A tune changes in pitch throughout, otherwise it is a drone. Tunes usually start on a given note and resolve to it, but not always. Tunes are written in keys and modes, which describe the pitch to be used and the intervals between notes within the tune.
Tunes in the Folk Tradition were not meant to be written down, being part of the Oral/Aural Tradition. However, ever since Composers and Collectors came across the tunes and maybe even earlier, there have been published versions of tunes that are called traditional.
Of course tunes can be written on the normal music score with a stave of 5 lines, and this is the normal way of communicating the tune. Increasingly, there are formats designed for the electronic age which can be converted from one format to another.
The most popular format for writing and transferring tunes over the internet is ABC. It is a simple yet powerful text based format which produces very small files. The file information is very human readable in the raw form, but is easily converted into a proper score or even a Midi file by appropriate software. It is supported by a range of free software and a huge repository of tunes, the best of which is John Chambers' Trillian.