There have been lots of tune coding systems over the years. The earliest I know of was in Le Cle du Caveau, a metrical index of French songs (about 3000 of them) from the early 19th century.

The biggest is probably the National Tune Index, a US project that indexed about 20,000 British tunes from 17th and 18th century books and manuscripts.

There is Charles Gore's Scottish Fiddle Tune Index, which covers about 20,000 Scottish tunes from c.1700-c.1900. It is supposedly based on a theme coding system developed for Irish music by Breandan Breathnach, which I have never seen in use.