The one that we might be call in English "Asturian song" is a type of melody that can be listened in a very concrete area of the Iberian Peninsula. First, "Asturian song" does not look like to me the most appropriate name, since there is no the only type of song in Asturies.
The Asturian songs can be individual or collective, in the context of dances, of the work or others as the cradle songs. The type of song to which we are speaking is called "asturianada" out of Asturies, and inside our land "tonada" (without the adjective "Asturian", unless it is a question of a specific work that tries to differentiate it from the melodies of other places).
The original area of the tune is very clearly Asturies, in the geographical plane, though also it can be listened in some regions of the close, such regions as the Ancares of Galicia and León, Fonsagrada's region, in the Galician province of Lugo, the Bierzo from Leon, and (traditionally) the west of Cantabria, though today in the latter region it is spreading and enjoys every time more popularity, in similar form that other manifestations of the traditional Asturian culture, as for example the use of the Asturian bagpipe or the elaboration of cider. That is to say, the region of Cantabria somehow every time assumes more cultural Asturian features. This also explains because in the past this region was not too different, forming a part of the original nucleus of the primitive Kingdom of Asturias (the plural name Asturias derives from the two provinces of the old Principality, Asturias of Oviedo and Asturias of Santillana).
Returning to the tune, which differs to this type of song from others consists principally of two things:
The first thing, a type of interpretation where are frequent the melismae, a class of inflexion of the voice, which it makes many observers think about the flamenco (concretly in the so called "cante jondo"), though this is based only on a slightly held up observation, since there are many more differences.
And another characteristic is the freedom of measurement, since this type of song does not possess a rhythmic regular metrics. That is to say, we might not follow the rhythm throbbing with the foot on the ground or disappointing the fingers on a table.
It is a unique genre in the whole Iberian Peninsula, and this is the reason of which out of Asturias it is called "asturianada".
It is very difficult to establish his origins, but in any case the specialists coincide in indicating these as very remote.
Possibly there has much that to see with the popular music of the former peoples dominated by Rome, which later would derive for cult reelaboration in two types of song: the Gregorian singing and the canticles of the Christian Mozarabic rituals. In these two types of melodies we can appreciate interpretative common features with the Asturian tune, specially the melismas, though the measurement already is regularized.
Adjusting to the musical popular traditional genres, the more similar thing that we can find to the Asturian tune in the European folclore is certain songs of Western Ireland and the Aran Islands, in which, sung in Gaelic and less frequently in English, we can find the same two fundamental characteristics: the free rhythm and the melismas.
It is therefore very possible that we think before a type of song that fixes her roots in the Celtic pre-Roman peoples, perhaps what the Asturian war prisoners were singing while they were crucified by the Romans, since some authors of the epoch mentioned admiring his valor.
Regards.