Chart of string tension as function of length and pitch?

[xnewyorka]

The question: If I am building a custom string set from singles, how can I find out the correct gauges to use in order to have uniform tension across all the strings?

The background: I just bought a cool 4-string custom "bass" (piccolo? alto?) with a 30" scale. It came with strings that look like wound guitar strings (since the ball ends are guitar-size not bass-size.) They measure approximately .020, .031, .041, .052. The seller said it was tuned ADGC, but I found the strings felt slightly loose, and they feel pretty good if I tune it to BEAD (guitar octave not bass octave). To my surprise, I was able to tune it all the way up to EADG without breaking any strings, but it did feel dangerously tight and I couldn't do any bending. While tuned BEAD, I can bend up about 3 half steps, which is a bit more than is ever needed on bass. But I see that as an indication that the strings may be a little loose.

I might like to experiment with tuning the bass BEAD, EADG, or perhaps even ADGC (all in the guitar octave.)


Is there a tension gauge I can buy that I could use to take measurements as I experiment? Or a chart where I can look up tension as a function of length and pitch without needing to actually experiment at all?/

While Googling this topic, I found Curt Mangan strings and I see that I can assemble a custom set with pretty much whatever gauges I want, which is very cool:

SINGLE STRINGS ELECTRIC - Nickel Wound Single Strings - Page 1 - Curt Mangan Fusion Matched Guitar Strings

[Edit: I just spoke with Curt and he suggested 20-30-40-50 or 24-34-44-54 and tuning it BEAD, and said if I wanted to tune it EADG I might need a smooth (not wound) 20 for the G.]

 

[ixlramp]

To understand tension more you can read the introduction here http://www.daddario.com/upload/tension_chart_13934.pdf
Those charts are a little old and may be slightly out of date for D'Addario strings. They are limited to one scale length and are not chromatic
For up an up to date and more flexible D'Addario calculator use String Tension Pro

For a wider range of gauges but roundwound/plain steel only (.008 to .266) you could use the Kalium's calculator Link Removed

A chart or calculator for one brand can be used to roughly approximate tensions for another brand if the string type (roundwound, flatwound, plain steel) is identical

And yes F is the limit for wound strings as a .020 or .022 has a thin core and is fragile at F, above that you need a plain steel.

 

[ixlramp]

First retune until the tension feels right, then use the known gauges and scale to calculate that tension, then use that tension value to choose new gauges for your new desired tuning.

 

[xnewyorka]

To understand tension more you can read the introduction here http://www.daddario.com/upload/tension_chart_13934.pdf
Those charts are a little old and may be slightly out of date for D'Addario strings. They are limited to one scale length and are not chromatic
For up an up to date and more flexible D'Addario calculator use String Tension Pro

For a wider range of gauges but roundwound/plain steel only (.008 to .266) you could use the Kalium's calculator Link Removed

A chart or calculator for one brand can be used to roughly approximate tensions for another brand if the string type (roundwound, flatwound, plain steel) is identical

WOW - this is awesome! This is exactly the type of info I was hoping existed somewhere. Thank you SO much for pointing me to it!

And yes F is the limit for wound strings as a .020 or .022 has a thin core and is fragile at F, above that you need a plain steel.

Are you referring to a 34" scale here? I have a 30" scale. I was able to get it up to G. But I put my safety glasses on first, and I was still wincing as I was tuning it, fearing the inevitable, which to my surprise didn't occur. But it felt mighty tight, a little too tight for comfort, and certainly too tight for bending.

I am wondering how a plain steel will sound.
Here is how the bass sounds when tuned BEAD. I kind of like it, and might just end up sticking with that after I try experimenting to see if I can achieve a nice enough sounding EADG tuning. I am just not sure I will be able to wrap my head around ADGC, since I have only just very recently started playing a 6-string. Then again, maybe playing ADGC would help accelerate my learning the notes on the C string. It sure is a different and unfamiliar world for me on that C string, everywhere on the neck!

 

[lz4005]

Another way of thinking about it is if you have a standard tuned set you like, start with strings half that thick for an octave up.

 

[xnewyorka]

Another way of thinking about it is if you have a standard tuned set you like, start with strings half that thick for an octave up.

That is very interesting! Is that just a coincidence, or does physics predict that?

 

[lz4005]

That is very interesting! Is that just a coincidence, or does physics predict that?

All physics. Just like half the length gives you an octave up at the same tension (ie a note at the 12th fret) so does half the thickness.

 

[ixlramp]

Wow a LeFay, lovely.

Are you referring to a 34" scale here?

Yes, and for roundwound, a plain steel is 'all core' so is much stronger and can go tighter. A roundwound .020 may only have a .010 or .012 core.
The High F in a 7 string set is tricky, some brands use roundwound .020 or .022, some use a plain steel .018 or .020.
A 30" scale is like the 2nd fret on a 34" scale, so tuning your 30" bass to EADG is similar tension to DGCF on 34", so you pushed the wound .020 to the limit.

Yes physics. It is a rough rule i have derived myself:

For 2 strings of equal scale length and equal tension, the gauge ratio will be roughly equal to the frequency ratio.
Frequency ratios are 2:1 for an octave, close to 3:2 for a fifth, close to 4:3 for a fourth.
The rule becomes much more innaccurate if one string is wound and one plain.
The rule is exact for two plain steel strings (because plains have constant density).