I am a guitar player and trying to figure out how a Ukelele is tuned. From what I understand, the Concert, Tenor and Soprano Ukeleles are tuned G4, C4, E4 and A4. So the lowest string is actually higher pitch than the second string. Can anyone explain why this is? Wouldn't it make more sense to have G3, C4, E4 and A4... especially for people who are used to other stringed instruments?
The tuning you mentioned in your question is the standard tuning. There are many string instruments that have octave displaced tunings, called re-entrant tuning, including the banjo (5 string), Cuban tres and even the 12 string guitar.
In the case of the ukulele this gives the ability to play its characteristic close chord voicings not normally available on a string instrument tuned in 4ths or 5ths. For example the open ukulele is a C6 chord with the G and A a 2nd apart. Guitar chords work because the notes are the same as the first 4 strings of a guitar up a fourth.
This is not etched in stone though, tenor and soprano ukuleles can alternately be tuned with a low G as an option and the baritone uke is tuned like the top 4 strings of a guitar.
I think it's a characteristic of the instrument that many of its basic major and minor chords - contain a duplicate note. For example its simplest G major chord (which is the same shape as a guitarist's D major chord) has two G4's in it. Any tiny tuning discrepancy between the open and stopped G4's will give the chord an interesting/charming/irritating quality that is part of its character. But maybe I'm a little mistrustful of the ukelele's ability to be in tune!
Also, btw, I don't think such a low-tuned ukelele string would sound great, but maybe they could produce a thicker(?) one that would work.
Incidentally, you do know that they can be tuned a few notes higher or lower, don't you? Sheet music often has (or used to have) an instruction at the beginning: "Tune ukelele A D F# B" for example.