Double Bass Calculating string tension differences

[DoubleMIDI]

Here are my formulas for recalculation of string tensions.
Due to stretching of the core reality might differ a bit from idealized calculation, so take it with a grain of salt.

Tension for a detuned string:
Retuned_Tension = Normal_Tension * ((2 ^ (Detune_Halftones / 12)) ^ 2)
(Negative number for Detune_Halftones for tuning down)

String length dependent tension:
New_Tension = Measured_Tension * ((New_Stringlength / Measured_Stringlength) ^ 2)

Interval dependent constant tension stringlength:
Endlength = Startlength / (2 ^ (Tempered_Halftones / 12))

Custom tuning deviation from 440 Hz:
Halftone_deviation = LOG(A_tuning_freq_Hz / 440) / LOG(2) * 12

Probably a candidate for a sticky...

 

[DoubleMIDI]

Just to explain the string stretching influence a bit more:

Everybody who has mounted strings themselves knows that, depending on the string, there is a lot of winding needed to get the string to pitch. But the string also stretches with tuning up, so gets longer under tension.

But that also means that the constant mass is now distributed over a greater length getting less mass per length unit. Less mass per length unit needs less tension to get it to pitch. So the calculated tension for a string tuned up is higher than on reality.

The amount of the difference is depending on the stretch factor of the string. Low for solid steel cores, a bit higher for spiral steel cores, significantly more for synthetic core strings and gut core strings, also depending on material and diameter of the core.

The stretching might also explain why the windings separate on stretchy (synthetic core) strings. The windings separate from its neighbor a very little bit with the stretching of the core. If they were moved close to its neighbor a gap that gets larger and larger as more windings move close to their neighbors can develop.
This is because not only the core stretches and moves past the nut but also the windings do.
So not only the mass from the core gets reduced but also the mass from the windings when the string passes the nut when tuned up.

Of course, some string comes from the afterlengths into the vibrating string area, the reason why the bridge is leaning towards the fingerboard if not compensated when tuning up. But it is less than what vanishes past the nut.

And don't forget: the whole tension is on the core only, the windings only add mass and make the string more flexible (and may add some damping) than a string with the same mass and a thick core.

 

[drurb]

Thanks for this, DoublMidi! Definitely "sticky worthy."

 

[DoubleMIDI]

I just added a calculation from a different tuning frequency to 440 Hz for the A. Result is in halftones.
You can use this if you find data for a different tuning to recalculate the tuning difference to 440 Hz.

If you want to calculate from 440 Hz to a different tuning, just swap plus and minus for the halftone result (or exchange the tuning frequencies inside the LOG function.

BTW, you can use a Log function to any base (E, 10, 2, whatever) as long as you use the same base for both Log function in the formula. That way you can use any calculator, even if you don't have a log function with a specifyable base.

 

[martinc]

I just added a calculation from a different tuning frequency to 440 Hz for the A. Result is in halftones.
You can use this if you find data for a different tuning to recalculate the tuning difference to 440 Hz.

If you want to calculate from 440 Hz to a different tuning, just swap plus and minus for the halftone result (or exchange the tuning frequencies inside the LOG function.

BTW, you can use a Log function to any base (E, 10, 2, whatever) as long as you use the same base for both Log function in the formula. That way you can use any calculator, even if you don't have a log function with a specifyable base.

double: I decided to reduce the tension on my bass a bit. For my wrists and for my bass. So I replaced the 3885 3/4 Spiro Weich A and D with 3/4 Weich S 42's .....and the Zyex Medium G with a Zyex Light G. The Mittel E stays.
I am very pleased with the results. There is a drop in tension, an improvement in the feel and the bass still has a full sound.

So if I need to quantify/justify what I have done to anyone, it looks like your mathematical formulae will help.

However I am somewhat mathematically challenged when it comes to using formulae. So I must confess it was an earlier post by you stating that the S42's would reduce the tension about 1-3 kgms from the 3885's on my 3/4 bass......that made me spring for the S 42's. Thanks!

 

[DoubleMIDI]

So if I need to quantify/justify what I have done to anyone, it looks like your mathematical formulae will help.

However I am somewhat mathematically challenged when it comes to using formulae. So I must confess it was an earlier post by you stating that the S42's would reduce the tension about 1-3 lbs from the 3885's on my 3/4 bass......that made me spring for the S 42's.

I was thinking about putting these formulas into a web page, but my own stuff is not always reachable since it stays on my server at home which gets a bit old and also my internet connection gets dropped sometimes.
If I find some time (which might take a while) for making a web page I may put it on my site and probably send it to the Talkbass administrators (if I cannot integrate it into a posting) for publication here. But some more formulas might help in some cases, so I might need to add something. Maybe during the Christmas holidays.

You reminded me that there are some standard cases like "how much less tension do I get if I tune Solo strings down to orchestral tuning", that could be part of the formula thread. I just need to think about what would be helpful beyond that.
The reason why I published the formulas and not a black box was that everyone can use them everywhere and at any time, since black boxes locked to a web site can vanish at any time and not everybody has internet access everywhere to access a web page.
For a similar reason we should collect the published tension data of all string manufacturers and silk colors and ball ends (even if they might change) to save this data in case a string might get discontinued or the data gets removed for whatever reason. And we might get a database of silk colors that way that might be searchable for unknown strings. I started this by myself getting some data out of a German DB string database and manufacturers data but stopped that when I started measuring my own strings, since that was more interesting to me. And that way we got the data for the Lycons that I measured a few months ago.
Now I don't have the spare time I had before, so it might even take some years before I can continue with that.

But finally I'm happy that I could help you with that old posting. As you can see it makes me think how that formula stuff could be made a bit more user friendly.

 

[DoubleMIDI]

I have just corrected the "Interval dependent constant tension stringlength"-formula.
I did get a shorter string length for a lower pitch before, now it is correct (lower pitch: longer string length).
FYI, I just replaced the multiplication after Startlength by a division.

Currently I'm testing the calculation and conversion formulas with JavaScript and may add it later here if possible, so you don't need to enter the formulas then, only your values in the right boxes. (Currently it works, but doesn't look nice, so I want to change that.)

 

[martinc]

Double:

I think your suggestion for a set of tables for string tension etc. would be a huge service for the double bass world.
It might also get the manufacturers to think more about their descriptions. "Medium" or "Light" tension is just not enough in this age of mixing strings. Especially when there is no standard for what defines "Medium" or "Light"!

 

[DoubleMIDI]

Currently I'm testing the calculation and conversion formulas with JavaScript and may add it later here if possible, so you don't need to enter the formulas then, only your values in the right boxes. (Currently it works, but doesn't look nice, so I want to change that.)

I forgot to mention here that the JavaScript calculation page "formulas.html" is available for public download here:

Talkbass - Dropbox

Just take any web browser with JavaScript enabled and open the file with it.

Feel free to take the other stuff from there too and pass it on.

I could have put it on a web server, but by downloading it it won't get lost as easily as it happened with the baen.tamu.edu string chart that I reconstructed and corrected (only the more important 105 cm chart, the 110 cm chart was full of errors due to a wrong recalculation formula anyway) and that could be found there too. You can also take it with you if you are offline.
The only place I wanted to have the formula page for immediate access is TalkBass, but I couldn't manage that yet.