The Functional Harmony invented by Hugo Riemann, using terms like dominant, subdominant, or tonica, was derived by Riemann from Hegel’s dialectics. Each part of the chord progression I – IV – V – I is related to thesis, antithesis and synthesis. Riemann takes this as an universality of music.
Aristoteles was inventing logic introducing syllogistics. Until the end of the 19th century and the advance of formal logic, syllogistics was the only logic around. It combines two sentences using three terms A, B and C with given relations A ->B and B->C to derive a relation between A and C. The most simple syllogism is Barbara with the example: Sokrates (A) is a human (B), therefore A->B, and all humans (B) die (C), therefore B->C, concluding that Sokrates (A) will die (C).
The functional harmony be expressed with the formal concept of syllogism. Several conclusions can be drawn. So the octave is the only interval with is logically
‘a must’, all other intervals are logically possible but no must. Also the major third is possibe, while the minor third is possibly not.
Another interesting result is that the reasoning of analogy is not concluding, according to syllogistic laws. Therefore an analogy says nothing at all!
Bader, R., Diezt, M.-K., Elvers, P, Elias, M., & Tolkien, L.: Foundation of a Syllogistic Music Theory. In: Bader, R. (ed. / Hrsg.).: Musical Acoustics, Neurocognition and Psychology of Music / Musikalische Akustik, Neurokognition und Musikpsychologie. Hamburger Jahrbuch für Musikwissenschaft 25, 177-196, 2009.