Microtones bring your attention to qualities of distance not available in equal temperament. It's all about resonance, both in and outside your ears, and the ears' ability to map space in your brain.
In addition to making harmonic use of the modes of limited transposition, he [Messiaen] cited the harmonic series as a physical phenomenon which provides chords with a context which he felt to be missing in purely serial music.[44] An example of Messiaen's harmonic use of this phenomenon, which he called "resonance", is the last two bars of Messiaen's first piano Prélude, La colombe ("The dove"); the chord is built from harmonics of the fundamental base note E.[45] - Wikipedia: Messiaen, Olivier. 1/4/11
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