Regarding String Tension...

Bill Sheehan

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Sorry if this has been hashed out already, but...
I'm not confident that I grasp the "physics" of this question as well as I might. In a nutshell, it boils down to this: if a player tunes a traditional-scale soprano uke to standard gCEA tuning, but the string tension feels a little too "floppy" for his/her preference, and the player doesn't want to tune the uke any higher (as a means of increasing the string tension), would an equally legitimate solution be to simply utilize the same string set, still in the gCEA tuning, but on a "longneck" (concert-scale) soprano? Phrased differently, will a "longneck" soprano have a "tighter" feel than a "regular" soprano using the same kind of strings/tuning? Thanks!
 
Yes, the length affects the needed tension for a vibration frequency.

Math formula is this: f = sqrt(T/u)/(2*L), where T = string tension force, u = linear density, L = scale length.
https://en.wikipedia.org/wiki/String_vibration

Above formula also explains the the mass thing, like why C string is thicker than A string in general.
 
Thanks guys! I have in fact tried the Freemont Blackline hard-tension strings, and although they're great strings with a nice tight feel, I tend to prefer the sparkle of the Martin M-600's. I am grateful for your thoughts!
 
While it is called a long neck soprano, it is really a concert scale on a soprano body. The soprano scale is about 13 3/4" in length, a concert is 15" so of course the longer scale will have higher tension no matter what string you use.
 
Thank you, Duane! That certainly makes sense. Somehow I had it in my head that a longer distance from saddle to nut would pull the string up to the desired pitch more quickly (with fewer turns of the tuning machine) than on a standard scale, thus causing the concert scale to actually feel more floppy. But I think I see now that the reverse is true.
 
About the intonation of stringed instruments and saddle compensations etc.

It is a desired feature that our strings remain all in same tension, but lower strings need more linear density and without adding that with wound strings, our saddle would need be seriously compensated in classical guitars and low G ukulele too.
Because of the beam effect would come and the above formula then not so true. It is done with using small strings at the core and not a single string in classical guitar. That is why low G wound string behave better with intonation in general.

In classical guitar the 4th D string is though the most delicate.

When it comes to acoustic guitar with steel strings, its 3 lowest strings need to have the windings. Also if not blues the 3rd string is better with wound as usual, cause of the beam effect. To add the mass to those strings. Without the 3rd G string is a somewhat not so accurate regarding intonation. Same as our re-entrant C string is too. Needs compensation maybe somewhat to scale.

Now acoustic guitar has a profoundly slanted bridge, so the base strings are made to have a longer scale. The windings also add to beam effect in those. In optimal situation the frets also had to be slanted, but the bridge slant takes care of half of that. And in general what with the acoustic box resonances and them not played so high up in fretboard, it is not done. The electric guitar strings are much thinner, so the bridge compensation is also only done. Not so much beam effect in those light strings.
 
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Thanks for the additional thoughts, Jarmo. I think I've now reached a satisfactory solution to my original concern, which was that the gCEA tuning seemed to feel a little "squiggly" on my soprano uke. So, yesterday I grabbed my longneck soprano (which I hadn't touched in ages) and installed the same kind of strings on it, and tuned it to gCEA, and I found that the extra scale length took care of the squiggliness and gave things a nice firm feel (without having to tune up a half-step or a full step). So, it seems to have all worked out! (I suppose another option would be to just use a concert-size uke; but I tend to prefer the soprano-size body, with the concert neck).
 
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