I can't possibly analyze Arvo Pärt well, let alone in one post. But here is a short introduction to the style that I think is proof of this return to the Medieval in High music. Here is an excellent article on the universality and "Bright Sadness" of Pärt's music, fitting for the season.
Tintinnabuli is derivative of the Latin word for "bells" and is essentially built off the interplay of two voices - one melodic and stepwise and one bell-like. "Tintinnabular". The main voice and the tintinnabular voice are the basic unit of Pärt's music, and he extends the logic in his grander and fuller pieces, creating a splendid diversity of emotion and expression. An example of the breath-taking potency in some of his sparser music is this section from the Kyrie of his Missa Sillabica.
You can see that the upper voice moves along the notes of a d-minor scale and the lower voice moves along the notes of a triad. This provides for considerable dissonance, but it's dissonance that you can, remarkably, only help but enjoy. Here is a sample of his Berliner Messe here.
The transcription of Missa Sillabica is done entirely by ear from "De Profundis" by Arvo Pärt, recorded by Paul Hillier and the Theatre of Voices.