Scale length Effect

[RocketMan]

What effect does the instrument's scale lentgh and resultant string tension variation have on its tone? Ie; 25 1/2" - higher tension vs. 24 3/4" - lower tension.

[Tele-Bob]

Here is a mystery for sure. It seems that P90 equipped guitars sound better with a 24 3/4" scale as opposed to a 25 1/2" scale. However, I have several guitars of varying scale lengths and they seem to defy physics. Some longer scales with .010s play more slinky than my shorter scale guitars. It's a mystery.

[fezz parka]

The shorter scale (24.75) actually has more tension than the longer (25.5) scale, it's just easier to bend the string to the required pitch due to the shorter scale length. 25.5 twangs more, and seems more difficult to play since you have to deflect (bend) the string farther to achieve the required pitch, due to the longer scale length. It's just a matter of physics.

Here's another thread on the subject: Scale Length

[Offshore Angler]

Fezz, not sure I agree. A shorter scale would need less tension.

Without going into the wave equation - look at it this way:

We know for a given tension the shorter the string the higher the frequency. Don't beleive it? How do the frets on a guitar work? Take a string and shorten it by fretting and it goes up in pitch.


Fret your G string at the first fret. Now holding the string fretted , to get back to the G you reduce the tension on the string.

The difference comes from the harmonic modes. The longer Fender scale favors more harmonics with it's longer length and higher tension. So more sparkel and twang from a Fender. It really is physics in action.

If you love differential equations you can play with it.

[fezz parka]

I stand by my analysis, but you're the rocket scientist (I'm not being snotty, you're a smart guy!). I'm just a dumbass guitarist.

Think about the strings on a piano or harp and get back to me...;)

[RocketMan]

Yes OSA, I've read and understood that the longer scale results in higher tension and I've experienced that too. As a test I've gone directly from my Tele with .010's to an LP with same gauge and it did feel "slinkier" both under my pick and my fretting hand.

Reason for the question is a axe build project I'm putting together on paper at this point and scale length is one variable that I've got to nail down. This Maple capped, Mahogany bodied unit will be double humbucker which means that humbucker sized P-90 's will also find their way in there at some point in time too.

What scale length would suit this combo best?
I do like the notion of added harmonic detail of the longer scale.

[Don]

I think fret size, neck relief, fretboard material and finish, bridge style and the length of string beyond the bridge and nut have more to do with how stiff the action feels on a given guitar than scale length.

A Les Paul with a wrap around and all else being equal will be easier to bend on than a Les Paul with a separate bridge and tailpiece. The same guitar with a trapeze tailpiece will be even tougher to bend on. This is because the WHOLE string, even the string past the nut and bridge (except on guitars with double string locks), needs to be stretched in order to bring it up to pitch. A floating tremolo will also make bending more difficult as the string needs to be bent farther to bring it up to pitch to compensate for bridge movement.

Low frets and less relief also typically equal tougher bending on a guitar.

A longer string (larger mass) needs to be tighter to reach as high a frequency as a shorter (lower mass) string of the same diameter and material. It also needs to be moved farther while bending the reach the desired pitch. This can make a Stratocaster harder to bend on than a Les Paul.

String diameter has as much to do with string tension as scale length does.

A larger diameter string (larger mass) needs to be tighter to reach as high a frequency as a thinner (less mass) string.

My easiest guitar to bend on is my USACG T-Style with brand new 6105 frets followed by my Les Paul Jr. with a wrap around bridge/tailpiece.

My most difficult electric to bend on is my ES-135 with rather small frets and a trapeze tailpiece that is very far behind the bridge.

[RocketMan]

Some good info comming in here thanks, but I am primarily interested in the scale length's effect on the instrument's tone. I've been playing a Tele for years (for quite some time with .012's) so bending effort (and I strangle the crap outta mine) is not an issue. Sounds like the longer scale yeilds more twang? Is this agreed on? Other nuances to be aware of here?

[fezz parka]

Longer scale = more twang!

[stratdude69]

I finished a 24 3/4 scale strat some months ago (warmoth conversion scale neck.)

String tension is reduced, much easier bending.....

Let`s say, a 24 3/4 with 0.10 = 25 1/2 with 0.09.......

The sound doesn`t change dramatically, it`s still pure fender even with a gibson scale size neck.........

I compared the short scale strat with my old 70 strat: if you tune down 1/2 step and use a capo at 1 fret, the 25 1/2 strat comes very close to the short scale in terms of sound and playability.

you can try this kind of short scale "simulation" first........

by the way... the short scale parts-o-caster has become #1,

[Don]

Longer scale length generally means more twang and better note separation like a group of singers, each having their own microphone.
I seem to be able to hear each individual note better.

On the other hand, shorter scale length can cause a smoother tone more like a group of singers around 1 mic.

I love them both.

[Tele-Bob]

A longer string requires more tension to get up to pitch than a shorter string.

That's why most people who play .010s on the Gibsons almost always play .009s on their Fenders. The tension feels almost equal. That said, the 25 3/4" scale neck I made plays slinkier than any of my other guitars. Physics says it should feel tighter, and on the old Tele body it did, but on the new hardtail Strat body it's very slinky. I hade to put .010's on it! Oh, and the 25 3/4" scale gives me no harmonic on the 4th or 5th fret.

[Offshore Angler]

My geekiness made me do some caculations. The wave in the string exists because it has inerta and elasticity.

So for a wave on stretched string, with some math gyrations and dimensional analysis we can determine the speed of the wave can be shown to be

Wave Speed = v =SQRT(t/u)

where t is the tension (lbs, Newtons, etc.)
and u is the linear density of the string (mass/lenght appropriate units)

So lets look at a guitar string. It is fixed at both ends, so the only standing waves if you think about it, must be integer multiples of 1/2 the wavelength - since the motion of the string at its first resonant frequency would be exactly one half of the wavelength of a standing wave.

So we can write

Rf = 2l/n where n=1,2,3,...
and Rf is the resonant frequency and l is the string length.

In the study of waves it can be shown that the wave speed can be computed as the frequency times the wavelength, so we can say that the allowable frequencies would be

f=nv/2l where n = 1,2,3,...

but since we want the first harmonic we can replace n with 1 so

f=v/2l

Since v can be written as a function of t, we can substitute the equations and derive that

t=(4*l^2*f^2*u)/(n^2) where n = 1,2,3,... but again we can set n to one and simply write

t=4*l^2*f^2*u

and examing the above equation shows us our answer.

Since 4 is a constant and u is a constant set by the choice of string, we can simplify the equation to

t= C *l^2*f^2 or rearanging

t/l^2 = C*f^2
where C is some constant of porportionality we don't really care about for this question.

But look what we can see. For a given tension, as the length goes up the frequency drops. Or we can raise the freqency by increasing the tension.

So take two guitars. One has scale length l1 and the other is longer l2. If we want the same frequency

t1/l1^2 = t2/l2^2

and there is the answer to the question at hand. If l2>l1, than t2 must be greater than t1.

So the longer scale has higher tension.

OSA - Official geek of TFF

[Don]

My geekiness made me do some caculations. The wave in the string exists because it has inerta and elasticity.

So for a wave on stretched string, with some math gyrations and dimensional analysis we can determine the speed of the wave can be shown to be

Wave Speed = v =SQRT(t/u)

where t is the tension (lbs, Newtons, etc.)
and u is the linear density of the string (mass/lenght appropriate units)

So lets look at a guitar string. It is fixed at both ends, so the only standing waves if you think about it, must be integer multiples of 1/2 the wavelength - since the motion of the string at its first resonant frequency would be exactly one half of the wavelength of a standing wave.

So we can write

Rf = 2l/n where n=1,2,3,...
and Rf is the resonant frequency and l is the string length.

In the study of waves it can be shown that the wave speed can be computed as the frequency times the wavelength, so we can say that the allowable frequencies would be

f=nv/2l where n = 1,2,3,...

but since we want the first harmonic we can replace n with 1 so

f=v/2l

Since v can be written as a function of t, we can substitute the equations and derive that

t=(4*l^2*f^2*u)/(n^2) where n = 1,2,3,... but again we can set n to one and simply write

t=4*l^2*f^2*u

and examing the above equation shows us our answer.

Since 4 is a constant and u is a constant set by the choice of string, we can simplify the equation to

t= C *l^2*f^2 or rearanging

t/l^2 = C*f^2
where C is some constant of porportionality we don't really care about for this question.

But look what we can see. For a given tension, as the length goes up the frequency drops. Or we can raise the freqency by increasing the tension.

So take two guitars. One has scale length l1 and the other is longer l2. If we want the same frequency

t1/l1^2 = t2/l2^2

and there is the answer to the question at hand. If l2>l1, than t2 must be greater than t1.

So the longer scale has higher tension.

OSA - Official geek of TFF

Or you could just put a capo on your guitar at the 5th fret, tune it down to E and notice the strings getting dramatically looser on your new 19" or so scale length guitar!

I'm just bustin' your ass! Nice work, I think, you lost me a while back. I'm only a country engineer!

[fezz parka]

My head hurts! Go play your Esquire!:hee

[ragtweed]

Short scale guitars have lower string tension. I might not be the brightest bulb on the tree when it comes to guitars, but facts is facts.

[Offshore Angler]

And yes, my fav new show is Numb3rs. And you can see why I love complicated effects processors.

[RocketMan]

Hey OSA, you've taken me right back to my calculus based physics courses in college and Dr. Plumer, that pinguin shaped,funny little man that tought them. Reet-on! Good show BTW, I tune in too.
Hard to beat those simple, single PUP Fender planks for tonal complexity isn't it.

Anyway, consensus is longer scale is twangier. Thanks for the input everybody.

[moonpie]

Here's an equation that should help:

+ :wail2 / :blbros =


I hate it when you guys talk smart:toobad


:blbros:blbros:blbros:blbros:blbros

[NeoFauve]

A short scale guitar slung low has a slimming effect.
A long scale guitar hanging just below one's rib cage can make you look a little puffy.
:%

[Offshore Angler]

Well dang Rocketman, you should have done it yourself, ya lazy bastage!

[sabby]

Longer scale length generally means more twang and better note separation like a group of singers, each having their own microphone.
I seem to be able to hear each individual note better.

On the other hand, shorter scale length can cause a smoother tone more like a group of singers around 1 mic.

I love them both.

This to me is the greatest difference. I used to think single coils had better note seperation (or, conversely, were harder to get smooth rythym sounds) until I played a few short scale jazz boxes and then a P90 Lester. The scale length twangs, as fezz says.