Lengthy disquisition, directed to nobody in particular, following:
fractional sizes, in bowed string instrument and classical guitar parlance, refer to
body size, whose reduction is accompanied by a visually proportional shortening of scale length. (Small reduction in body measurements in the three dimensions go a long way in reducing cubic inchage: a 3/4 violin is not dramatically that much smaller than a normal one - certainly not 3/4 shorter in either scale length nor in total length.)
Instruments which have been more or less standardised (violin, cello) have student sizes that have more or less agreed-upon dimensions; instruments that haven't (viola, double bass) much less so: as upright players know, there is a lot of variation among basses called "3/4", which defines a ballpark rather than an exact size - and is also, as mentioned above, the de-facto
standard ballpark (4/4 being harder to find and, I would imagine, play).
Classical guitars are kind of in between - a standard 4/4 being there (albeit with a certain amound of wiggle room for tweaks) means a 7/8 is
usually a slightly smaller one, with one fret's worth of scale length reduction (i.e. a resulting ~24" scale); a 3/4 guitar tends to have a capo-on-2st scale length (~22.7"), or thereabouts; a 1/2 is a capo-on-3rd (21.5"), -on-4th (20.2", in which case 21.5" is called 5/8), or somewhere in between; a 1/4's scale equals capoing a standard guitar at the 5th fret (19",
ou traditional baritone ukulele scale); a 1/8 at the 7th (17", tenor uke scale).
(Neck width is often less proportional, and thinner than expected for easiness of playing.)
Regarding solid-body electric guitars, body size being essentially irrelevant to tone led to it being not standardised: this means that usage of fractions (by those who do use them at all) to refer to student-size electrics tends to be a carryover from classical guitars, and to indicate scale as expected with the latter (in other words, a 1/4 electric guitar has a 19" scale like 1/4 classicals do) rather than body size.
What about electric basses then?
- some manufacturers and vendors' "3/4-size" is essentially good ole 30", short scale (SX, Stagg, Gear4Music), whereas 28.5" is 5/8 scale (Shredneck);
- for others, like
this gentleman, "3/4" equals 28.5" scale.
I side with the former (30" scale being about the same as capoing a 34" standard bass at the 2nd, it is 3/4 to me, on bass as well as guitar).
...fin