String and note relationship

[bcdon***]

Is the note that a string plays only a function of its tension? In other
words, could you use a single string gauge (assuming it doesn't just
break) for every note on the guitar? The reason I ask is that I was
looking at this 7-string guitar http://www.rondomusic.com/product3192.html
and it is setup like this:

String Gauge: 009, 011, 016, 024, 032, 042 and 056. Setup tuned to B, E, A, D, G, B, E

Sorry for the newbee question.

don

[Ch0jin]

Not quite.

When you pluck an open string it will vibrate at it's resonant frequency.

A strings resonant frequency is determined by it's Length, Mass, and Tension where Length is the distance from nut to bridge. Mass is string gauge, and Tension is your tuning peg adjustment.

On your guitar, Length is a constant, as is Tension.

(note: technically these values aren't constants as your string length will vary slightly as a result of saddle adjustments for intonation, and tension will vary slightly with tuning, but for the sake of explanation, they are close enough to constant)

So if there are three factors that determine resonant frequency and two of them are fixed, that leaves your string's mass, or "gauge" as the only variable.

Therefore, without some sort of serious redesign, I don't think it possible to use all the same gauge of strings on a guitar.

You'd end up with some kind of variable scale length and/or a gradual increase in tension from string to string which would tend to want to warp the neck I'd think.


Does that help?

Also the math isn't that hard (if I have it right that is)

- An E string vibrates at 82.4Hz and its buddy the A string vibrates at 110Hz
- If you double the Length, you halve the Frequency.

So if your E and A were the same gauge and the same tension, lets see what the scale would look like.

If we start with a "standard" LP scale length E string of 628mm (thats 24.75'' for you heathens) and we calculate that 110Hz is close as custard to 25% higher in frequency than your E.

Therefore we can extrapolate that to gain 25% in F we need to reduce the L by 25% resulting in a scale length of only 471mm (18.54") for the A string.

If you carry that formula on up the strings, you can quickly see just how impossible this would be on a traditional guitar shape.

[Plank_Spanker]

I'm no luthier or guitar physicist, but the notes are a function of tension and string length for a given tension. The reason you can't use just one string gauge is that the lower strings use less tension and need a be of heavier gauge in order to be playable. Imagine an E (1st) string used in the E (6th) position........................it would just flop around.

That 7 string setup is fairly typical. You need a beefy gauge string in the 7th position to keep it playable.

I hope this makes sense, and maybe someone else here can explain it better.


EDIT......looks like ChO has chimed in with the good word.

[bcdon***]

Not quite.


Does that help?

Also the math isn't that hard (if I have it right that is)

- An E string vibrates at 82.4Hz and its buddy the A string vibrates at 110Hz
- If you double the Length, you halve the Frequency.

So if your E and A were the same gauge and the same tension, lets see what the scale would look like.

If we start with a "standard" LP scale length E string of 628mm (thats 24.75'' for you heathens) and we calculate that 110Hz is close as custard to 25% higher in frequency than your E.

Therefore we can extrapolate that to gain 25% in F we need to reduce the L by 25% resulting in a scale length of only 471mm (18.54") for the A string.

If you carry that formula on up the strings, you can quickly see just how impossible this would be on a traditional guitar shape.

What a great explanation, thanks! I had been thinking of gauge simply as diameter thickness, totally forgetting about mass. And the maths is fun too (as is the heathen crack!) Thanks again!!

don

[bcdon***]

- An E string vibrates at 82.4Hz and its buddy the A string vibrates at 110Hz

What are the oscillation frequencies for the remaining notes? And where does the 25% figure come into play? Is that the ratio between notes?

[Ch0jin]

The reason you can't use just one string gauge is that the lower strings use less tension and need a be of heavier gauge in order to be playable.

That's true in part, but my research this morning over a coffee reveals string tension should be fairly uniform assuming your using a matched set of strings rather than a "fat bottom" set or similar.

If your string tension varies too much you risk placing unexpected stress on the guitar. There's some wicked in depth info here actually. Also, having a relatively consistent tension means the strings "feel" similar.

In short they (Noyce Guitars) have done the math, and on a 6 string, your string tension varies from 7.28Kg to 9.03Kg, but importantly, and this is the deal breaker, it's not a linear increase down the strings (which would try to warp the neck) they determined that E has 7.71Kg of tension and e has 7.28Kg. So although the tension does vary a little across the strings, it's kind of spread out.

To see why I refer to a difference of almost 2Kg's as "Constant", you need to see it in context, so I've done the math.

If we were to crank up my magic formula from before this is what happens...

- E to A is a 25% increase in frequency.
- Lets keep the scale Length constant this time.
- It takes 4X the tension to double the Frequency
- Low E is under 7.71Kg of tension, and on a regular guitar, A is under 9.03Kg (which is the largest differential on a guitar actually)

So if 4xT=2xF then (if I got this right) then 2.5T=1.25F.

That means that if you used the same gauge string for E and A, and your E was under normal conditions, your A string, instead of being under 9Kg's of tension, would be under almost 20Kg.

I would definitely be wearing eye protection for that experiment!!!

EDIT......looks like ChO has chimed in with the good word.

Haha, yeah, I was a bit bored this morning.

[Ch0jin]

What are the oscillation frequencies for the remaining notes? And where does the 25% figure come into play? Is that the ratio between notes?

Hi Don, they are, in Hz

Guitar Low E string 82.4
Guitar A string 110.0
Guitar D string 146.8
Guitar G string 196.0
Guitar B string 246.9
Guitar E string 329.6

The 25% is the percentage increase in frequency from 82.4Hz (low E) to 110Hz (A)

(110-82.4)/110 x 100 = 25.1% Increase.

As you'll see if you want to get the calculator out again, not ALL the strings vibrate 25% faster than the one above it, I think I see some 25%'s and at least one 20%. I just used the E and A strings as examples of why we need different string gauges on a guitar.

[Ch0jin]

Also, just for the record. Cask wine is evil. I had three glasses last night and I feel like I polished off a case of beer.

[Plank_Spanker]

The next time a query like this comes up here, I'll just stay out of it and wait for ChO.............................

A very concise expanation that can't be argued, ChO.

[bcdon***]

Hi Don, they are, in Hz

Guitar Low E string 82.4
Guitar A string 110.0
Guitar D string 146.8
Guitar G string 196.0
Guitar B string 246.9
Guitar E string 329.6

Very interesting, thanks!

[Plank_Spanker]

Also, just for the record. Cask wine is evil. I had three glasses last night and I feel like I polished off a case of beer.

Could have been tequila...........................Mas Tequila!

[Ch0jin]

The next time a query like this comes up here, I'll just stay out of it and wait for ChO.............................

A very concise expanation that can't be argued, ChO.

Haha no don't be like that. As I've mentioned before, I'm not really able to offer much in the way of guitar playing advice so I like to dive in headfirst when there's something I actually know something about. In this case I had a vague memory of high school physics that I enjoyed reading up on again.

..and regarding tequila. I Love tequila! Regarding wine though, I would usually spend around $20 on a bottle, but in a moment of weakness I bought a cask (4L) for $15 (reputable brand and all). Now I know WHY it was so cheap. It was clearly contaminated with headaches.....


Also to Don, I wouldn't call your initial question "noob". I'd suggest there are quite a few guitar players who would stumble over the answer to your question.

[poodlesrule]

This thread and answers reminded of an local player I discovered last December, note his 8-string acoustic guitar:

see here

(not sure if this is the right way to link to youtube?)

He is very local to me, and teaches too, I may try to establish contact, for the fun of it.

[Katastrophe]

This thread has officially given my heathen pea brain a headache.