inches further. At the bridge end I created two anchor points for the ball end of the string - one at 1 inch form the saddle, and the second 6 inches further from the saddle. At the centre point of the vibrating length of the string (the 17" mark), I mounted a dial gauge that would accurately measure the amount of deflection of the string.

Using this rig, compliance could be measured by suspending a weight from the centre point of the string and measure the deflection of the string on the dial gauge. The more deflection there was for a given suspended weight, the more compliant the string was. Or conversely the amount of force required to deflect the string a given amount could be determined.

Compliance in such a test would be defined in terms of two elements: the amount of deflection that occurs as the string is plucked (floppiness), and the amount of force it takes to press the string to the fret (stiffness). This would be the perceived tension of the string. The tests would illustrate what happens to compliance as the string afterlengths are changed.

I started by installing a string from the inner anchor points, the tuner closest to the nut and the ball end of the string at the closest point to the saddle. I tuned the string to pitch - I was using a D string, so I tuned to D. Later I would repeat the test with an A, E and B string but the outcomes were the same. With the string at pitch I suspended a 250 gram weight at the centre of the string and measured the amount of deflection. Then I restrung using the outermost tuner and ball end location, retuned to pitch and suspended the same weight mid-string. I measured the amount of deflection. It was different. So I then repeated the test with the string on the outer mounting points but changed the weight until I achieved the same amount of string deflection as in the first test. So I had data that reflected two ways of looking at string compliance - one that measured how much a string deflected for a given force, and how much force it took to deflect the string a given amount.

The Results:
1. The longer afterlength resulted in a further string deflection with the same force applied.
2. The longer afterlength required less force to be applied to deflect the string a given amount

Conclusion:
Added afterlength makes the string more compliant, which should result in less perceived tension.

It makes sense that the string would be more compliant with added afterlength. Part of the string's compliance has to do with its stretchiness. The more overall length there is to the string, the more string there is to stretch. If a 12" string will stretch 1" under a certain tension, it follows that at 24" length will stretch twice as much - there's twice as much string to stretch. Adding afterlength to a string adds stretchable length to the string, making it more compliant, or less tense.

Getting back to the question of whether a spacer behind the bridge would increase the string tension, it has proven to be false. And this test shows that that spacer would actually increase compliance, making the string more "floppy", not less. Any explanation for a difference in "perceived tension" is yet to be uncovered.

Okay, it's Saturday morning at the Zooberwerx household and there's absolutely no room for well-engineered inquiries or outcomes.

Given the observations, would it be safe to assume that we can decrease compliance simply by minimizing the number of string wraps? Conventional wisdom holds that a string is cut ~3.5" past the tuner post resulting in 3+ wraps. Let's reduce this by 2" resulting in 1-1.5 wraps (...or less if equipped w/ Sperzel lock-downs).

A more extreme example would be the typical Steinberger configuration: lock-down at the nut, maybe 1-1.5" between the bridge saddle and tuner "claw".

Riis

 

[JRA]

great stuff, turnaround!

so, as a user (non-expert), and on these boards: it's "compliance" not "tension" i'd be talking about if i stated that i like my strings to feel more like rubber bands than bridge cables/stays. (?)

 

[Turnaround]

Okay, it's Saturday morning at the Zooberwerx household and there's absolutely no room for well-engineered inquiries or outcomes.

Given the observations, would it be safe to assume that we can decrease compliance simply by minimizing the number of string wraps? Conventional wisdom holds that a string is cut ~3.5" past the tuner post resulting in 3+ wraps. Let's reduce this by 2" resulting in 1-1.5 wraps (...or less if equipped w/ Sperzel lock-downs).

A more extreme example would be the typical Steinberger configuration: lock-down at the nut, maybe 1-1.5" between the bridge saddle and tuner "claw".

Riis

Good observations Riis. The compliance is in part the stretchiness of the string - the longer the string, the more stretchy and complaint. So more wraps on the tuner would equal more string length and thus more stretchiness. But we would have to factor in the friction of the string on the tuner post. Where on the post does the real termination point occur? Somewhere on the post the slip of the string on the post stops, otherwise we would never be able to tune up. And if the slippage has stopped I think we could call that point the anchor point. So anything beyond that point would not contribute to compliance.

I should point out, if I haven't already, in my compliance tests I found that longer afterlengths made the string more compliant. But the degree of added compliance was very small, and that was with an added afterlength of about 9 inches. So I would think that extra wraps around the tuner post would have such a tiny effect, if any, to be meaningless to a player.

 

[David Jayne]

Some time ago I did a study on string tension to try to prove or disprove the claims being made about various schemes to improve string tension on basses. Conventional wisdom says that any increase in tension on a given string will raise its frequency of vibration, raising its pitch. We know that since we increase tension on a string by turning the tuner so that it stretches the string more. And it is largely understood that increasing the mass of a string (heavier gauge) will require more tension to bring it to pitch than a similar string of lighter gauge. And we also know that if we increase the scale length of the string, we will need to increase the tension on it to bring it to the same pitch. The science of this is all well-known.

A number of years ago a "fix" to increase string tension surfaced, particularly for floppy B strings. It advocated placing a spacer at the end of the string, between the ball end and the anchor point on the string. Another scheme suggested that the B string tuner should be closer to the end of the headstock to improve its tension. These arguments suggested that since the overall length of the string was increased it would require more tension to bring the string to pitch. Unfortunately, these schemes were based on a faulty understanding of the physics involved. The vibrating length of the string remained the same and in order for it to vibrate at a given frequency (pitch) it had to have a specific tension regardless of what was happening beyond the vibrating length. But in spite of the fact that the tension could not be changed by such additional string length beyond the vibrating length, a number of players said they could feel a difference. To them, regardless of the actual tension, the perceived tension increased. Arguments ensued with skeptics suggesting that the perception of increased tension was a figment of the players' imaginations.

The phenomenon of increased tension was addressed by luthier Liutaio Mottola several years ago in an article titled "Lutherie Myth/Science: Human Perception of String Tension and Compliance in Stringed Musical Instruments". In it he made the distinction between string tension and stiffness. He named a number of factors that contributed to the stiffness of the string and called those collective factors "compliance". Compliance is the term he would then use to describe the "perceived tension" of a string, one having less perceived tension as having more compliance. He referenced some work in this area that had been done years before by Master archtop guitar maker Bob Benedetto. In the same article Mottola noted that there were no comprehensive studies that looked into the extent to which humans can distinguish differences in compliance.

To shed further light on the subject I decided to run a series of test to illustrate what happens when the overall string length is increased while leaving the vibrating length the same. I would extend the length of the string between the nut and the tuner, and between the saddle and the anchor point of the string. To test "compliance" I would measure how much force it took to deflect the string a measured amount while changing the "afterlengths". I define afterlength to mean that section of the string at either end beyond the vibrating part of the string. The test rig consisted of a hardwood board with a nut affixed to one end, a bridge affixed 34" away from the nut (scale length). At the nut end I affixed two tuning machines, one 1 inch away from the nut, another 6 inches further. At the bridge end I created two anchor points for the ball end of the string - one at 1 inch form the saddle, and the second 6 inches further from the saddle. At the centre point of the vibrating length of the string (the 17" mark), I mounted a dial gauge that would accurately measure the amount of deflection of the string.

Using this rig, compliance could be measured by suspending a weight from the centre point of the string and measure the deflection of the string on the dial gauge. The more deflection there was for a given suspended weight, the more compliant the string was. Or conversely the amount of force required to deflect the string a given amount could be determined.

Compliance in such a test would be defined in terms of two elements: the amount of deflection that occurs as the string is plucked (floppiness), and the amount of force it takes to press the string to the fret (stiffness). This would be the perceived tension of the string. The tests would illustrate what happens to compliance as the string afterlengths are changed.

I started by installing a string from the inner anchor points, the tuner closest to the nut and the ball end of the string at the closest point to the saddle. I tuned the string to pitch - I was using a D string, so I tuned to D. Later I would repeat the test with an A, E and B string but the outcomes were the same. With the string at pitch I suspended a 250 gram weight at the centre of the string and measured the amount of deflection. Then I restrung using the outermost tuner and ball end location, retuned to pitch and suspended the same weight mid-string. I measured the amount of deflection. It was different. So I then repeated the test with the string on the outer mounting points but changed the weight until I achieved the same amount of string deflection as in the first test. So I had data that reflected two ways of looking at string compliance - one that measured how much a string deflected for a given force, and how much force it took to deflect the string a given amount.

The Results:
1. The longer afterlength resulted in a further string deflection with the same force applied.
2. The longer afterlength required less force to be applied to deflect the string a given amount

Conclusion:
Added afterlength makes the string more compliant, which should result in less perceived tension.

It makes sense that the string would be more compliant with added afterlength. Part of the string's compliance has to do with its stretchiness. The more overall length there is to the string, the more string there is to stretch. If a 12" string will stretch 1" under a certain tension, it follows that at 24" length will stretch twice as much - there's twice as much string to stretch. Adding afterlength to a string adds stretchable length to the string, making it more compliant, or less tense.

Getting back to the question of whether a spacer behind the bridge would increase the string tension, it has proven to be false. And this test shows that that spacer would actually increase compliance, making the string more "floppy", not less. Any explanation for a difference in "perceived tension" is yet to be uncovered.

Nicely done! I'd thought to do more or less the same thing but the other way around. I wanted to make the deflected distance a constant and hold the string with a hook connected to a load cell to measure force. But now I don't have to, thanks!!! : D

 

[Turnaround]

Nicely done! I'd thought to do more or less the same thing but the other way around. I wanted to make the deflected distance a constant and hold the string with a hook connected to a load cell to measure force. But now I don't have to, thanks!!! : D

Two ways to arrive at the same outcome. What a team!

 

[Bruce Johnson]

Here's a copy of a post that I wrote several years ago. It's really about the same topic. The question was about whether adding extra string length between the bridge saddles and the tailpiece on a short scale bass will increase the "tension" on the strings. The same question often comes up about adding string length at the headstock; reverse headstocks. But the better question is whether the extra length changes sound and feel of the string. And players usually describe that feel as Tension.

Does adding extra string length at the headstock increase the tension on the string?

Well, no, but yes. The actual tension in the string is the same. The tension is determined by the scale length (the distance between the bridge saddle and the nut), the gauge/construction of the string, and the note that it is tuned to. Adding extra length at either end, between the saddle and the anchor point/tailpiece, or between the nut and the tuner, does not change the tension of the string.

However, adding that extra length at either end does change the sound and feel of the string. It's a factor I call the "snap" of the string, which is often confused with the tension. It works like this: When you pull sideways on the string, as you are plucking it, the string is stretching like a long spring. Then you release it, and it snaps back to straight, overshoots it, and goes into the back and forth oscillation.

When you add extra length to the string at either end, you are making that spring longer. So, you have to pull it farther sideways to get the same feel on your fingertip, because the string stretches easier.

For example, suppose you have two basses, same scale length, same string, tuned to the same note. One has the standard short distance between the bridge saddle and the anchor point. The other has an extra 3" of length back to the anchor point. Again, the actual tension in both strings will be the same.

But, if you pull the string sideways with a force of, say, 1 pound on your fingertip, there will be a difference. With the extended string, you have to pull the string a longer distance to the side to reach that 1 pound load. It's because there's more length of string to stretch.

Now, when you release the strings of these two basses, the extended string has a longer distance to travel to get back to center. The physics of it is that they will both accelerate at the same rate, because the tension is the same. The extended string will take longer to reach center, but it crosses over center at higher velocity and goes farther to the other side before rebounding. This is the effect that I call "snap". Increasing the overall length of the string increases the snap, regardless of the scale length.

How does this affect the sound? Increasing the snap mainly changes the attack curve of the note. It increases the pulse at the beginning of the note, which is why I call it snap. Think of the percussive sound of upright basses. They have a huge amount of snap because of the very long overall string length. The increased pulse can be heard through the amp, and also unplugged.

The funny thing about increasing the snap is that players will describe it in opposite ways. Some will say that the tension is higher, because they hear that extra pop on the note. Others will say that the tension is lower, because the string feels softer to their fingertip. But actually, the tension is exactly the same.

It's the same factor in all those long arguments about reverse headstocks, and how increasing the length between the nut and the tuner of the B string will increase the "tension" of the string to improve the sound, etc. It doesn't actually increase the tension, but it increases the snap. Which may make the B string sound more like the other strings.

So, a reverse headstock increases the "snap" on the lower strings, the most on the B, while reducing the snap on the upper strings. That may add more balance to the feel and sound across the strings. But, it's not actually increasing the tension.
​

Note: What I'm calling Snap isn't quite the same thing as what Richard is calling Compliance. Compliance is how stiff or soft it feels as you pull on the string. Snap is the effect when you pull the string sideways, then let go.

 

[walterw]

great stuff!

it comports with other tests i've seen on guitars, increased outside length leads to having to push a bend farther to get to the same pitch and requiring more force once you get there

hadn't really thought about the effects on the plucking, @Bruce Johnson's idea of "snap" makes a lot of sense.

this all implies to me that if you want your bass to be easier to play and sound more in tune and you don't do any bending then you want lots of excess string length! that'll reduce it's accidentally getting pushed out of tune with aggressive fretting, while less force on the plucking hand will move the string the same amount.

conversely if you want to do a bunch of soloing with bending and vibrato then you want as little outside string length as possible. i suppose you also get a faster plucking hand, a given amount of plucking force moves the string a shorter distance making super-fast plucking easier

this comports with guitar tendencies, where more rhythm-oriented players gravitate to guitars like gretsches, ricks, jazzmasters and gibson semi-hollows with trapeze tailpieces and their extra string length. more lead-oriented guitar players like stuff with short outside length, strats, teles, stop-bar gibsons.

 

[walterw]

has anyone here messed with evertune guitar bridges?

they use big springs balanced against the individual strings to essentially create near-infinite excess length, to where you can push the string as far across the board as you want and even literally reach up and twist the tuning key up and down and the pitch does not change

you'll see a little bridge lever piece moving back and forth while you bend the string, showing you that a spring on the other side is stretching in and out and taking all the tension change so none of it affects the string itself.

 

[David Jayne]

has anyone here messed with evertune guitar bridges?

they use big springs balanced against the individual strings to essentially create near-infinite excess length, to where you can push the string as far across the board as you want and even literally reach up and twist the tuning key up and down and the pitch does not change

you'll see a little bridge lever piece moving back and forth while you bend the string, showing you that a spring on the other side is stretching in and out and taking all the tension change so none of it affects the string itself.

Seems that would prevent bending or even vibrato.

 

[Bruce Johnson]

From my design viewpoint, I deliberately add extra string length on my basses to make the feel and sound more percussive; a bigger pop on the attack curve. More like a bigger upright bass. That's why I refer to the Snap. It's a combination of sound and feel.

If you look close at my Scroll Basses, I mount the bridge up on two long jacking screws that rest in rounded sockets down deep in the body. The whole bridge is able to pivot forward and backward a small amount. Then I put the tailpiece way back, separate from the bridge. This all helps to add more Snap to the note, plus some Warble and Bloom. These are the mechanical features that I put in to shape the attack curve of notes on my basses.

The effects on bending are another thing, which I'm not really concerned about. My players don't tend to be benders. They are mostly fretless players.

 

[walterw]

Seems that would prevent bending or even vibrato.

it does, entirely!

they actually have a setting for that, where you basically keep winding up the string until that "excess length" spring runs out of travel, at which point the string will respond to bending and vibrato again. the idea there is to adjust until it just hits that stop, at which point you can bend the string up but it will not go flat.

players do things like adjusting their three plain strings to this threshold so they can bend them, while leaving the three wound strings in the middle of the "no pitch change" range, so they can do solo bending of high notes but the strings otherwise will not change pitch no matter what.

 

[Ralf1e]

Now we have an answer, grounded in hard evidence, regarding actual tension and compliance with different afterlengths, I still find the question of the reasons for the sometimes reported, perceived increase in tension with a longer afterlength intriguing. Why is it so? Why do players occasionally report impressions that run not just...sideways to, but contrary to the aforementioned evidence? And why did (/does?) Fodera place their B-string tuner beyond the other two in the upper row in some models (/specimens)?

As was mentioned in the original thread, @Bruce Johnson has a theory on what longer afterlengths bring to the table, namely a slight difference in the tone of the attack (what he calls a stronger "snap"), as expounded in these posts:
love of Ampeg and other Scroll Basses, Part 2
Did They Ever Make A Shortscale That...
(the latter reproduced here
Does a reverse headstock add tension? )

I ain't no physicist nor a luthier (nor that good or experienced a player, for that matter); however, I was wondering about whether there be any difference as to the pitch envelope of a note upon the attack, scale being equal, with different amounts of afterlength.
Is it possible that a string with a shorter than standard scale, but still quite long total stretched length (and a healthy amount of travel upon nut and bridge) has a more stable oscillation between sharp, flat and Goldilocks pitch at the start of a note, with a less evident (=either reduced in Hertz, and/or shorter in duration) "sproing", so to speak, reminiscent of what happens on a longer scale? Could this possibly be the specific correlate of high-tension feel that long-scale players re-encounter on a shortie-plus, and not on a shortie without significant extras?

With the appropriate recording hardware and software (which I don't have), the pertinent quantities could be measured. Just thinking e-loud.

What you are talking about is Adsr. Attack decay sustain release. Synths specialize in being able to alter all of those parameters at the turn of a dial, tap of a button or pad and I dare say there will be someone out there that has the electronic equipment to measure them. I would suggest the shorter scale has faster attack, faster decay, less sustain and quicker release than a long scale which is why our long scales are perceived by our ears as having more depth of tone. Apologies in advance to all those that may be upset by my observations but tone is the key thing we all seek for is it not