Usually dance tunes have two halves (conventionally called the "A part" and the "B part"), and each half can be divided into four "phrases"; short, identifiable segments of the tune. These phrases can be as short as one bar, or as long as several. Often they do not start at the beginning of a bar, but with an anacrusis (up beat); however, the four-phrase structure remains. This classification of a tune consisting of two four-phrase sections describes possibly 99 per cent of all traditional Celtic dance tunes.
Within these two four-phrase sections can be seen other formulaic elements. To give two quick examples, the third phrase of a tune is often a repeat of the first phrase, and the ending of the B part of the tune is very often note for note the same as the ending of the A part.
Let's apply this theory to a tune. Below is a tune called "Bonnie Lass Come Ower the Burn", a song air based on an old Scottish tune called "The Braes o' Mar" and also known in Ireland as "Johnny Won't You Marry Me."
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In this tune the phrases each consist of two bars. The opening phrase sets the tone of the piece - once you hear it, you know what sort of tune it is, what its "flavour" is; and the third phrase (bars 5 and 6) is simply a repeat of the first phrase. The fourth phrase in this type of piece is usually quite different to the other phrases, as here, and sounds like the ending of a section, almost always resolving to the root key, in this case G. The second half of the tune follows the same pattern: first and third phrases are identical, and the fourth phrase is a repeat of the A part ending.
In a genre which values the ability to play tunes by memory without the aid of written notation, anything which helps the process of learning tunes is an advantage. Recognition of formulae such as those outlined above makes it easier to break down tunes, easier to identify repetitious components, and it helps to accelerate commitment of the tune to memory.