Strings String Tension Spreadsheet

Ed1

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Please take a look at http://ed1.cc/Ukulele/StringTension/
That will take you to the pdf of the string tension spreadsheet I did a few years ago.
If anyone is interested in the spread sheet in excel format, pm me.

I'm about to close down the website in 10 days, so if you want the excel file, you might want to look at the URL above to understand it better.

P.S. You might also be interested in http://ed1.cc/Ukulele/Pineapple/Creation.html which shows David Hanson's creation of my soprano pineapple which is tied with my Kamaka for my favorite soprano.
 
I found this info very useful a while back, and I hope you don't mind, but since you're dropping that web page... I thought I'd copy the info here. The PDF is attached, and the descriptive content of the web page is below. You could probably attach the Excel file here, as well. If it chokes on the PDF, you could probably attach it as a zipped file. Thanks for your efforts!

UkuleleStringTensions.pdf Explanation​

The Tension that is bold is the uke size recommended by the manufacturer for that string set.

There are two approaches in this table for string tension:

The first approach is the tension listed by the manufacturer is highlighted in yellow. This allows the other size ukuleles to be calculated by the following (Currently this is true only for Aquila and D'Addario):
  • Going from soprano to concert multiply by 1.33136
  • Going from concert to tenor multiply by 1.28444
  • Going from soprano to tenor multiply by 1.71006
  • Going from concert to soprano multiply by 0.75111
  • Going from tenor to concert multiply by 0.77855
  • Going from tenor to soprano multiply by 0.58478
The second approach is to use the string size, when only that is given, with the formula:
  • tension = (Frequency2 * Length2 * diameter2 * density2) / 3122
  • Unfortunately, the densities of any one type of string may be slightly different and the constant my not be completely accurate.
The ”% Tension of Column Max” picks out the highest tension number in the column and gives it 100% and then gives the rest of the column the % ratio to that 100%. The colors go from the lowest tensions in dark green to the highest (100%) in bright red.

The problem with needing two approaches for string tension is that the “% Tension of column Max” may not be accurate for all strings. The idea of this column was that you could look down a column for a string (the “G” string for example) and see visually how the tensions related for all manufacturers of that string. However, at this time the only ones that would be completely accurate to compare would be the Aquila and D’Addario strings where the tensions are highlighted in yellow. Also, tensions are probably incorrect for other tunings than C6, and wound or low-G strings.
 

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I found this info very useful a while back, and I hope you don't mind, but since you're dropping that web page... I thought I'd copy the info here. The PDF is attached, and the descriptive content of the web page is below. You could probably attach the Excel file here, as well. If it chokes on the PDF, you could probably attach it as a zipped file. Thanks for your efforts!

UkuleleStringTensions.pdf Explanation​

The Tension that is bold is the uke size recommended by the manufacturer for that string set.

There are two approaches in this table for string tension:

The first approach is the tension listed by the manufacturer is highlighted in yellow. This allows the other size ukuleles to be calculated by the following (Currently this is true only for Aquila and D'Addario):
  • Going from soprano to concert multiply by 1.33136
  • Going from concert to tenor multiply by 1.28444
  • Going from soprano to tenor multiply by 1.71006
  • Going from concert to soprano multiply by 0.75111
  • Going from tenor to concert multiply by 0.77855
  • Going from tenor to soprano multiply by 0.58478
The second approach is to use the string size, when only that is given, with the formula:
  • tension = (Frequency2 * Length2 * diameter2 * density2) / 3122
  • Unfortunately, the densities of any one type of string may be slightly different and the constant my not be completely accurate.
The ”% Tension of Column Max” picks out the highest tension number in the column and gives it 100% and then gives the rest of the column the % ratio to that 100%. The colors go from the lowest tensions in dark green to the highest (100%) in bright red.

The problem with needing two approaches for string tension is that the “% Tension of column Max” may not be accurate for all strings. The idea of this column was that you could look down a column for a string (the “G” string for example) and see visually how the tensions related for all manufacturers of that string. However, at this time the only ones that would be completely accurate to compare would be the Aquila and D’Addario strings where the tensions are highlighted in yellow. Also, tensions are probably incorrect for other tunings than C6, and wound or low-G strings.
Hi, amazing work on the chart! One thing is confusing me. There are several cases of a lighter guage string set of the same model having more tension than a heavier guage. For example with the Super Nylgut the 100u Soprano Set has higher tension than the 103u Concert Set despite being a smaller guage set. There was another case like that i cant remember. Is this a misprint or mistake? Thanks Alot

Edit. I think i see what might be goung on with the Daddario set. Daddarios listed tensions for the Soprano set are for a higher tuning of A D F# B. I suppose that might be whats going on with the Aquilas though i cant find that info published.
 
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I wrote that post a year ago, and it was info that I COPIED from a website that was being taken offline. Not my work. Can't answer your question definitively.

But, without looking. You're asking why a particular string has a different tension on a Soprano vs a Concert. Physics. To bring a string up to a particular note or frequency requires more tension on a longer scale instrument.

As noted in what you quoted: tension = Frequency squared * Length squared * diameter squared * density squared... all divided by 3122.

Notice that it's all a function of the length of the string squared. The difference in length between soprano and concert is significant. That's probably what you're seeing. Just a guess.
 
Hi, yeah i realize it wasnt your work. Shouldnt have bothered you with it. And what i was saying is that there is a mistake with several sets where the lighter guage set is having more tension than the heavier guage set of the same model for the same scale length. Where it should be the opposite. I see why in the case of daddario ej65 where their soprano set tensions are listed by daddario at a higher tuning than standard. So that threw off the numbers in the sheet. I just checked with EdC in another thread. Sorry for your time and thanks again for the spreadsheet.
 
Hi, yeah i realize it wasnt your work. Shouldnt have bothered you with it. And what i was saying is that there is a mistake with several sets where the lighter guage set is having more tension than the heavier guage set of the same model for the same scale length. Where it should be the opposite. I see why in the case of daddario ej65 where their soprano set tensions are listed by daddario at a higher tuning than standard. So that threw off the numbers in the sheet. I just checked with EdC in another thread. Sorry for your time and thanks again for the spreadsheet.
Maybe it was a copying error. I think that the approach was to use the included gauges, scales, and frequencies with established formulae that use the density of string materials in a consistent way. This was then also validated against tensions posted by manufacturers. So if the same calculation was done then it should be consistent. However if manufacturer information was copied in for some sets then there is a potential source of error.
 
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