Tension and Scale length vs. string length

[Volitions Advocate]

Something dawned on me and I wanted to ask the peanut gallery for opinions and experience (because this is my favorite peanut gallery)

I've been interested in jumping into the extended range guitar world and right now there are a lot of crazes going on like headless guitars, multi-scale necks, and non-wood materials etc. and I've been thinking of building a guitar from scratch for the first time.  I was debating whether or not I want to bother with a multi-scale, but I got to thinking.

The longer the string the more tension it requires to bring up to pitch, correct?  But is it actually the scale length that determines that or is it the entire length of the string from behind the bridge saddles all the way to the tuning peg.

All other things being equal I would assume that with 2 guitars, both 25.5 inch scale length, same bridge, both tilt back paddle, but one is a 3+3 and one is a 6 in-line with all tuners on the treble side, wouldn't the low E string on the 6-in line guitar require more tension to bring it up to pitch because of the longer length over the break of the nut? 

I guess what I'm asking is..  do fanned frets actually affect tension in a meaningful way compared to how much string you need to tighten up after the nut anyway?

I won't argue the ergonomic benefits, but I feel perfectly comfortable playing a normal guitar with a single scale length, so that was never an issue for me, but the string tension question is the only reason I'd consider getting a multi-scale guitar.

I'd love your thoughts.

 

[swarfrat]

I run regular (for me, sort of heavy for most people, but not 'Baritone' strings on my baritone guitars. Or I do on my electric (my Alvarez jumbo is strung 16-72 IIRC and tuned B-B).  Most baritones are really only about two frets longer than their 'parent scale', and if you like a tight string you can tune em D-d' or similar with regular gauges. I find that suits my voice quite well, but the acoustic likes the heavier strings to drive the top, and gives me another option if I show up with too many flat top players sawing away in open chords.

The length of string behind the bridge does not impact the pitch of the string. Only the distance between the nut or fret and bridge matter.

Scale length (and this applies to fan frets too) - basically for regular string gauges, one fret difference is about equal to the jump to the next string gauge is about equal to a half step up or down. 

 

[stratamania]

To achieve a given pitch for a particular string gauge and scale length the tension required remains the same between the nut and bridge regardless of how much length of string there is beyond those points. Change the tension the pitch changes.

Some may perceive bends feel easier if there is more string beyond the nut or bridge, but that has nothing to do with the tension required to achieve the pitch.

 

[Rick]

It's pretty subtle.  On my current build, because I'm getting locking tuners so difficulty stringing doesn't matter, I'm thinking about a reversed or upside down fender style neck.  This will shorten the high e and lengthen the low E.

The reason I like the in-line headstocks is that with the 3x3's I forget which way to turn the tuning key.  There might be some very small change in overtones, but it's incremental.

As for fanned frets, and string tension, gotta be the same, deminimus. 

 

[BroccoliRob]

Yo, here's something I've always wondered (jk, it just crossed my mind reading this thread): is the string tension different between a 7/8 Warmoth and a Strat with a Gibson-Conversional neck, all other things being equal? I don't yet own a 7/8 but am considering it if it wouldn't look silly on my XXL man-beef.

 

[bagman67]

All other things being equal, you would expect strings of the same gauge tuned to the same pitch on two different-scale-length necks to be at higher tension on the longer scale length.


Your variables are string mass, string tension, and scale length. 


They operate as follows:


All other factors being equal, pitch rises as scale length shortens.  This is why you get a higher pitch when you fret a note.  You are shortening the sounding length of the string.


All other factors being equal, pitch lowers as string mass increases.  This is why heavier strings are used to play lower notes.


All other factors being equal, pitch rises as string tension increases.  This is demonstrated when you use your tuning machines.  Turn one way, the string loosens, and the pitch goes down. Turn the other way, get the opposite result.


So:  Using the same strings, your 7/8 sized (or 24" scale) axe, tuned to standard, will have a looser string tension than the 24.75" Gibson-conversion scale neck on a standard sized body.

 

[BroccoliRob]

But the 7/8 guitars are 24-3/4" scale the same as a Strar/Tele with a conversion neck. The 7/8 is 24 frets vs 22 on the conversions. I'm guessing the diff bridge position on the 7/8 would make the string tension the same as a conversion, but that's why I brought it up.

Is like, of the same scale legnth, is the low-e at a lower tension on a reverse 6 in line compared to a regular 6 in line? I'm thinking it will be since the overall length is different.

Have I been hitting too much ranch? I don't think that's possible but you #neverknow

 

[bagman67]

Ah, there you have me.  I mistakenly thought the 7/8" scale length was 24".  You are correct - the string tension - pitch and string gauge being constant - will be the same on a 7/8 scale instrument and on a Gibson conversion length.

 

[Cagey]

Is like, of the same scale legnth, is the low-e at a lower tension on a reverse 6 in line compared to a regular 6 in line? I'm thinking it will be since the overall length is different.

The length of the string matters not; it's the scale length (speaking length) of the string that matters. If the scale is 24 3/4", you can have extra string beyond the bridge to the tailpiece or beyond the nut to the tuners going on for several feet and you won't feel/hear it. The string for a given mass (gauge/material) and speaking length has to be at a certain tension to vibrate at a certain frequency. You'll hear people argue all the time about reverse headstocks or excess string past the bridge (as on a Jazzmaster, for instance) changing how the strings feel to play, but it's the remarkable power of suggestion that they're experiencing, not any actual change in tension.

For example, D'Addario says if you want to play a high E using one of their alloy strings, it needs to at 16.2 lbs. of tension. If you change the scale (speaking) length, that tension will change, but if you change the overall string length, it will not.

 

[BroccoliRob]

I could swear the tension feels lower on the high-e of my Hombre than on my Warhead, but yeah, it could just be my mind tricking my mind into perceiving that. Or maybe my thetan levels are off again.

 

[Cagey]

You're not alone in that perception. But, what's the tuner doing? Loosening or tightening the string. Changes the tension, which changes its pitch. Anything else that would change the tension would do the same thing.

 

[amigarobbo]

The tension will be the same, but the bendability of the string will be easier if there's more string to stretch.

Assuming free movement at the nut/bridge.

Imagine if you've got a slightly stretchable rope, 25.5" will stretch less than 35" of rope for the same effort.

Or to put it another way, if 1 inch of rope or string can stretch 1/16 of a inch with so much effort, so 16" of rope will stretch a whole inch, but 21" will stretch 2 inches for the same effort.

Or something.

 

[Cagey]

So, a longer rope (or string) will stretch farther than a shorter one. That's a given. But, you're trying to get to a specific tension, not a specific length. If you need 15 pounds of tension, you gotta stretch it until that's where it's at.

 

[amigarobbo]

So, a longer rope (or string) will stretch farther than a shorter one. That's a given. But, you're trying to get to a specific tension, not a specific length. If you need 15 pounds of tension, you gotta stretch it until that's where it's at.

If it's easier to stretch then it requires less force to bend (or fret) a note, even if the tention over the playing section is identical.


Or to put it another way, on a locking nut with a fixed bridge when freting you're forcing 64.77cm of sting to stretch to (say) 64.80cm


64.77 / 64.8
= 0.999537037037037

With no locking nut and the effective length of the string, say 75cm (assuming no friction at nut) So the whole string has to stretch the same amount 75.03

75 / 75.03
= 0.9996001599360256


NIGHT AND DAY!!!!  :icon_jokercolor: :evil4:

But there is a physical mathematical rational behind why excess strings beyond the nut/bridge would feel more 'slinky', even at the same string tension.

:icon_scratch:


Or another example, grab a geetar, stretch an open string at the 12th fret up a cm, easy eh? Now fret the last note on that string, and hold it so tight the string can't move at that point, now try to pull the string up a cm halfway between the fretted note and the bridge.

The tension on the string is the same, but one is easier than the other.  :icon_biggrin:

 

[amigarobbo]

:sad:


Of course obsessing over these things, well, that way to madness leads.

:turtle:

 

[mayfly]

So, a longer rope (or string) will stretch farther than a shorter one. That's a given. But, you're trying to get to a specific tension, not a specific length. If you need 15 pounds of tension, you gotta stretch it until that's where it's at.

If it's easier to stretch then it requires less force to bend (or fret) a note, even if the tention over the playing section is identical.

Sadly, this is not true.  I proved it to myself in a university lab decades ago, and I prove it to myself every time I bend the b and e strings on my bender telecasters.  If you're bending to a particular note, it requires the exact same force independent of how much string is beyond the bridge.  When I did my experiment back in school, I used to test setups:  one with a string length that was double the speaking length, and one that was exactly the speaking length.  To bend to a particular note, both test setups required the same applied force as measured with a digital tension meter (and my fingers  ). 

 

[amigarobbo]

Did you publish your methodology?  :evil4:

:sad:


Of course obsessing over these things, well, that way to madness leads.

:turtle:

Of course if it sounds like this,

[youtube]pFXSJVByZXg[/youtube]

That's not such a bad thing.

 

[BroccoliRob]

I'm gonna stop trying to wrinkle my brains about all this snizz.

 

[mayfly]

good point!  time to do some scales.

 

[Seamas]

I'm just going to ask this because I think it has some relation:

What effect, would a reverse  6-per-side headstock have when depressing the vibrato compared to a standard headstock?

I seem to think that the bass strings tend to lower pitch a bit more than treble strings (with a standard headstock) when depressing the vibrato, but I have never really measured it.
Now I suspected that this would change with a reverse headstock, but am reading that there would be no change at all.
Is that right?