Scale Length vs String Tension

[swarfrat]

So I've been planning all along on a 24 3/4" scale neck for my guitar,  all the while wanting a baritone strung normally and tuned down a whole step for my after next guitar. So  I have to ask... How much of the shorter scale tone is nothing more than string tension?

For instance consider the following:
25.5"      XL140 (light top / heavy bottom) @ concert pitch = reference tension
24.75"    XL140 @ concert pitch  = -6%
25.5"      XL140 @ 1/2 step down (Eb)  = -11%
28.625"  XL140  @ 3/2 step down (C#)  = -11%
25.5"      XL125 (super light top/heavy bottom) @ concert pitch = -19%
28.625"  XL125 @ 1/2 step down (Eb) = -9%

The other factors which are harder to monkey with are:
* pickup location wrt scale length - but this changes depending on string length
* pickup aperture wrt scale length - also changes depending on string length
* string length to diameter ratio - again - has an impact (try playing your wound strings at the 21st fret sometime) - but changes with position
* voodoo

 

[JaySwear]

Hm. Very interesting numbers. Kind of surprised by the difference in tension in some of them (a whole 19%?!) but this is really cool.

 

[swarfrat]

Yeah -that's only 10's, 9's and 11's.  8's or 12's can be pretty dramatic. I took the D'Addario chart and finally stuck them in a spreadsheet, w/ lookups for the string numbers. Messed with it enough times already now that I should've done it a long time ago.  What's interesting, is while the actual tension goes by square, the relative change between any two pitches of the same interval is the same, and changes at the same length as scale length, and going up or down a string guage is similar.

The 28.625" necks are good example I've mentioned a few times. 25.5 * 2^(2/12) happens to be 28 5/8", or two frets longer, with the same spacing on the rest of the neck.
If you string it the same gauge as your 25.5" neck, and tune down a whole step the string tension will be the same as a concert pitch 25.5"
A 28.625" neck w/ 9's tune to concert pitch has almost the same string tension (+2%) as a 25.5" scale neck w/ 10's @ concert pitch. (And that would be a good counterpoint to this discussion - would it be more open/articulate, or sound the same?

Of all the cases I ran, the closest I came to 24.75" scale tension was to go up to 11's and tune down a whole step. (-4%)

 

[Ace Flibble]

While those numbers are interesting, I think ultimately you've just got to try stuff out, see what feels right to you. I can't play on a 25.5" scale guitar, then a 24.75" scale guitar, and tell "oh yes, these strings are 6% looser!".

 

[AutoBat]

That's good mathwork Swarfrat.

I like my 25.5" scale strung with 9-42's and tuned to Eb.  I'm guessing that's less tension than most players.
If I have the need to play something in tuned to E I throw a capo on there, or I just deal with it.

 

[drewfx]

From:
http://en.wikipedia.org/wiki/Vibrating_string

where T is the tension, μ is the linear density, and L is the length of the vibrating part of the string. Therefore:
the shorter the string, the higher the frequency of the fundamental
the higher the tension, the higher the frequency of the fundamental
the lighter the string, the higher the frequency of the fundamental


The linear density is effectively determined by the string gauge.

EDIT: And since you know the scale length, fundamental frequency and tensions from D'Adderio, you can calculate the linear densities for each string gauge from that, and then play around with the numbers in Excel...

 

[swarfrat]

arty07'Addario gives the equations in form for tension and for density, and yes I already have it in a spreadsheet. I'm not that masochistic. And yes, I realize you have to try it out. But if you don't do your planning first, you can burn through a bundle trying out stuff with little result.

 

[Superlizard]

Don't forget tension-wise:

- string construction for wrapped strings.  Some strings are "slinky" with a smaller core; others have a bigger core
and therefore produce more tension even at the same gauge as the "slinky" ones.

 

[swarfrat]

The mass per unit length is given directly in the D'Addario tables. No need to calculate it. So it works for nylon vs nickle roundwound vs stainless flatwound, depleted uranium hexagonal core, etc...


Ultimately this is about whether I need a 24.75 scale neck to get the sound I want, or can I go with the right string gauge (well strung?) and tuning on 25.5 or even a baritone and still get that.

 

[Superlizard]

Ultimately this is about whether I need a 24.75 scale neck to get the sound I want, or can I go with the right string gauge (well strung?) and tuning on 25.5 or even a baritone and still get that.

I don't have any scientific tables to prove so, but I'd say that you cannot copy 24 3/4" scale using 25 1/2" scale with different types of strings/string tension/tuning.

Even a 25 1/2" tuned down a 1/2 step; while "slinkier" than concert pitch tuning and somewhat fatter tone as well, still doesn't quite do the 24 3/4" thang.

I don't know what exact sound you want, but I say if you want 24 3/4" scale tone, go 24 3/4".

 

[jackthehack]

Using the same set/brand of .009 standard set strings I've been playing for 40 years, I can't tell the difference between a 24.75 and 25.5" scale length; maybe my fingers are too strong?

 

[Strat Avenger]

Using the same set/brand of .009 standard set strings I've been playing for 40 years, I can't tell the difference between a 24.75 and 25.5" scale length; maybe my fingers are too strong?

I don't feel much difference in string tension either, but I do feel the fact that the frets are further apart on the 25-1/2" scale.