twelve-tone equal temperament

Beautiful beats of major third (minor sixth) and minor third (major sixth) in twelve-tone equal temperament.
Semitone pitch ratio = 12th root of 2 = 1.0594631... which is one of our marvelous irrational numbers.
The same major third beats are there one octave and two octaves higher too, like blinking stars, babbling river, tree leaves in the wind. Also perfect fifth (perfect fourth) makes music with living harmony.
Maybe all the intervals have beautiful effects.
Thanks to gifts of God.

1.0594631,twelve-tone equal temperament,piano tuning,