Francesco Landini, the most famous composer of the Trecento, playing a portative organ (illustration from the Fifteenth-century Squarcialupi Codex)
The Trecento, from about 1300 to 1420, was a period of vigorous activity in Italy in the arts, including painting, architecture, literature, and music. The music of the Trecento pioneered new forms of expression, especially in secular song and in the use of vernacular language, Italian. In these regards, the music of the Trecento may seem more to be a Renaissance phenomenon; however, the predominant musical language was more closely related to that of the late Middle Ages, and musicologists generally classify the Trecento as the end of the medieval era.
Secular music before the year 1500 was largely the work of jongleurs, troubadours and mimes. This was the age of the great vernacularization of language in Italy—indeed, throughout Europe; that is, people started to write and sing songs in their native language, which was not Latin, but whatever brand of vernacular medieval neo-Latin was spoken in their area. Thus, Dante showed with the Divine Comedy in 1300 that the common language (his was called "Tuscan" and not "Italian" until as late as the 18th century) could be a vehicle for fine literature. Logically, that extended to the lyrics of the songs that people sang.
Two points are worth mentioning in this regard: (1) we know much more about the words of songs than we know about the actual sound of the music. Words were written down with much more ease than melodies were notated. (See musical notation). Thus, we know that there was a vibrant troubador tradition in the 12th century in the Provence in their language and we know that 1000 miles away on the island of Sicily there was also a vibrant troubador tradition at the Hohenstaufen court of Frederick II, songs sung in the dialect of the people (very much influenced, for example, by Arabic), but it is conjecture as to exactly what either one sounded like. We only know that southern French folk music, today, sounds quite a bit different from Sicilian folk music. Since folk music is relatively conservative in that it resists rapid change, we may assume that at least some of the obvious differences in melody, scales and approach to vocalising that exist now, existed then. It is interesting that the call and response nature of much popular choral singing in the Middle Ages—that is, a soloist singing a line that is then answered by a group—found its way into medieval church music as a way of involving all members of the congregation.
Check out the Prikosnovenie label
This is a French record label featuring neoclassical/neofolk artists from several European countries. One very nice ensemble on this label is Caprice, a Russian chamber orchestra performing original settings of songs by J.R.R. Tolkien and William Blake. Other labelmates include Louisa John-Krol (sort of an Australian Loreena McKennitt), Daemonia Nymph (medieval Greek), and Francescho Banchini (medieval Italian).
Of course you are already familiar with Dead Can Dance (perhaps the first modern "neoclassical" ensemble to bring early European art music to an audience outside the tuxedo culture), and if you enjoy their treatments of medieval and renaissance material you should also look into artists like Unto Ashes, Collection d'Arnell Andrea, L'Orchestre Noir, Angels of Venice, Amber Asylum, Sally Doherty, Chirleison, Dark Sanctuary, Algiz, Nature and Organization, Lupercalia, Vas, A…