Well I know at least w/ Gibson they are called 3/4s, even tho it's more like 7/8. I had gotten interested in the rarely seen Melody Maker 3/4 with the mid 60s SG body shape. .. just lasted 3 years or so.
Of course you can see on the earlier Melody Maker 3/4s it's just single bridge pickup, but wondered if the SG style of these had a covered up neck pickup rout like lots of others ( original Fender Musicmaster, etc.) I know some are down on the little Melody Maker single coil p/u. I think it's ok but hear there are some repros that really bring up the sound. Also some say that odd Vibrola they had isn't worth a damn, other say they can be tweaked into being decent.
Pretty sure these were all the narrow 1 9/6th nut.