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This existing answer and comment (https://music.stackexchange.com/a/17818/23919) sort of addresses my question.

I don't know anything beyond mode I was dorian, lots of music was dorian, and Fux starts with dorian in the Gradus. But my question is whether dorian was theoretically the central or fundamental tonality? Was it specially taught that way?

Modern textbooks don't necessarily say "the major scale is the central tonality" but so many books start with a C major scale (usually pointing out the position of the half steps) that for all practical purposes that is the modern conception.

Did teachers in the Medieval era think similarly about dorian mode? Also, did they describe dorian as 3 perfect fifths ascending and descending from a center, or two minor tetrachords, to highlight the symmetry?

In other words, was the symmetry of dorian a conscious reason for the apparent preference of the mode?

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Medieval modes were developed as a means of categorizing chant melodies. Generally speaking, chant melodies would have an often-repeated pitch around which the chant orbited (the tenor or reciting tone), an ending pitch (the final), and an overall range of roughly an octave. So the modes were defined in those terms.

As the tonal system emerged from the medieval modes, minor -- based on A -- became the principal mode. However, major eventually took over; naturally on C, being the relative major. The modern Dorian mode -- the second mode from the major -- is so named because it corresponds intervalically to the medieval Dorian mode, but it arises from an entirely different theoretical basis.

The idea of intervalic symmetry is of more modern compositional significance.

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