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I'm contemplating scale length for my build right now. I'm a bit confused about which way to go, and also the theory in general.

I've read everywhere that the shorter the length the less tension. I'm confused by this because I've experienced just the opposite on many occasions. There may have been other variables involved, that's why I'm asking you guys. For instance... I have a couple of 24.75" Gibson archtops. Now to me the string tension has always felt very tight. In some instances making it a bit uncomfortable to play. I've tried to play around with the action (via the bridge) but can never achieve a looser feeling without getting some buzz on certain frets(the necks are in good shape and straight). Now the weird part is that a couple of other archtops I own have a longer scale. The most comfortable one with the least tension happens to have a 25.5" scale.

Can anyone explain what's happening here? Is it a Gibson thing? So right now it looks like I'll probably build something that at least hits the 25" ballpark.

It's a setup thing.

Physics is physics. Shorter scale, lower tension. No ands, ifs or buts.

Yes, the set up, assuming you are using same gauge strings. Sometimes strings under less tension vibrate at a larger amplitude, and the builder compensates for buzzes by making the action higher. Thus, it is harder to push the strings down farther.

Grumpy is right, but being grumpy he said it fairly brusquely.

Assuming you're using the same gauge of strings on the two, and tuning them the same, a guitar with a longer scale length will have more tension on the strings. The thing is, that's what you might call 'physicist's tension', a simple measure of the force that is trying to pull the nut toward the saddle. A lot of players use the term 'tension' for something else; the amount of force it takes to fret the strings. This 'players tension' is a much more complicated thing, as it involves things like the action height at both ends, fret height, relief, and possibly even neck stiffness.

Suppose you have a guitar with a short scale, and you want to get 'the same' volume and sound out of it as a similar instrument with longer scale. There are several problems. Foremost is simply that the energy in a vibrating string will be proportional to the tension and the square of the amplitude. Action height limits the amplitude, of course, so with less tension you will need to raise the action a bit. Note that, in the extreme case of 50% lower tension, you only need to raise the action by 40% to get the energy back, but still, you need to raise it. You may also need to use more relief to keep the strings from buzzing, and that amounts to higher action, particularly in the 1st through 7th frets.

Even with the action raised the sound may not be 'the same'. For one thing, the shorter strings have lower impedance; they don't push on the bridge as hard. You might find that you need to go to a heavier gauge. This increases the tension, of course, and also makes the strings intrinsically less flexible. Yeah, with the tension back, you can drop the action a bit, but that added stiffness....

I haven't hit all of the variables yet, but you can see where they're going. 'Players tension' is pretty complicated.

Personally I'd rather they didn't use the term; to me, as, I gather, to The Grump, 'tension' means simply that one force that wants to fold up the guitar. But the fact is that people _do_ use the term in different ways, and we have to deal with that. So, yeah, it's possible for a shorter scale guitar to be harder to play, but with the same strings it's still carrying less tension.

This is one of the points of discussion that often drives me nuts. I know that people do use the word tension in different ways, but I simply can't tolerate it. "Stiffness" may be a good word, but I hold that tension specifically means and should only ever be used to describe the amount of force along the length of the string. There is simply no way a person can directly feel the tension unless they are pulling on the end of the string to pull it up to pitch. The amount of force needed to deflect a string perpendicular to it's length is not tension. I don't care how many people call it that in error, I will not bend on this one.

If a shorter scale length guitar feels stiffer to you, it's probably just because it's set up poorly. That or the obvious heavier gauge strings, but there are tons of other variables as well. Feel is such a subjective thing, and I can set up two guitars of identical scale length and strings to identical setup measurements, and some players may perceive one as feeling stiffer than another. Different neck shape, fingerboard radius, fret wire size, even if it may take the same measured amount of force to press the string against a fret, there can often be a subjective though very real difference in the player's perception.

If your short scale feels stiffer than your long scale though, it's most likely due more to a truly bad setup than subjective perception.

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Eschew obfuscation, espouse elucidation.

Keep in mind, though, that if two strings of different lengths have the same tension ( not the situation here, since we're talking about higher tension in the longer string to maintain the same pitch) the shorter string will actually be stiffer laterally.

The lateral stiffness of a string ( excluding the bending stiffness of the string, which is generally negligible) is proportional to the string tension and inversely proportional to the string length.

This increase in stiffness in the shorter string does not make up for the decrease in stiffness due to the decreased tension. The decrease in tension for a shorter string ( at the same pitch) is a square function of string length, so it is greater than the increase in stiffness due to the shorter string length.

To try to simplify this, here's an example. If you make a particular string 5 % shorter and maintain the pitch, the tension decreases by about 10%, but the lateral stiffness decreases by only about 5%, or, half as much as the tension decrease.

Phil

You should also consider the string length as the point from the tuner post to the ball end, since that entire length must be tight.The speaking length may be 24.625 but the whole string is under "tension",not just the nut to saddle part.
It is possible to have different scale lengths "feel" similar if the string length is similar.

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How long is that in luthyears?

Strings stretch from tuner post to bridge pin or tailpiece, but that can be affected by friction at the bridge or nut.

I prefer to call what the player senses, "string feel", and my esteemed colleagues above are quite right in that "tension" is a measurable factor made up of scale length, string linear density, and pitch. Al alludes to neck stiffness affecting string feel, and I totally agree with that, as subtle as it it. Don't forget that good players have incredibly sensitive scientific instruments...their ears and their fingertips...built in. Those human tools still outperform most lab equipment in relating and sorting out subjective effects with instruments...and a lot of it is actually amazingly objective as well. The classic example is how in the 1970s golden eared audiophiles could hear TIM (Transient Intermodulation Distortion) in transistor amplifiers as objectionable, yet there were no measurements for it in those days. Walt Jung figured out how to measure it, and discovered the link to slew rate. Bingo! It turned out that the ears had been hearing what the 'scopes weren't measuring, and the golden ears were vindicated, much to the chagrin of some amplifier designers whose measurements showed their amps to be near perfect. Not!

I agree with David Collins that we _should_ only use the term 'tension' to refer to the force of the string pulling the bridge and nut toward each other. Rick's 'string feel' is as good a term as any for talking about the player's subjective experience. However, that's neither her nor there; the players do use the term 'tension' to describe what they feel, and unless we can educate them out of it, we'l just have to get used to it. Look at the success I've had with getting luthiers to stop saying 'flamed' when they mean 'curly'.

NOT

Man, I just can't believe no one followed up on that one.

"Loosen up a bit Dave, you're just way too tense about things like this."

or,

"Don't get all strung out about it, cut the guy some slack"

Where are the obnoxious punsters when I want 'em? I handed you that one on a platter, and nobody bit. Talk about getting stiffed....

_________________
Eschew obfuscation, espouse elucidation.