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Short-scale string tension 'scaling' question


My question is at the very end - if you are impatient with keyboard dysentery, just go there...

but if you'd like to know what craziness is driving this experiment, read on without paragraph-skipping...

I am selecting strings for a short-scale 'tenor' that was 'converted' from a baritone ukulele. Aside from being told I can't put 'steel strings' on it...(too bad, that just means I will find a way with more stubbornness...), I have figured out the math confidently enough to realize there are many ways I can do it.

Whether it sounds like garbage (or insert your preferred expletive) or not remains to be seen. I didn't like how it sounded to start out, the string stretching phenomenon and string life on the wound d & g (that's how they accomplish d-g-b-e' tuning), so if I am happier with the result, that's all that matters. It was a lot cheaper than a travel guitar, and I agreed with the argument that it's essentially 'full-sized' for it's range...

...anyway, my question(s)...

The solution to my dilemma involved comparing the string tension on the provided D'Addario EJ87B strings, and studying the string physics...D'Addario has a publication with the sub-title A complete technical reference for fretted instrument string tensions , and provide comprehensive data on nearly all their strings...

Eventually I came to realize that since my ex-uke is for all practical purposes like a classical guitar regarding the pinless glued-on bridge, I just needed to understand what each string's tension 'scales' to on a shorter scale.

I've also run into a guy who builds instruments on the Mandolin Cafe forum, and he liked my logic. We traded some ideas and each had a Plan B to explore & compare.

Basically, I select strings that have appropriate tension on the shorter 20.3" scale. D'Addario claims their string tension for guitars is based on a 25.5" scale. The math shows a scaling factor of (20.3/25.5)^2, so for a string tension at the proper pitch and the shorter scale, I divide the 25.5"-referenced tension by 1.58 (or multiply by 0.634, if easier on your slide rule).

The EJ87B strings at 50.7# would be comparable to 80.0 # on a 25.5" scale and only the top four strings. I've looked at scaling the uneven tension distribution the original strings had, but think that it was probably because they used 'titanium' fluoropolymer on e' and b, and silver/copper/nylon on g & d, and this just results in uneven tension because of the physical difference. I did not like the uneven sound between the two types of strings, but most guitars have a mix of string construction, so that's life, I guess.

I've taken two approaches - a) plain steel top two, and phosphor bronze wound bottom two, and b) all plain steel. I'm really leaning toward balanced tension on each string, and just read a recommendation to do this on someone else's site...

All this micro-study led me to the realization I can just look for standard guitar strings with 20# tension at 25.5" scale, and at 20.3" I get 50.7#. I now have several 'signature' string sets to choose from.

Finally, the question*:

While D'Addario says all their published guitar tensions are for 25.5" scale, when I went to look at their EJ83 gypsy family of strings, something is odd...PL010 and PL011, apparently the same strings used on other instruments, have somewhat higher published tension in the Gypsy series. At first I assumed there was no such 25.5" scale Gypsy guitar, but I think that's irrelevant...they are 'normalized' to 25.5" for a uniform way of specifying them.

What I think may be present in the Gypsy string tension specification is that the floating bridge and (mild) archtop trait vs. a flattop results in a longer string 'path' on the gypsy guitar for the same 'theoretical' scale length on a flat top.

Looks like I can only (directly) select by scaling EJ83/84 strings for the top two anyway...the next two lower pitches are far too high in tension in the Gypsy set to comply with my self-imposed target of not exceeding the original uke string set tension.

*Anyone have an opinion about why the tension for a plain steel string in a Gypsy set is higher than for other guitars in the D'Addario charts? EJ83M PL011 for e' = 21.04#, and PL011 in other guitar sets have a tension of 19.6#. Maybe the EJ83/84 PL011 isn't really plain steel, but they imply it is. I don't think there is any implied difference for 'electric' guitar strings based on the type of instrument. I'm reluctant to say there is an error in the data...I think I just don't understand something. I did ask D'Addario early in this effort for some suggestions - I think this was a little too far 'outside the box' for the person who got my e-mail.

Thanks for reading this far, those of you who are still awake.

It's been several months and no splinters yet...I also installed a piezo (polymer coaxial) pickup under the saddle and an end-pin jack preamp, so I have to get the setup/action back down where it should be...probably in May.

OK, here are some pics...I don't really want this to be the permanent place for them, but it works for now...


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