Below are two ASCII drawings of two systems of equal scale length. The string hangs over a roller o. The x anchors it. The weight provides the tension. The first system has more overhang than the second. Neglecting friction it is axiomatic that the tension in the string is the same in both cases since the weight is the same.

 o----------x
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/ \
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 o----------x
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/ \
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Joe

The horizontal lines are the scales in the two figures. The o is a pulley which acts as the nut. The vertical lines are the overhangs of different lengths. The trapezoid at the end of the overhang is a weight that is the force or tension, which is always measured at the string end. Let's say the two weights are both 30 lb. This is the tension everwhere in the strings. Since the strings have the same tensions and same scale length, they will play the same pitch. If you add more length to the overhang, but use the same weight or tension, the note played by the scale will not change. You will not need to add more weight or tension to get the same note, no matter how long or short you make the overang. The same note will always require the same tension. Only if you change the scale length will you need to adjust the tension to get the same note. I don't see how this could be any clearer.

(For longer discussion of the myth that longer string length means more tension, read the next post.)

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Student of the Steel: Zum uni, Fender tube amps, squareneck and roundneck resos, tenor sax, keyboards

[This message was edited by David Doggett on 08 July 2006 at 11:49 AM.]

The relevant equation from physics is:

Hz =1/(2L)*(SQRT(F/m))
Where:
Hz = frequency in vibrations per second.
L = the nut to bridge distance = scale length (not string length).
SQRT = square root
F = force applied in the direction of string length = tension.
m = mass, which is proportional to string gauge.

Solving for tension, F:
F = m (2 L Hz)^2

Notice that the tension (labeled F here) refers to the force on the string end pulling the string taught. The feel of the string as one presses on it, or attempts to deflect it sideways, is related to the string end tension, but also to the amount of stretch in the string, caused by its innate elasticity and the amount of string beyond the scale, if the nut and/or bridge are not locked. We will call this force deflectivity, to keep it separate from the string end force or tension.

Because the string has elasticity, it will stretch as force is applied to the end. There is a certain amount of elasticity or stretch per unit length of the string. Therefore, a longer string will require more longitudinal stretch to achieve a given tension or pitch, as well as more lateral stretch to deflect the string enough to reach a given pitch. We will call these factors longitudinal stretch and lateral stretch.

Also notice that the total string length is not a component of the tension equation. That is because it has no effect on the tension over the scale, and it is only the tension over the scale that determines pitch. If you accept this, you are done here, and can save yourself a lot of time by moving on to some more useful pursuit. If you cannot see this, then read on for some thought experiments that will save you from having to rig up a force meter and pulleys to prove the obvious.

If the nut is not locked, but is essentially friction free (for example a roller nut, or very slick bar nut), then the tension over the scale is the same as the tension beyond the nut and the tension over the whole string. If increasing the distance from nut to tuner post increased the total string tension, then the tension over the scale length would also increase, and the pitch would change. That is in fact how one tunes the instrument. You turn the tuner to increase the tension, both behind the nut, as well as in front of it over the scale, and that raises the pitch. You cannot increase the tension at the tuner post without raising the pitch over the scale. Conversely, if you tune to the same note on the scale side of the nut, and the pitch is not changed, but the string is merely attached to a more distant turner post, then the tension cannot have changed, over the scale or over the whole string. That should convince most people that it is a myth that longer string length, and greater distance between nut and tuner increases tension. But if you are a diehard believer in the TSL myth, read on.

There are many quotes that are alleged to support the TSL myth. On another thread Curt Langston, a firm believer in the myth, did us the favor of collecting several such quotes, some from very prominent steelers or builders.

quote:

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Buddy Emmons
Member
From: Hermitage, TN USA
posted 08 January 2005 09:54 AM profile edit
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Carl,
In reference to your earlier post, my only experience with the 25” scale other than the Sierra was when Shot Jackson and I were building Sho~Buds. It was during the time the high G# was added to the tuning that we encountered the string breakage problem and had to reduce the scale 24 ½ inches.
To be different than Sho~Bud and possibly reduce string breakage even more, I had fifty 24 ¼” Emmons atom fret boards made in Nashville and gave them to Ron to use on the first guitars. By that time, the Sho~Bud fret board had proven that the longer scale didn’t work so there was no need to experiment with the Emmons guitar. Ron had built a Sho~Bud clone prior to my meeting him and may have been referring to that guitar, but the Emmons guitar started at 24 ¼” and stayed there.

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quote:

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from Carl Dixon:
quote:

2. Because of a longer string string length(bridge to key peg), string breakage tends to be more frequent. Too much tension.

And this, from the same thread:
quote:

I can, and have proven it beyond ANY shadow of a doubt. The tension on strings 3 thru 7 is MUCH less on a keyless guitar. And tension IS what breaks strings. True, they happen to break at the top of the changer in most cases. But the root cause is the tension, in this analogy.

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Without an actual measurement of tension, this is flawed reasoning: strings break more with longer TSL, and strings break more if there is more tension; therefore, if strings break more, there must be more tension with the longer TSL. But there are other, more plausible explanations of why there might be more string breakage with longer TSL. If the scale length, gauge and pitch are held constant, increased TSL due to more nut-to-tuner length also causes an increase in the longitudinal stretch required to raise the string the half step from G# to A every time the raise pedal is activated. That means more changer wrap-around and more bending at the changer end. That leads to more heat and stress, which are very plausible reasons for more string breakage with the longer pull. There may be other plausible mechanical reasons. That the longer TSL means more tension is not plausible, according to the physics described above.

From Michael Johnstone:

quote:

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Michael Johnstone
Member
From: Sylmar,Ca. USA
posted 02 May 2002 09:08 AM profile send email edit
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What I meant is that a 24" scale keyed guitar is really a 27" guitar(changer-to-tuner)and a 25" scale keyless guitar is really a 25&3/4" guitar(changer-to-tuner).So there is less tension on a 25&3/4" string tuned to G# than a 27+" string of the same guage tuned to G#.

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Another Johnstone quote:

quote:

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As far as scales lengths go,most keyed guitars max out at 24.5" before you run into excessive string breakage because the section of string under tension(changer to tuning post)is as much as 27" on the middle strings of a keyed guitar.Conversely on a keyless design,say on a 25" scale,the section of string under tension is only 25" in total. So there is actually more tension on most of the strings on a keyed 24.5" guitar than all the strings of a keyless 25" guitar.

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This writer is confusing scale length and TSL. If there were no nut, then the 25 ¾” string tuned to G# would have less tension than the 27” string tuned to the same pitch. With no nut, the scale lengths and TSL would be the same within each guitar. The string with the longer scale/TSL would have the higher tension. But if nuts are used to make the scale length 24” with the 27” TSL, and 25” with the 25 ¾” TSL, then the guitar with the shorter scale and longer TSL would have the least tension. The scale length determines the tension over the scale for a given gauge and pitch, and if the tension over the scale is less, then with a frictionless nut the tension over the whole string must be less, regardless of its longer TSL.

And here is the famous Sierra ad copy quote:

quote:

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New technology fulfills the 30 year dream of tone plus sustain. Remember the old beautiful rich tone and everlasting sustain of the long-scale steel guitars? Due to excessive string breakage, scale lengths had to be shortened when pedals were added to steel guitars. Even though this also reduced sustain and tone quality, it was necessary to keep the strings on the guitar. Sierra's advanced engineering and manufacturing quality of the 'Gearless Tuner' allows a 25-inch scale with shorter string length than a keyed or geared guitar with a 24 inch scale

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This clearly implies that a longer scale length could be used without increasing string breakage because the gearless tuner allows a shorter TSL. But notice that it does not say the shorter TSL reduced tension, or that reduced tension was the cause of the ability to use a longer scale without unnaccetable breakage. As above, there are plausible explanations other than tension. It may well be that the ad writer believed the TSL myth, we don’t know from this quote. But without actual tension measurements, that writer’s opinion would not prove the TSL myth or disprove the laws of physics described above.

Here’s a Bill Stafford quote that has been cited to support the TSL myth:

quote:

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And "tighter means brighter". The overall string length is shorter with the keyless configuration. This is one of the reasons there is less string breakage and allows for a longer scale. I bet a lot of us can remember how great those 26" scale Fender Stringmasters sounded??? (We are working our way up to that, hopefully).
Bill Stafford

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But Bill doesn’t mention tension as the reason for less string breakage with the keyless with shorter TSL. In fact, his "tighter is brighter" statement indicates he realizes the longer scale (and shorter TSL) keyless has more tension. Bill is a pretty smart guy. I’ll bet he would agree that less string bending at the changer because of the less stretch with the keyless is a more plausible explanation than rewriting the laws of physics regarding tension being dependent on scale length rather than TSL. Here is Ed Packer’s explanation of this situation:

quote:

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So, G# TSL Show Bud = 28.5”,Scale length = 24.0”
..G# TSL Bill’s Sierra = 27.0”, Scale length = 25.5”
Result = longer TSL Sho Bud with the shorter scale length has the lower tensioned G#.
The Shorter TSL Sierra with the longer scale length has the higher tensioned G#.
Why does the shorter TSL have the higher tension? (Both by calc, and by measurement here and now…yes I have one of Bill’s Sierra units).
How can one say that the higher tension might have less string breakage?
Could one of the “other” reasons be that there is less stretch for a halftone change on Bill’s Sierra (or for that matter on his EXCEL that came along later?

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A quote from Curt Langston:

quote:

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Remember the longer the TSL, the greater the tension required to bring the guitar up to pitch.

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quote:

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A keyed 24 1/4 inch scale guitar is under more TOTAL tension, from TUNER to CHANGER than a keyless 25 inch scale. And TENSION is what breaks strings.

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quote:

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quote:

"Total String Length" matters when tension is changed in order to change the strings pitch. At that point, a longer "Total String Length" (assuming that TSL means from clamp to clamp) enters the picture to provide increased finger rotation requirements, and related problems.
___________________________________________
Exactly.
As observed when raising the G# to A.
Longer TSL=increased tension
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quote:

My conclusion is, that until stretching is introduced, string length beyond the scale length is of no import re fundamental pitch.
_________________________________________

Of course not. That is why the old non pedal Stringmasters could have those long scales.(you could even have a G# in your Beast, providing you did require raising it up to an A)

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Here is a typical quote from Chris Lang on his agreement with Curt Langston:

quote:

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i think that long string overhang makes the total string length quite a bit more tension. I don't think it gives advantage at all. Fact is:I think it hurts more than it helps. When you got all that hangover string to mess with, it makes the G# string have too much tension, and breaks.
…My take on this string length thing is if you have more than about 2 inchs of overhang, you will break the 3rd string more than if you have a really short space, like a keyless. Because the longer the whole string is the more tension it takes(pounds)

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Ed Packer has actually measured string tension on guitars with various lengths of scale, nut-to-tuner distance, and TSL. He confirmed that scale length determines tension, not nut-to-tuner distance or TSL.

quote:

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…I measured the Tension and it was greater on The Long Scale, short TSL Sierra…

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Now here is some evidence that Jim Sliff brought to bear from outside the Steel Guitar Forum:

quote:

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This subject has been discussed at length on just about every 6-string board I've been on. It's been demonstrated over and over by engineers and guitar manufacturers...and string makers...that total string length is completely irrelevant.
"Regular" guitarists just consider this an engineering fact. It's also an easy thing to "feel" when you bend strings (and fret them) *by hand*, not with pedals, bars and levers.
Curt, call Fender Gibson, PRS, Martin, Santa Cruz, D'Addario, GHS, Ernie Ball - you'll get the same answer from every darned one, and most of them will likely have the data on hand that they could email or fax to you. I remember when someone brought up the idea that Steinberger headless guitars would have lower string tension than "regular" guitars - that argument lasted mere minutes. Even Ned Steinberger agrees, and he's the engineer who designed and patented the headless 6-string.

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Like in the "Tuning Wars", I must remind you of one thing:

If there is a mindset that cannot comprehend something that is appearant to you, long posts are self-defeating in getting through to them.

Quotes and bullet points are especially futile.

Off to the gigs today and tonite.

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Got Twang ?

Mark

[This message was edited by Mark Fasbender on 08 July 2006 at 03:31 PM.]

Ironically it was on a sonometer in the Physics Laboratory that I used to play the hits of the time (50s) using a glass test tube as a slide. Someone recommended I put a pick up on the thing ! I guess a steel guitar is just an electric sonometer with multiple strings.

[This message was edited by Alan F. Brookes on 08 July 2006 at 07:17 PM.]

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Got Twang ?

Mark

David, see b0b's post on Curt's Experiment.

quote:

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Actually, I think I see your point. I believe that I have been wrong all this time.

...So, basically, the scale length on a guitar has to be under 25 inches, because if it is much longer, then you have too much tension and the G# won't hold up.

Maybe, the 24 1/4 inch scaled guitars that broke the G#, were doing so because of some sort of resistance created by the roller nut. Or, perhaps too sharp a bend at the nut. (seems like I heard that somewhere)

And come to think of it, 25 inch scale keyless guitars seem to be a little tighter.

Eureka!

It all seems so logical now.

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I just read your posts, and a few others a few more times, and BAM! a light went off.

I feel really stupid now that it has finally sunken in. But, like I said in my last post over in b0b's thread,
you gotta be able to laugh at yourself once in a while!

quote:

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Never underestimate the ability of a hidden semantic dissagreement to create an argument among people who otherwise agree on the facts.

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Thanks for all the patience. No telling how long I would have went had you gave up on me!

Live and learn I guess.
Oh well, I can only laugh about it now!

[This message was edited by Curt Langston on 09 July 2006 at 08:49 PM.]

Well, you know.

Now If only I could have one...

Now if Mr. Doggett and a couple of his less good humored friends would only see the light on tuni...

Never mind..

I am also curious about how the shallower angle of the string over the changer affects tone. I once heard a builder say that a smaller radius changer has better tone, but more string breakage. So the typical changer radius is a compromise between tone and string breakage. It would seem that a shallower bend at the changer, with a string that does not roll with the changer might allow a smaller radius changer/bridge. This might be the best of both worlds in terms of tone and string breakage. I would be interested in your impressions. And perhaps at some point Ed's measurements can shed some objective light on this question.