As of July 2011, the current thinking is that the first digit probably denotes the year, while the following numbers remain a mystery.
This only pertains the pre-Fender Korean-made guitars.
The Fender-era 51xx guitars follow the normal Fender numbering scheme.
After World War II, some guitars had a serial number embossed on the head, but reliable numbers didn't really appear until the advent of the first labels, around 1949.
Early labelled Gretsches will usually have a printed serial number and a handwritten model number.
If you'd like to learn more about Gretsch serial numbers, we highly recommend Ed Ball's "Gretsch 6120: The History of a Legendary Guitar." Ball is one of the key researchers who have determined the actual dates, years and features Gretsch serial numbers correspond to.
Gretsch began date-coding serial numbers in August 1966.
Also, on guitars built in October, November or December, the third AND fourth digits denote the month.
Serial numbers on Korean made guitars in this era were printed on a sticker affixed to the back of the headstock.
This sticker, along with the "Made in Korea" sticker, went missing almost immediately — sometimes before the guitar even left the store.
In addition, these guitars followed no known numbering scheme.
For example, 27136 should be February (2), 1967 (7) and the 136th instrument made that month. (i.e., 1974 would be 4) Last 3 digits = number of the instrument.
A hyphenated number was embossed on the back of headstock. For example, 3-8094 would be March (3), 1978 (8) and the 94th guitar made that month. The next three digits are the model number, without the 6 at the beginning.
Most Electromatic hollowbodies carry a KS designation, although KP was fairly common prior to about 2007.