How comes that some brands (like, for example, Worth and Oasis) offer the same unique fluorocarbon string set for either soprano, concert or tenor ? How can a string work properly for a 13 inch scale and a 17 inch scale? I guess that such strings will have high tension on a soprano and low tension on a tenor. To add confusion: D'Addario, instead, offer a fluorocarbon set for soprano and concert, and a different fluorocarbon set for tenor. But...the strings diameter is exactly the same on both sets.
Can someone help to me to understand? Thanks.
You have two questions. But first the the three line review I always give myself on this:
Frequency is:
inversely proportional to string length -> shorter string means higher pitch
proportional to square root of string tension -> higher tension means higher pitch
inversely proportional to square root of string density -> thinner string means higher pitch
So if you want the same note with the same string with the same tension on a tenor and soprano, you will be shortening the length of the string by about 13/17ths on the soprano which means it will have a higher pitch. So you must LOWER THE TENSION ON THE SOPRANO TO GET THE SAME NOTE AS THE TENOR.
Another way of looking at the above is to take a tenor G string and fret at the 5th fret which makes the length about the 13 inches, which is the length of a soprano, and gives the higher note (C) that will only become a G by decreasing the tension on the string.
Regarding D'Addario, since they make their own strings, I would guess they can change the density while still keeping the diameter about the same. That's just a guess on my part.
Finally, In the past, I've had some of the same thoughts as you, but with Tenor and Concert ukes using the same strings. However, I don't think about it much anymore because I noticed that Kamaka and LaBella use the same diameter string for their A and high G strings. I then realized that the G at the second fret (an A note) on a tenor is about a Concert length, and I can't tell much difference in the tension between the G string and the A string on the tenor when playing.
I hope this helps and the last paragraph isn't too confusing.