Unfortunately for specifically Welsh musical traditions there are no primary manuscript sources we have found for secular songs pre-1066. The secular tradition for music of the ordinary populace was oral, as was the tradition with court bards as well, and wasn't written down until the 1700s. We can infer what sort of music there might have been from secondary sources but as far as I'm aware we have no way of piecing together what the songs themselves specifically were.

The earliest example of these secondary sources we've found so far is from a sixth century monk called Gildas and his account De Excidio et Conquestu Britanniae, in which he berates Maelgwyn Gwynedd (lord of Gwynedd and Anglesy) for preferring his own court bards over the 'tuneful voices' of Christians singing melodious church songs. From his account we can gather that there were at least two contrasting styles of singing: the harmonious ecclesiastic style, and the more impassioned/baudy bardic style. It is worth noting that Gildas was highly pejorative towards Gwynedd in particular, going as far to compare him and four other British kings to beasts featured in the Book of Revelation and the Book of Daniel, so take this with a pinch of salt as always. We also have mentions of the types of instruments used in this period, for example, 50 years after Gildas we have a churchman Vinantius Fortunatas writing of a type of lyre that the Britons used "the crotta". This is something we see in later medieval and early modern periods as well, cerdd dant or the craft of the strings.

Sources:

- Music in Welsh Culture Before 1650: A Study of the Principal Sources, Sally Harper

- Welsh Traditional Music, Phyllis Kinney