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String Tension And Elasticity


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I recently got my hands on some decades old Honduran mahogany that is just incredible. I'm planning on building a guitar with a few experimental features, using the good pickups and hardware from one of my upgraded cheap guitars.

One of these is that I'm going to try out a flat radius board and an asymmetrical neck carve. SS frets.

But the other idea I had involves the overall string length.

We all know that pitch is determined by mass, tension, and speaking length of the string. Two 25 1/2" scale guitars with the same strings on them will have the same tension at concert pitch, whether they have a locking nut, tremolo, string through, stop tail, or some other design.

But what I'm thinking about is the actual mechanical elasticity of the strings. This is purely anecdotal, but I have several 25 1/2" scale guitars all strung with 10's, a couple with trems, a string through hard tail and a top loader hard tail. It's been my subjective experience that the top loader feels stiffer than the others.

My theory is that (all else being equal) the more string length past the anchor points of the strings the more mechanical give the strings will have. This is of course providing the strings can move freely over the nut and saddle slots. So a hard tail top loader will have less give than a string through because the overall length of the string is less even though the speaking length is the same.

The way I've illustrated this is to picture two lengths of cable. One is five feet long, the other is twenty feet long. You anchor both ends of each cable to posts and crank things up until the tension on both cables is 30 pounds.

Now you try to pull each cable from it's resting point enough to raise the tension to 35 pounds. The shorter cable needs to pulled only a little off it's resting point to achieve this, but it feels very stiff.

When you pull on the twenty foot cable, you have to pull it further from it's resting point to achieve the same increase in tension, but it feels easier because the work is spread over a longer distance and the increased length means whatever mechanical give is inherent in the cable is multiplied.

Strictly speaking, from a physics standpoint I suppose the work needed to raise the tension is identical, but the subjective experience is that the longer cable is looser and easier to work with, even though you have to move it further.

How this applies to my idea is that I was thinking of making a guitar with the strings running freely through the back of the bridge to either a tail piece or ferrules mounted at the back of the guitar, so that the length of the strings past the saddles is maximized. I would route a ramp into the top of the guitar so the angle of the strings past the saddles wouldn't have any friction or binding points.

So the only points where the strings touch anything is at: ferrules or tail piece>saddle>nut>tuner post. I would use a graphite nut, tilt back headstock, possible roller saddles (though I think that's pushing it).

The point is that the strings would be as long as possible and as unbound and frictionless as possible along their entire length. My theory is that this would result in a looser and easier feel to the guitar as the strings could give more mechanically. If my idea is correct, it would also probably mean I would have to bend further to achieve the desired note than otherwise, but again that relates to the cable analogy. Same work, spread over greater area, easier feel.

This would most likely be a Tele since I already have all the hardware and such, so picture a Tele with a flat radius board, tilt back headstock, and a tail piece or string ferrules mounted at the back of the body with a ramp routed out of the body toward the back side to allow the strings to reach from the saddles through new holes I would drill in the back of the bridge to allow them to run through without touching anything along the way.

I don't know if I've explained this very well, but that's the idea. The physics of it seem sound to me, and I think it might look pretty cool and unique if I did it right.

What do all you guys think?

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I recently got my hands on some decades old Honduran mahogany that is just incredible. I'm planning on building a guitar with a few experimental features, using the good pickups and hardware from one of my upgraded cheap guitars.

One of these is that I'm going to try out a flat radius board and an asymmetrical neck carve. SS frets.

But the other idea I had involves the overall string length.

We all know that pitch is determined by mass, tension, and speaking length of the string. Two 25 1/2" scale guitars with the same strings on them will have the same tension at concert pitch, whether they have a locking nut, tremolo, string through, stop tail, or some other design.

But what I'm thinking about is the actual mechanical elasticity of the strings. This is purely anecdotal, but I have several 25 1/2" scale guitars all strung with 10's, a couple with trems, a string through hard tail and a top loader hard tail. It's been my subjective experience that the top loader feels stiffer than the others.

My theory is that (all else being equal) the more string length past the anchor points of the strings the more mechanical give the strings will have. This is of course providing the strings can move freely over the nut and saddle slots. So a hard tail top loader will have less give than a string through because the overall length of the string is less even though the speaking length is the same.

The way I've illustrated this is to picture two lengths of cable. One is five feet long, the other is twenty feet long. You anchor both ends of each cable to posts and crank things up until the tension on both cables is 30 pounds.

Now you try to pull each cable from it's resting point enough to raise the tension to 35 pounds. The shorter cable needs to pulled only a little off it's resting point to achieve this, but it feels very stiff.

When you pull on the twenty foot cable, you have to pull it further from it's resting point to achieve the same increase in tension, but it feels easier because the work is spread over a longer distance and the increased length means whatever mechanical give is inherent in the cable is multiplied.

Strictly speaking, from a physics standpoint I suppose the work needed to raise the tension is identical, but the subjective experience is that the longer cable is looser and easier to work with, even though you have to move it further.

How this applies to my idea is that I was thinking of making a guitar with the strings running freely through the back of the bridge to either a tail piece or ferrules mounted at the back of the guitar, so that the length of the strings past the saddles is maximized. I would route a ramp into the top of the guitar so the angle of the strings past the saddles wouldn't have any friction or binding points.

So the only points where the strings touch anything is at: ferrules or tail piece>saddle>nut>tuner post. I would use a graphite nut, tilt back headstock, possible roller saddles (though I think that's pushing it).

The point is that the strings would be as long as possible and as unbound and frictionless as possible along their entire length. My theory is that this would result in a looser and easier feel to the guitar as the strings could give more mechanically. If my idea is correct, it would also probably mean I would have to bend further to achieve the desired note than otherwise, but again that relates to the cable analogy. Same work, spread over greater area, easier feel.

This would most likely be a Tele since I already have all the hardware and such, so picture a Tele with a flat radius board, tilt back headstock, and a tail piece or string ferrules mounted at the back of the body with a ramp routed out of the body toward the back side to allow the strings to reach from the saddles through new holes I would drill in the back of the bridge to allow them to run through without touching anything along the way.

I don't know if I've explained this very well, but that's the idea. The physics of it seem sound to me, and I think it might look pretty cool and unique if I did it right.

What do all you guys think?

I think there might be some other problems with the idea of extending the strings, since the extension of the string acts as an independent string (although short but still a string) that might produce overtones (undesirable) that will interfere with the tones you are playing (you're probably familiar with that oriental instrument that the bridge is the middle of the string and the player plucks both sides to play the melody).

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The elasticity of strings beyond the vibrating lengths imposed by the saddles/frets/nut has an effect on vibrato, for sure. I prefer reversed headstocks for stretchier low strings, which is why I did a reverse banana headstock on my 27" Explorer conversion neck to balance out the increased tension. I'm sure Hendrix' right/lefties had a similar effect on the playability.

I find that string bending on my Ibanez S (main axe) is a little restricted in range due to the presence of the locking nut and locking-block Edge Pro (trem disabled - blocked off with a bit of birdeye map).

Bergeros: As far as the additional vibrating string length possibly interfering and causing overtones - I don't believe that it's always undesirable, as in some ways it contributes to the character of the instrument. I find additional vibrating length behind the nut undesirable on my eight-strings, whereas I believe it probably contributes positively to the character (of say a Les Paul) behind the bridge.

I think you're referring to a Koto, yes?

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Archtops have a fair bit of string behind the bridge.

Interesting idea that is worth a try - but I wouldn't commit old-growth Honduran mahogany to an experiment that might not work out. Especially since you're addressing issues of playability rather than tone.

Quite right, after I made the original post I realized that I had enough other mahogany and black walnut to do a sexy laminate body without having to cut into the old growth.

I'm not even sure what I'll do with it in the end. It's a pretty big chunk, 15"x20"x3". I wonder if that would be worth a chunk of change instead of using it myself?

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