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String Formula - How Useful?
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rojarosguitar
Posts: 243
Joined: Dec. 8 2010
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 String Formula - How Useful?
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I refer to an older post I took part in, that has been closed, but I think this could be of some value to reflect:
quote:
ORIGINAL: Richard Jernigan
The formula and a link to its derivation are in the audio/video upload section
http://tinyurl.com/2frjypu
RNJ
That's the textbook formula I meant. As I wrote, its usefulness is slightly limited by two quite different factors:
i. It is only valid for 'ideal' strings that are 'infinitely thin' as compared to their length, and only inasmuch the string properties stay same independently of tension.
This is obviously not true for a string tuned up to pitch, which is not that far from breaking point.
ii. You need to know the 'linear density' of the string, which is only roughly known for certain standard material (nylon, fluorocarbon, nylgut, steel) and which can vary quite a bit with specific formulae used by the different makers, so that the practical calculation is always to be taken with a grain of salt.
Also stretching the string while tuning up deletes some mass from the vibrating length (as you can clearly understand from the fact the more and more material is wound up on the roller of the tuner) while the length stays the same, which would suggest that the linear density is not held constant when tuning up.
So in the end of the day you need to rely on the feeling and on how the actual string sounds on the actual guitar. Eg. when I calculate the tension of Seaguar Premier fluorocarbon 0.91mm on the Arto's String Calculator (available online) I get a ridiculously high tension of almost 8 kg (660mm scale) but it doesn't feel exactly that way.
And the formula is completely at loss with wound strings which are much more complex in their behaviour. One could calculate their frequencies by using some kind of experimentally won linear density, but I'd suspect their density is changing even more with tuning up as the windings get slightly spread (again evident from the fact that you get more and more of the windings on your roller while the length of the string didn't change).
Also how a string actually feels depends on its 'stiffnes' which is the resistance against sidewards bending. Some materials are softer, some are stiffer. Recently I tried Dogal g-string and it's so stiff it almost hurt my fingers, though I do play a lot.
So scientists love to have one simple and clear formula but in the case of the guitar strings it is quite far apart from the practicalities of playing.
Best
Robert
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REPORT THIS POST AS INAPPROPRIATE |
Date Mar. 22 2014 17:29:28
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Richard Jernigan
Posts: 3430
Joined: Jan. 20 2004
From: Austin, Texas USA
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RE: String Formula - How Useful? (in reply to rojarosguitar)
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quote:
Also how a string actually feels depends on its 'stiffnes' which is the resistance against sidewards bending. Some materials are softer, some are stiffer. Recently I tried Dogal g-string and it's so stiff it almost hurt my fingers, though I do play a lot.
In my own experience, the 'feel' of the string depends a good deal more on its linear Young's Modulus, and on the diameter of the string.
The linear Young's Modulus relates to how much the string tension increases as it is stretchedi n length. The stretching occurs when the string is fretted. You push it sideways, but it increases in length as a result. Fluorocarbon typically requires more force to stretch it than does ordinary nylon.
The fingertips are sensitive not so much to the total force exerted on them, but to the pressure. A smaller diameter string requiring the same force to fret as a larger string will exert more pressure on the finger tip, since the same force is applied to a smaller area. Pain in the fingertips is to a considerable extent the measure of pressure, not of force.
As poster of the formula in the first place, I would point out that the only way I have ever selected strings is by putting them on a guitar, letting them settle in and playing them.
Like most "idealized" formulas in physics, this one only illuminates general relationships and points the way to an approximate result, like "If I knew what the tension on the third string was (from measurements, or from the manufacturer's published specs), how much would the tension be if I tuned it down to f#?" Or "if I knew the string tension on a 664 mm scale, what would the tension be for the same string at the same pitch on a 650mm scale?" The formula would get you pretty close.
A particular case where the formula's answer deviates from reality, sometimes to an audible extent, is in the calculation of overtones. The idealized string formula gives overtones in the harmonic series. Real strings, with bending stiffness, produce overtones that gradually grow sharper relative to the harmonic series. This is why pianos are tuned with "stretched" octaves, so the treble strings will be in tune with the sharp overtones of the bass.
The "impure" overtones of the thick, relatively low tension third string are the main reason third strings are often duller than the first of second on many guitars. It's also why stringed instrument makers went to wrapped bass strings a few centuries ago. They have notably less bending stiffness than solid gut strings tuned to the same tension and pitch. But I doubt that anyone in the string business back then studied the idealized string formula in any depth.
A lighter string like fluorocarbon, can be tuned to higher pitch for a given tension, according to the formula. The reduced bending stiffness can result in a "purer" overtone series, with a resultant increase in volume, and a change in tone quality. The precise numbers, as the OP points out, are to be obtained not just by calculation, but by experiment.
After centuries of wandering in the wilderness of logic and speculation, people finally came to realize that experiment is the criterion for validity, not just calculation. Having had this beaten into my head by a lifelong career as engineer and scientist, it never occurred to me to point it out in the original post.
RNJ
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REPORT THIS POST AS INAPPROPRIATE |
Date Mar. 22 2014 23:33:16
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