Mudcat Café message #753028 The Mudcat Café TM
Thread #49771   Message #753028
Posted By: JohnInKansas
23-Jul-02 - 10:39 AM
Thread Name: Guitar string tension v gauge
Subject: RE: Guitar string tension v guage
The weight referred to is what the string weighs if you throw it on a scale.

Calculating the relation between pitch and tension for an arbitrarily chosen string is fairly complex, since it is difficult to know how an arbitrarily chosen string is put together.

In most cases, the manufacturer will tell you the tension required to bring his particular string to the "usual" pitch - on a guitar with the "usual" string length.

The only "dimension" the manufacturer usually gives you is the diameter of the string; but he won't tell you the diameter/material/heat treatment or other details of the "core wire" and of the "winding."

Regardless of any details of how the string is put together, for any one string, the tension required to tune to E is 1.26 times the tension required to tune the same string to C. That's because the frequency of an "E" is 1.26 times the frequency of the next lower "C" and the only thing you're changing when you retune a particular string is the tension.

While there are fairly simple formulas for calculating the relation between pitch and tension for an arbitrary string, you can't use the most accurate formulas without detailed knowledge about how the string is assembled. You would need to take the string apart and make a bunch of rather difficult - and very accurate - measurements to get the "values" needed in the formulas. It's a lot easier just to read the label on the package.

For practical purposes though, the tension at a given pitch depends only on the total weight of a length of the string equal to the distance between bridge and nut. If one string weighs 1.2 times as much as another, then the heavier string will require 1.2 times the tension of the lighter one to bring them both to the same pitch.

Since you are tuning down from E to C, the ratio of the frequencies is 1.26. If you use a string that is 1.26 times as heavy as your original "lightweight" E, it will have the same tension at C that the original string had at E. If your "heavy" string weighs less than 1.26 times what the same length of your lightweight string weighs, you will not have a higher string tension with the heavy string at C than you had with the light one at E.

All that the more complex formulas do for you is to incorporate ways of calculating the total weight of the active part of the string from the details of the string's construction.

In order to produce a "pleasant tone," a string must be under enough tension to act as a "linear" spring. That means that the change in tension must be strictly proportional to the amount of "stretch." Steel strings, or steel-core strings, are generally designed to work with the core at about 80 percent of "yield." The "yield point" is the point at which the length of the string starts to increase without any significant increase" in the tension - (because the metal is "flowing" and the diameter - somewhere - is decreasing, making it less "strong").

If you attempt to tune an "80%" string up by the same 4 semitones - E to G# - it will probably break (.80 times 1.26 = 1 and you've reached the yield point).

By tuning down - assuming you're using a string designed to the 80% stress level - you would be at about 63%, which is probably sufficient for a reasonably "musical" tone, but the string may start to get pretty "flabby" if you go very much lower.

Your biggest risk in using the heavy strings "tuned down" is that someone will pick up your guitar (maybe even you) and try to tune it "right." That could put more tension on the instrument than it likes.

John