I solved my sopranino string problem more simply than I expected – I just put new strings on it. Regular soprano strings, Aquila. And it sounds great, with the typical ukulele GCEA tuning! That was a great relief to me. I had thought it needed special strings or a special tuning to sound good.
I’d like to find better strings for my sopranino ukulele, which is a bit smaller than the usual soprano ukulele. With the soprano strings currently on it, if I use the most common ukulele tuning (GCEA), the strings are a bit slack and it doesn’t sound good. If I tune it up a step (ADF#B), it sounds good but I have to mentally transpose everything.
I found a luthiers’ formula that gives the relationship among tension, frequency, length, and mass of the string. I ought to be able to achieve a more typical tension at the common frequencies by using slightly bigger strings (more mass).
I spent some time last night on this. Aquila provides data on the tension and diameter of their soprano ukulele strings. From the tension and frequency and my ukulele’s scale length, I could compute the mass of the string; then using the diameter, I could work out the density of their string material. From all that, and the shorter scale length of my sopranino ukulele, I could work out what diameter string I ought to need.
I found data from another string manufacturer, D’Addario, on the weight per unit length of all the strings they sell, which ought to let me work out if some of their strings would work too.
Then I woke up this morning and realized something: strings stretch. So the mass of a given length of string depends on its tension and how much it stretches. And none of this data takes that into account. Drat!
I’m afraid I’m going to have to resort to trial and error, which really bugs me when it seems I should be able to work out the right strings and just go buy them.