Guitar string tension v gauge

Subject: Guitar string tension v gague
From: Chris Amos
Date: 23 Jul 02 - 01:51 AM

Hi,

I play a lot of stuff in open tunings DADEAD, DGDGGD etc, recently I decided my limited vocal range better might fit better if I tried Martin Carthy's trick of tuning it down to C (CACAAC etc). I got a set of heavy strings tuned it as above, the guitar sounds wonderful and my singing feels more relaxed.

Martin recommend that nothing heaver than medium strings is used on the guitar, does anyone know the mathematical calculation that will tell me the tension I am getting tuning heavies to C as compared to medium to E ?

Regards

Chris

Subject: RE: Guitar string tension v gague
From: JohnInKansas
Date: 23 Jul 02 - 03:42 AM

The frequency is directly proportional to the tension, and inversely proportional to the weight.

The ratio in frequency going from C to E (4 semitones) is 1.05946^4 (1.05946 x 1.05946 x 1.05946 x 1.05946 = 1.2599), so for a given string, tuning from C up to E requires a tension at E 1.26 times whatever the tension was at C

Working backwards - tuning down, if you know the tension for the heavier string tuned to E, you can divide by 1.26 to get the tension for the same string at C.

Dividing by 1.26 is the same as multiplying by 0.7937, so you can estimate that the string tuned to C has about 80% of whatever tension it would take to tune the same string to E.

Clear????

John

Subject: RE: Guitar string tension v guage
From: Murray MacLeod
Date: 23 Jul 02 - 04:27 AM

John, physics was never my strong point in school so could you elaborate on your first line "The frequency is directly proportional to the tension, and inversely proportional to the weight."

When you speak of "weight" do you mean the number of pounds it requires to raise the string to the required pitch? Which would be the same as tension, wouldn't it?

D'Addario print the tensions at standard pitch on the packet, so there should be no problem calculating the total tension using the above formula. My feeling is that tuning the bass to C requires a heavy gauge string.

Murray

Subject: RE: Guitar string tension v guage
From: Steve Parkes
Date: 23 Jul 02 - 05:25 AM

John means the mass or the density of the string. But we can take the area of cross-section (since mass = area x length x density): length & density are constants, so the frequency is directly proportional to the cross-section area.

Well, that's true for a plain string; it's a bit complicated for a wound string, because the area isn't circular, and the core and winding may have different densities. But this is being a bit picky: the difference is going to be slight (for steel strings--not nylon!).

And more good news: pi is a constant too, so . This means if you double the diameter, the pitch drops by two octaves if the tension is the same. For one octave, increase the dia. by about 1.4 (square root of 2); to go up an octave, decrease it to 0.7 of the dia.

What we really want here is for someone to come and quote us some guages!

Steve

Subject: RE: Guitar string tension v guage
From: Steve Parkes
Date: 23 Jul 02 - 05:30 AM

Whoops--some of my words have evaporated! Should be
pi is a constant too, so freq is proportional to the diameter squared.

Steve

Subject: RE: Guitar string tension v guage
From: Pied Piper
Date: 23 Jul 02 - 09:01 AM

Great thread. The thing you really need too know is the tension at which the string snaps. I understand that to get the best sound a string it should be tensioned a certain percentage under its breaking strain. For unwound strings this is presumably proportional in some way to the diameter. With wound stings the diameter of the core must be found to optimise string tension. I'd appreciate a more rigorous analysis with values if some one can do it. All the best PP.

Subject: RE: Guitar string tension v guage
From: JohnInKansas
Date: 23 Jul 02 - 10:39 AM

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

Subject: RE: Guitar string tension v guage
From: wysiwyg
Date: 23 Jul 02 - 10:48 AM

So....... to get the tone he wants and the tuning he wants, he may want to go to a just-slightly-lighter string?

~S~

Subject: RE: Guitar string tension v guage
From: Steve Parkes
Date: 23 Jul 02 - 10:51 AM

Anyone trying to tune my guitar is more likely to get a broken arm than a broken string!

Seriously, my 12-string is tuned down five whole frets: I use a "normal" set of strings all moved up one place, with a b-i-g one for the bottom "E" (which is tuned to B) and a normal G to double on the second. I really need to do some work on the nut to make the strings sit better, but I never round to it ...

Steve

Subject: RE: Guitar string tension v guage
From: nickp
Date: 23 Jul 02 - 11:02 AM

This may help - or hinder. I'm sure I've seen a better one but can't find it.

http://www.mindspring.com/~lonzoh/gauges.htm

Subject: RE: Guitar string tension v guage
From: Grab
Date: 23 Jul 02 - 12:02 PM

Piper, the bigger worry is the tension at which the neck begins to bend out of shape...

Graham.

Subject: RE: Guitar string tension v guage
From: Pied Piper
Date: 23 Jul 02 - 12:07 PM

Thanks for clarifying things John. It may seem odd that I a bagpipe player should be interested in this, but I have a "Bardic Harp" that I made from a kit and it uses Guitar strings. The tension is quit important; at the gauges supplied it produced a very sad boyoying noise so I put the tuning up a tone and that fixed it. The problem is that (in order to know where you are on a Harp) a steel wound string is introduced among the phosphor bronze to indicate octave and fifth, which are now on the wrong notes. I should be able to work out appropriate gauges for the strings from your info. All the best PP.

Subject: RE: Guitar string tension v guage
From: John in Brisbane
Date: 24 Jul 02 - 08:48 AM

We had a similar discussion here a few years ago, but I haven't searched for it. From memory one of us unearthed a site that calculated the tension for various string lengths, frequencies and weights. There was some rough rule of thumb for wound strings.

I remember using it before converting a six string guitar to an eight string bouzouki.

Regards, John

Subject: RE: Guitar string tension v guage
From: JohnInKansas
Date: 24 Jul 02 - 02:42 PM

Pied Piper -

A couple of manufacturers make "white bronze" wound strings that might give you the marker color for the the white strings with minimal difference in string properties.

For all practical purposes, the optimum tension of the string is determined by the size of the core wire, and the manufacturers won't tell you directly what that is. If you really want all the strings at equal tension, the they will all have the same core wire diameter - regardless of length.

Most instruments I've looked at string to about 30 pounds per string, which means they all have a (steel) core close to 0.011 to 0.016, since that range gives good stress levels.

The winding adds the weight needed to bring the pitch down to whatever you want, but doesn't contribute anything to the "strength" (indirectly the tension) of the string. Bronzes of various kinds are the common winding materials, although a lot of things have been tried. The density of available bronzes can vary over a fairly wide range, so the "wound diameter" isn't a very good indication of the actual weight (pounds on the scale) of the string - unless you know more than the string people like to tell you.

Differences in core diameter of as little as 0.0001 inch can make a significant difference in the string stress level, and the "guages" are rounded off rather crudely. In addition, nearly all strings are plated or otherwise coated with something, and since the platings go on "annealed," they don't contribute much to the wire "strength" - so a "very accurate" actual measurement of the finished wire diameter may not tell you too accurately how big the "core of the core" is.

John

Subject: RE: Guitar string tension v guage
From: Chris Amos
Date: 24 Jul 02 - 03:13 PM

Right,

I've done some calculations based on John's advice, one gives he tension (in pounds) for a set of Heavy strings tuned to concert, second is Heavy strings tuned to CGCDGC and last a set of medium strings tuned to concert.

		Heavy		Heavy		Medium 
  		Conc.		C		
  
  1st		31.8		25.24		27.4
  2nd		29.5		23.42		26.3
  3rd		38.4		28.76		35.3
  4th		45.2		40.27		36.8
  5th		40.0		35.64		34.0
  6th		32.2		25.56		29.0

Diameter for heavy set is .014, .018, .027, .039, .049, .059.

So it would seem by using these strings tuned as they are I am not putting undue strain on the guitar. Is this the best diameter to use for what I want?, should I use lighter as WYSIWYG suggested?, if I were to design a set of strings to fit this tuning at optimum tension what would they be like?

I am surprised that the 6th string exurts less force than the 4th and 5th.

Many thanks this is a good thread.

Chris

---

Added pre-format tags (<pre> and </pre> ) and line breaks (<br>) to get the table right.. --JoeClone

Subject: RE: Guitar string tension v guage
From: Chris Amos
Date: 24 Jul 02 - 03:20 PM

Sorry the table didn't come out as it should I'll alter it in the morning.

CA

Subject: RE: Guitar string tension v guage
From: GUEST,Claymore
Date: 24 Jul 02 - 04:25 PM

D'Addario makes a heavy gauge string set with a 63 gauge bass E, but you have to special order it from a music store. I use a bastard set with the 63 bass, a GHS 50 A, and the rest are Martin SP mediums on my Martin, with no problem percieved after two years. I don't know what the tension numbers would be, but I love the bass from E down to C, and no fret buzz. Good Luck!

Subject: RE: Guitar string tension v guage
From: Bill D
Date: 24 Jul 02 - 07:16 PM

here is an online string tension calculator

and here is a downloadable one from a lute maker...

Subject: RE: Guitar string tension v guage
From: Bill D
Date: 24 Jul 02 - 07:20 PM

just to be sure you see the start...here is the main page from the first one, as he has other things.

Subject: RE: Guitar string tension v guage
From: JohnInKansas
Date: 25 Jul 02 - 02:18 AM

With very red face....

I have just discovered that the (mostly reliable) source where I first found that the string frequency equations can be rearranged to give the results based "only on the string weight" neglected a "minor" square root dependency. I hadn't needed the formula recently and (hanging head in shame) didn't check back to "original sources."

For a simple string, meaning basically an unwound single wire, the relationship between frequency (f), tension (T), length of the string between bridge and nut (L) and total weight of the string (W) can be written as:

f = SQRT(T/kWL)

Another way of putting it is that for a given string ( f x f x W x L / T ) is a constant.

If you use all of the right "units," the constant k is 3.14159.... but the important thing is the relationship between the factors included.

For purposes of my previous comments, the relationship can be stated as:

"The square of the frequency is proportional to Tension, divided by weight and length."

At 23-Jul-02 - 03:42 AM: the italicized words should be inserted:

23-Jul-02 - 03:42 AM
The square of the frequency is directly proportional to the tension, and inversely proportional to the weight.

The ratio in frequency going from C to E (4 semitones) is 1.05946^4 (1.05946 x 1.05946 x 1.05946 x 1.05946 = 1.2599), so for a given string, tuning from C up to E requires a tension at E equal to the square root of] 1.26 ( = 1.122) times whatever the tension was at C

Working backwards - tuning down, if you know the tension for the heavier string tuned to E, you can divide by 1.26 1.122 to get the tension for the same string at C.

Dividing by 1.26 1.122 is the same as multiplying by 0.7937 0.891, so you can estimate that the string tuned to C has about 80 90% of whatever tension it would take to tune the same string to E.

At 23-Jul-02 - 10:39 AM:

Regardless of any details of how the string is put together, for any one string, the tension required to tune to E is the square root of 1.26 (which is 1.122) 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.
...
Because only the ratio T/W appears in the equation, the following paragraph is still correct:

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 1.26 times as much as another, then the heavier string will require 1.26 times the tension of the lighter one to bring them both to the same pitch.

But:

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 x 1.26 = 1.59 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 1.59 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.

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).

You should be able to increase an "80%" string's tension by a factor of 1.20 to get to the "yield point". An increase in tension by 1.2 increases frequency by the square root of 1.2, or 1.095, which is between one and two semitones. The "fact" that you can, in practice, tune more than a semitone up may or may not mean that you started with a stress level of 80% of yield. When you reach yield, the string will continue to stretch by reducing its diameter (permanently) - hence the pitch can continue to go up because the weight decreases - for a little ways until the string breaks.

Again, my apologies for the error in the equation - particularly to those who spent time using it to look at something.

John

Subject: RE: Guitar string tension v guage
From: Chris Amos
Date: 26 Jul 02 - 01:24 AM

JohnInKanas,

Many thanks for all this information, I shall get to grips with it at the weekend.

Regards,

Chris

Subject: RE: Guitar string tension v guage
From: open mike
Date: 26 Jul 02 - 01:51 AM

speaking of string tension, is there any truth to the rumor that strings should be loosened if taking your guitar on an airplane? if so--how much?? (to equal the tone of the next lower string??)

Subject: RE: Guitar string tension v guage
From: Murray MacLeod
Date: 26 Jul 02 - 10:43 AM

It is intuitively obvious to me that the probability of a headstock fracture due to inept baggage handling is much reduced if the strings are slackened off.

It is not intuitively obvious, however, to the L'Arrivee guitar company, who recommend keeping the strings at full tension while travelling by air.

I do not think for one moment that this is a cunning ploy to keep their repair personnel busy ....

Murray

Subject: RE: Guitar string tension v guage
From: open mike
Date: 27 Jul 02 - 02:36 AM

best (though not practical) plan is to buy it (her?) a ticket and strap the guitar in the seat beside you!

Subject: RE: Guitar string tension v guage
From: Pete_Standing
Date: 12 Oct 04 - 04:56 AM

When Murray says

"My feeling is that tuning the bass to C requires a heavy gauge string."

that is exactly what Martin Carthy and Chris Foster do (and probably many others too), using a 59 for the 6th string. However, Martin Simpson uses medium gauge strings going from 13 to 56, even when tuned down to C, but then he might have a longer scale length which, I am told, raises the tension of the strings anyway.

Subject: RE: Guitar string tension v guage
From: GUEST
Date: 12 Oct 04 - 05:28 AM

Yep Peter, the longer the scale length, the tighter a given string will have to be to reach the same pitch. If you think about it in terms of playing and moving up frets to get higher pitched notes, it is quite clear.

The example you cite could be personal preference though. People vary a lot with strings as they do with choices of picks. There are limits beyond wich you could damage an instrument or have a string so sloppy it is horrible but there is room to manouvre and no real right or wrong.

I tend to think that once a person has some "ballpark" gauges, it is best for them to experiment from there to find what suits them best.

Subject: RE: Guitar string tension v guage
From: Strollin' Johnny
Date: 12 Oct 04 - 08:07 AM

Malcolm Newton (he of 'Newtone' hand-made strings, which are as good as it gets) says that the important factor in the 'correct' string for a given tuning is diameter of the core wire, nothing at all to do with the overall gauge (check out the 'Newtone Strings' website if you thing I'm talking shite!).

I use his Open 'C' strings which are standard gauge lights (12-53) but which have a heavier core and are wound with lighter wrapping wire. Result - a set of strings tuned CGCGCE which have exactly the same tension as, and feel just like, a standard 12-53 set tuned EADGBE. Marvellous!

Warning - because they feel like standard strings you need to keep in mind that they're not standard, and resist the temptation to tune them up to DADGAD or EADGBE! Ouch!

Subject: RE: Guitar string tension v guage
From: GUEST,Redhorse at work
Date: 12 Oct 04 - 08:44 AM

Slacking guitar strings for flying isn't about baggage handling (though it would help), i'ts about temperature. Aeroplane holds tend to be unheated, so the strings will try and shrink. Since the guitar stays the same size, they can't shrink, the tension goes up, strings break or guitar bends. That's the usual argument.
On the other hand, if the guitar has a steel truss rod, I suspect the neck length would also shrink , so you wouldn't need to slack the strings. Mind you I've never heard anyone recommend slacking the truss rod before flying.
Any luthiers out there who can advise on this one? ( Other than the obvious advice of not putting guitars in aeroplane holds! )

nick

Subject: RE: Guitar string tension v guage
From: GUEST,Grab
Date: 12 Oct 04 - 02:47 PM

Coincidentally Johnny, I emailed Malcolm Newtone about the exact same thing! I'd noticed that on his mandola strings, the D string in the "medium" set was a thinner gauge than the D string in the "light" set, so I wrote to ask him what the deal was with that. That was his reply to me too - the difference is more in the core, so all wound strings of the same gauge are not created equal as far as the tension to get them up to a particular note goes.

Graham.