Are tetrachords used in medieval/renaissance music the same way as modern chords are used in modern music (as a base for the melody)? And if so... how are the applied?
Since no one actually answered I'll give it a try.
A tetrachord is a specific melodic sequence of steps, specifically
Whole - Whole - Half
As an example, Do, Re, Mi, Fa, the first 4 notes of the major scale. The next 4 notes are also a tetrachord, Sol, La, Ti, Do. The Major scale is built from 2 tetrachords separated by a whole step.
Chords, on the other hand, are a group of notes typically played together to harmonize a melody. They are built from consecutive thirds in the major scale. Example the major chord is built from the 1, 3, and 5, in C that would be C, E, G.
This simple sequence is the foundation of Western Music, everything else follows from it. Melodies are based on the diatonic scale (built from tetrachords) and chords are made from the same sequence, but from a different formula. In a sense the tetrachord could be seen as a source for all western melody and harmony.
Yes, you will find it in medieval music in both contexts. A follow up question to yours might be Did Medieval musicians use the same formulae as modern musicians for composing melodies and harmonies? The formalism of modern music theory didn't really solidify until later in history.
Keep in mind that one can make up melodies and chords without knowledge of these specific sequences or formulas, and with accidentals (chromatic scale). It appears that what is called "theory" today is a list of best practices that have evolved over hundreds or thousands of years. There is no denying that we as a culture prefer to build up melodies and harmonies relative to the major scale (and its derivatives). Even when we "play out" this is a relationship between what is typical vs. atypical (relative to major).
From a theoretical point of view one could say
And these are used to build melodies and progressions. There is a formulaic way to choose how a melody should be harmonized which has roots in multi voice choiral church music. But again, these are agreed upon best practices. Relative to modern music theory some Renaissance music does not follow modern rules and sound a little unusual. Specifically I refer to cadences. Many older lute pieces arranged for classical guitar do not have well defined endings, the chords circulate in a pattern and stop. There is no 7-->8 and 4-->3, and no adherence to the principles of resolution. They still sound nice.