The Triad has a special beauty and fairness beyond all numbers, primarily because it is the very first to make actual the potentiality of the Monad oddness, perfection, proportionality, unification, limit.
[Tonality is] the special meaning [functions] that chords receive through their relationship to a fundamental sonority, the tonic triad.
"The medieval musician ... did not hear a triad as a triad ... a textbook definition of tonal coherence is not the same as the phenomenon of tonal cognition as experiences."
When people listen to my music, I hope that they will notice that if you take a piece by a composer like Schubert, the major and the minor triad is an extermely important thing not merely as harmony, but in creating melodic lines. Schubert is always walking up and down with arpeggios on C, E, G and so forth. I am not doing anything different really, except using a different system of harmony.elliott carter
I think the origin of all this clamour for tonality is not so much the need to sense a relationship to the tonic, as a need for familiar chords: let us be frank and say "for the triad"; and I believe I have good reason to say that just so long as a certain kind of music contains enough such triads, it causes no offence, even if in other ways it most violently clashes with the sacred laws of tonality.Alban Berg