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I'm intruiged by the fact that some stringed instruments, like the ukulele, are traditionally tuned in the way of reentrant tuning where the strings are not ordered from the lowest to the highest pitch.
I do not play ukulele, or a similar instrument, but on first sight this seems illogical. There must be, aside from historical reasons, a good practical reason for this style of tuning. What is it?
Strings for these instruments were, historically, made from sheep gut or cow gut. In some situations it wouldn't be possible to make a thicker lower string, so a higher-octave string is substituted. In other situations there would be a point at which it isn't possible to make a thinner string that could be tuned higher. Such a string would be too weak and would break just from tuning it up to pitch. So the solution was to use a string tuned an octave lower in its place.
Reentrant tunings and strings have been used as long as there have been stringed instruments that were used to strum chords. That would take us at least back to the early 1600s with the appearance of the Baroque guitar.
Update:
The ukulele only dates from the 1880s, but it is descended from the Portuguese guitar (brought to Hawaii by Portuguese traders and colonizers) which is, in turn, descended from the Baroque guitar. The Baroque guitar used a reentrant tuning from its inception around 1646. Before that there was the lute, going back to antiquity, and also using reentrant tunings.
So one reason that the ukulele has a reentrant tuning is that it comes from a continuous line of reentrant-tuned instruments going back hundreds of years before the invention of the ukulele.
The practical reason for reentrant tuning is to make it easier to play the chord voicings with simple chord forms (the way your fingers make the chords). Each chord voicing has a different sound and the high G string would make for a brighter sound with simple chord forms.
You can hear this in any music store that has a variety of stringed folk instruments in a variety of tunings. As you try different chord forms and scales on these instruments you'll find that the stuff that is the easiest to play tends to be the signature sound of the music that the instrument is played in.
It's for this reason that on guitar I will capo for A and D tunes. And I almost always capo for Bb and F. It's not because I don't know the closed chord forms, I do. It's that the particular voicings I'm looking for are easier to play.
Different reasons in different instruments.
For ukeleles, it's simply that they were based on an instrument without reentrant tuning, but made in such a way whereby the lowest string could not practically be made. The instrument players wanted an instrument where the chord positions were still possible, and hey presto, you get a uke.
The ukelele was based on an instrument similar to the modern day Cavaquinho, but made with what materials were available
Some instruments were actually designed that way for a reason though, like the the 5 string banjo, which allows the whole "diddly diddly" banjo roll sound to be possible.
Without the higher pitched string available to the thumb, things like this just would not be possible
If the fourth string were down an octave, a g'-c'-e'-e' ukulele would be tuned like the top four strings of a guitar with a capo on the fifth fret, meaning that chord fingerings that would work for that instrument would work on the ukulele. While it would be possible for larger ukulele to have a string tuned to the g below middle c, it would be impractical to play a note that low on an instrument as small as a soprano ukulele. Tuning that string up an octave from where it would be if the instrument were patterned after a guitar changes how chords sound, but still allows them to keep the right collection of notes.
My own Flat Finger Tuning G-D-d-f-g#-b tunes the fifth string higher than the fourth string to make it easy to strum a chord using the D-d-f-g#-b strings without having to mute the G string. If one is trying to design a tuning for playing 5- or 6-string movable chords which has the strings in pitch order and the bottom strings are separated by any interval less than a fifth, any movable chord rooted on the sixth string will require that the fifth string be either muted or be played on a different fret from the sixth. If the bottom strings are separated by the fifth, it will be difficult to tune the upper strings in a way that can conveniently accommodate major and minor rooted on both the fifth and sixth strings. Moving the fifth-highest string to the sixth position avoids both of those issues. An F major chord may be played as x-3-3-4-4-6 without having to worry about fretting the G string, and a Bb major chord may either be plucked as 3-x-3-5-6-6 or strummed as 3-3-3-5-6-6. Strumming will cause the fifth string to sound an F which is below the Bb root of the chord, but is generally not objectionable.
