String tension - a little help needed

Construction and repair of Classical Guitar and related instruments
tkoehler1
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String tension - a little help needed

Post by tkoehler1 » Fri Aug 11, 2017 3:39 am

Not sure where to post this.... seems like a good spot.

I have a 650mm scale guitar with normal tension savarez strings on it. I tuned it down a half step and I really like the resulting string tension. A little easier to fret and a better feel (for me).

My question is: at 65cm down a half step with normal tension, is that equivalent to say, normal tension normal tuning 640 scale? Or 630? Something in between?

I'm wondering if there is a way to calculate the total pull of the stings down a half step and compare to the other scales.

Thanks for any help,

TK

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guitarrista
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Re: String tension - a little help needed

Post by guitarrista » Fri Aug 11, 2017 4:10 am

String tension is proportional to the square of the frequency (well, the frequency is proportional to the square root of the tension).

So if T1 is the string tension at 440 Hz standard tuning, and you tune down half a step, equivalent to A=415.3 Hz tuning, then:

T2 = T1*(f2/f1)^2, or about 11% lower tension (89% of the original).

If you want to compare to the changes in tension for shorter scales, since tension is also proportional to the square of the scale length, i.e. T2 = T1*(L2/L1)^2, just note that L2 = L1*(f2/f1).

This means a guitar would have to have a 613.5mm scale to have the same 11% lower tension as that from tuning a semitone down.

A 640mm scale guitar would have 3% less tension; 630mm scale guitar would have 6% less tension.
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souldier
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Re: String tension - a little help needed

Post by souldier » Fri Aug 11, 2017 1:46 pm

I think it is important to remember there are multiple factors that determine the feel of the strings. For example I currently play on a 660 scale guitar, yet I have found it to feel softer on the left and right hand than a 630 scale guitar that I recently played, even if the 630 scale guitar had less tension.
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soltirefa
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Re: String tension - a little help needed

Post by soltirefa » Fri Aug 11, 2017 2:47 pm

souldier wrote:
Fri Aug 11, 2017 1:46 pm
I think it is important to remember there are multiple factors that determine the feel of the strings. For example I currently play on a 660 scale guitar, yet I have found it to feel softer on the left and right hand than a 630 scale guitar that I recently played, even if the 630 scale guitar had less tension.
So true! I have short scale guitars with light tension strings that feel taut to the left hand and longer scale guitars with extra high tension strings that feel easy on the left hand. I think the guitar's top has a lot to do with it.

Imbler
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Re: String tension - a little help needed

Post by Imbler » Sat Aug 12, 2017 1:19 am

well, it is easier to fret the farther you are from the fixed points (nut and saddle), so long scale has higher tension but perhaps easier fretting because frets are farther from the nut?

tkoehler1
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Re: String tension - a little help needed

Post by tkoehler1 » Sat Aug 12, 2017 6:00 pm

guitarrista wrote:
Fri Aug 11, 2017 4:10 am

This means a guitar would have to have a 613.5mm scale to have the same 11% lower tension as that from tuning a semitone down.
Thanks for the responses and thanks for the technical explanation guitarrista. I don't quite follow the math but I respectfully think that it may be incorrect. I would think if I put those strings on a 61cm guitar they would be far more loose and floppy. I admit I can't prove it but that's my feeling :D Normal tension on my 630 are too loose and they get a little buzzy.

Unless as people have mentioned, there are other factors that have a greater impact than I think.

Also I've noticed a few guitars out there with 645mm scales, I never paid much attention as to why they were built to that scale, now I wonder if they are after that same feel.

Last and even more odd I think the guitar sounds better tuned down. The same volume but richer, fuller sounding.

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petermc61
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Re: String tension - a little help needed

Post by petermc61 » Sat Aug 12, 2017 9:13 pm

It think it more likely the maths is correct but you don't understand how to apply it to your case.

Paul Micheletti
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Re: String tension - a little help needed

Post by Paul Micheletti » Mon Aug 14, 2017 9:36 pm

You might also consider other makes of strings. I've been running D'Addario EJ45 (medium) strings on my 645mm guitar, and recently changed to Savarez Corum 500CR (medium) strings. My left hand feels almost like I switched to low tension strings compared to the D'Addario strings. The wound bass strings in particular are much easier to fret.

The sound has unfortunately dropped off as well. I'm keeping these Savarez strings for now as I'm learning songs with more barre chords now and they were killing my left hand. I can play a bit longer with the Savarez each session. Tone is much less important to me right now than pain.

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attila57
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Re: String tension - a little help needed

Post by attila57 » Mon Aug 14, 2017 11:09 pm

tkoehler1 wrote:
Sat Aug 12, 2017 6:00 pm
guitarrista wrote:
Fri Aug 11, 2017 4:10 am

This means a guitar would have to have a 613.5mm scale to have the same 11% lower tension as that from tuning a semitone down.
Thanks for the responses and thanks for the technical explanation guitarrista. I don't quite follow the math but I respectfully think that it may be incorrect. I would think if I put those strings on a 61cm guitar they would be far more loose and floppy. I admit I can't prove it but that's my feeling :D Normal tension on my 630 are too loose and they get a little buzzy.

Unless as people have mentioned, there are other factors that have a greater impact than I think.

Also I've noticed a few guitars out there with 645mm scales, I never paid much attention as to why they were built to that scale, now I wonder if they are after that same feel.

Last and even more odd I think the guitar sounds better tuned down. The same volume but richer, fuller sounding.
Hi tkoehler 1,

Even if you use the same strings, at different scale lengths the feel will be different, because feel depends on tension and scale length, too.

7 kg tension feels fine at 650 mm scale length, but feels too much at 432 mm for instance. It is because feel phisically means the force you have to push the string sideways.

To understand this force one must consider that the shorter the scale, the fewer are the elastic particles in the string. The total elastic stretch of the string is the total of the elemental stretch units of these particles. A shorter string has less elastic particles, therefore less stretch and so less yield to your fingers. Mathematically written, sideways force is proportional with the reciprocal string length (1/L).

This is exactly why guitaleles are tuned to A. As their scale is 432 mm, which is 2/3rd of the normal 650 mm, with the same string tension (7 kg) they should be tuned a fifth higher, to H, not A. (2/3rd string length is the 7th fret, i.e. the fifth diatonic step.) Still, if you tune a 432 mm guitalele up to H, you'll feel that its strings are too tight. This proves that feel - sideways pushing force - is inversely proportional with the scale length. With calculations it can be shown that if you reduce scale length to 2/3, the sideways force remains the same if you tune it to a fourth diatonic step higher instead of the fifth. Lengthwise pull of 432 mm guitaleles is only about 6 kgs, still their feel is the same as a 650 mm guitar at 7 kg pulling force.

As you'll just see, in reality, the situation is a bit more complicated.

Let's consider the string sections that are close to the saddle. The string pulling force there is the same as it is in the middle of the string. It is because longitudinal force spreads evenly along the unimpeded string. Still, if you want to push it sideways, or pluck it near the saddle (or nut), it will feel very tight and difficult to pluck, not so nice and soft as in the middle. Why? Because you must consider both sides of the string, i.e. both directions from the place of plucking. As the string is very short to one side, the elastic length in that direction is short, so the sideways pushing force is bigger than in the middle of the string.

Attila
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Sweets with sweets war not, joy delights in joy...

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tkoehler1
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Re: String tension - a little help needed

Post by tkoehler1 » Tue Aug 15, 2017 1:01 am

Thanks Atilla that makes sense! it's trickier than It looks.

I played for a bit tonight, I really like the sound and feel a half step lower. That will be my new normal.

Long term (like when I commission my first classical) I'm going to have to think about how to get this feel at standard tuning.

tkoehler1
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Re: String tension - a little help needed

Post by tkoehler1 » Tue Aug 15, 2017 1:05 am

I've never liked the feel of strings after putting on a capo either.

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attila57
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Re: String tension - a little help needed

Post by attila57 » Tue Aug 15, 2017 8:16 pm

tkoehler1 wrote:
Tue Aug 15, 2017 1:01 am
Thanks Atilla that makes sense! it's trickier than It looks.

I played for a bit tonight, I really like the sound and feel a half step lower. That will be my new normal.

Long term (like when I commission my first classical) I'm going to have to think about how to get this feel at standard tuning.
Actually, I like drop tunings, too. Some guitars have much better tone in D than in E. My much quoted guitalele is in G instead of A (or H...). And my favourite tuning is C# minor. C#-G#-c#-g#-c#'-e'. You can use it in practice as if it was d minor of course.

BTW half step lower is something like 425 or 430 Hz for middle A, isn't it? No wonder it sounds better to your ear. 440 Hz is too tense for many of us, I think. And half step lower is much more string-friendly, too!

Just be sure to tell the other members of the guitar orchestra before going on stage.. :D .
Music to hear, why hear'st thou music sadly?
Sweets with sweets war not, joy delights in joy...

William Shakespeare, Sonnet 8

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joachim33
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Re: String tension - a little help needed

Post by joachim33 » Tue Aug 15, 2017 8:58 pm

attila57 wrote:
Tue Aug 15, 2017 8:16 pm
tkoehler1 wrote:
Tue Aug 15, 2017 1:01 am
Thanks Atilla that makes sense! it's trickier than It looks.

I played for a bit tonight, I really like the sound and feel a half step lower. That will be my new normal.

Long term (like when I commission my first classical) I'm going to have to think about how to get this feel at standard tuning.
Actually, I like drop tunings, too. Some guitars have much better tone in D than in E. My much quoted guitalele is in G instead of A (or H...). And my favourite tuning is C# minor. C#-G#-c#-g#-c#'-e'. You can use it in practice as if it was d minor of course.

BTW half step lower is something like 425 or 430 Hz for middle A, isn't it? No wonder it sounds better to your ear. 440 Hz is too tense for many of us, I think. And half step lower is much more string-friendly, too!

Just be sure to tell the other members of the guitar orchestra before going on stage.. :D .
415 Hz is a halftone down from 440 Hz.

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attila57
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Re: String tension - a little help needed

Post by attila57 » Tue Aug 15, 2017 9:18 pm

joachim33 wrote:
Tue Aug 15, 2017 8:58 pm

415 Hz is a halftone down from 440 Hz.
OK, thanks Joachim, 415 Hz, I haven't got my frequency chart with me, but it doesn't make much difference. Lower tension to the string and ear alike...

Attila
Music to hear, why hear'st thou music sadly?
Sweets with sweets war not, joy delights in joy...

William Shakespeare, Sonnet 8

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