I would like to take a different approach to this answer.
Microtonal sounds (outside of the traditional 11 notes you get before an octave repeats) have been around for a long time. Piano, as an instrument is not designed to be microtonal. However, some folks have created ways of “bending” notes on a piano to achieve microtonal colors.
As far as the “weirdness” or “dissonance”, you’ve been hearing it your whole life. Turkish music, Indian music, Native American singing, music of the Far East. Heck, find a group of excellent horn players and they will show you how they have to adjust some notes to get them to be “in tune with the chord”.
But piano was designed to provide a specific kind of sound and it’s harder to deviate than other stringed instruments.
In harmony and melody, it’s all about color and a tension and (maybe) release. Microtones take a 12 bit set up and make it potentially infinite. Approach with an open set of ears and a desire for new flavor.
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