Tension List for Ukulele Strings

Ed1

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Thanks to mimmo from Aquila for giving the formula that let me calculate the tension of various strings that weren't listed here in the past. The URL below will take you where I have put the pdfs for the tension calculation.

I'm fairly certain that the math for the various tensions is accurate, there could be typos in the rest of the spreadsheet. I have double checked my original and found many errors/changes to the strings which I have corrected here. If you see any errors, please let me know. Also, if you can add a few strings (name, type, and diameter in inches) let me know that and I'll add it to the final version of the spreadsheet.

Go to http://ed1.cc/Ukulele/StringTension to get the tension list and information.
 
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Wow! Ed, that's a lot of work! Thanks for doing it.
 
Thanks Ed...geez, my eyes hurt now though! At least I think I can see the strings I have now compared to the ones I want next time I restring!
 
Why does the phrase "It was my understanding that there would be no math....." come to mind? Nice work.
 
Thanks Ed! Already printed out and tacked on the wall of my uke area for quick reference.
 
I have changed the images on the first post. There were many errors and updated diameter changes that needed to be made. If you printed the images, you may want to do it again with these new, corrected images.
 
Everyone: Please check out the First Post. I created a PDF and removed the almost impossible to read jpgs. Since the URL will always be in the first post, the PDF will be easy to update and find.

Mimmo: I'm curious why my tension numbers are different than yours. They're not that different - but they are different.

I use the lengths of 13,15,and 17 inches for soprano, concert, and tenor. The p(rho) numbers are titanium 1.08 nylon 1.04 nylgut/new nylgut/supernylgut 1.3 fluorocarbon 1.78

Here's an example of the new nylgut soprano A string in excel. As you can see, I wanted the final tension to be in Kg.
(POWER(440,2)*POWER(13/39.37008,2)*POWER((0.0236*25.4),2)*1.3/3122)

In the big picture, it's not that important as long as I'm using the same (assuming it's correct) formula for every string. However, if there is something I can do to improve it, please let me know.
 
You have no idea how many years I've been looking for just this! I don't have the math skills to do it for myself, and as far as I know, you're the first one to get it done. Bravo!!!
 
the numbers are different because probably you have old production datas.
Over the years we have done some improvement in the research of a better tension balance.
These ones are the very recent and definitive measures. These tables are of a week ago or so on.
Mimmo
 
the numbers are different because probably you have old production datas.
Over the years we have done some improvement in the research of a better tension balance.
These ones are the very recent and definitive measures. These tables are of a week ago or so on.
Mimmo

That's probably the reason. So, using your formula for tension with the string sizes for s/c/t being .35, .38, and .43 I was able to get all my calculated tensions from your diameters to within half of one per cent of your tensions by changing either the overall density (rho) or constant by 5% or -5%. That means a rho of 1.36422 or a constant of 2973 (Take your pick; I have no idea which way to go. :) )

Overall it doesn't matter much for my chart because the numbers are relative to each other and to slightly different string lengths. But is was a good exercise for me. Thanks again for the formula and the help.
 
Thanks ED1 but....
but consider, generally speaking, that all these are not the real tensions one find when the strings are installed.
The real tension is when on takes the gauges when they have finished to settle up in tune and to stretch: the gauges becomes thinner.
But they becomes thinner in different manners: the 1st and 4th has the higher stretch factor, then the 2nd string and then the 3rd. here is explained why the tensions in theoretical way has a scaled profile. When they settle up in tune the slope drop following more or less an equal tension profile that it is also an equal feel of tension profile, that is the right one.

All the strings must give the same feel of tension between them.

Nobody consider this thing. For example: our nylgut theoretical tensions can seems to be higher than those of other brands than employ nylon strings.

But Nylgut stretch twice than nylon strings so, at the end of the day, the real tension is more or less those of nylon sets.

Mimmo

Yes, I have considered the 'stretch factor' when I have designed all our sets.
 
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Great explanation. It's clear and explains a few things about the different numbers, especially why I had to change things to make it fit with others.

So, while your formula might give slightly lower tension for some strings than the tension found before they settle in, the tension from a certain diameter that shows in my list using your formula might turnout to be the best overall way to do a list like this; The string does get a little thinner and therefore less tension when settling in compared to the other tension numbers.

So, I'll keep updating the list as it stands (using your formula with given diameters) and keep giving the advice to folks to try different strings to find what they like. In the end, it's always about what one likes in both sound and playability.

Thanks again, Mimmo for the info.
 
I updated the pdf with a few more strings and corrected the Seaguar Blue and Premier sizes. Now the tensions for each string are across all sizes with the string makers' recommendations in bold. Please let me know if you find any errors.

http://ed1.cc/755/UkuleleStringTensions.pdf
 
I'll admit to not really having considered string tension objectively until very recently. Since I am no longer able to source the strings I've been using for years, I've been pointed to Uke Logic, which offers a Soft or Hard Tension option. According to this chart, the Soft Tension is higher than the Hard Tension.

When I checked the string diameters listed against those at HMS at found them to be pretty far apart from those on the chart. The diameter for the Hard Tension strings is listed as larger than the Soft Tension, while this chart shows them to be smaller. It seems that if the strings are made of the same material, the larger string would be at higher tension.

To be fair, I should leave room here for the possibility that I am misunderstanding the whole thing. I think I'll order one set of each and just approach the comparison subjectively. My fingers and ears will probably tell me the answer pretty quickly!
 
niwenomian, thanks for catching the mistake. I worry that there could be some others like that. Early on I had a lot of bad data, but lately I think it's also my late night typing that's the problem. I fixed the uke logic size numbers. If you see anything else, please let me know.
 
Thank you this is quite interesting. I am surprised about how poorly balanced some of the sets are. It seems that the E string often has lowest tension of the set whereas the G and A strings are very high in several sets, which likely causes a more treble oriented sound. For future string purchase I would highlight s the sets that have consistent high tension across all strings, seems like around 5kg seems desirable for tenor.
 
One more revision. I added the Martin Polygut sets. I removed the Romero strings because I couldn't find a place to double check them and the size numbers for the same name didn't make sense.

At this time, for the A string, the Worth BL/CL fluorocarbon is the thinnest and the LaBella 100 Uke-Pro Nylon is the thickest.

http://ed1.cc/755/UkuleleStringTensions.pdf
 
I appreciate the work done here, but I have to admit I am struggling with some of the data. For example, the list shows the tenor A string for Martin M620s as having a higher tension than the Worth Clears - but I can't imagine that is the case. I use both strings regularly - switching them on and off many tenors. When strung on a uke, the Worth A string has noticeably higher tension than the Martin. Am I missing something here? Does the tension calculations take the density of the strings into account?
 
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