2edo: Difference between revisions

The mapping of both [[3/2]] and [[4/3]] to the 600-cent tritone, as happens in the [[patent val]], means that 2edo tempers out [[9/8]], and thus supports [[Very low accuracy temperaments #Antitonic|antitonic]] – a temperament named based on the functionality of the 600 cent interval relative to the Tonic. In fact, it even [[support]]s both the 7-limit and 11-limit extensions of antitonic as it also tempers out both [[15/14]] and [[12/11]] respectively. However, the significance of 9/8 in particular being less than half the size of a single step should not be underestimated, as because of this, 2edo is the first edo to demonstrate 3-to-2 [[telicity]] – that is, when not counting the comparatively trivial 1edo. Given this, it is no surprise that 2edo represents the [[3-limit]] [[consistent]]ly. If we treat [[5/4]] the same way as [[81/64]] – which is mapped to the unison courtesy of the tempering of 9/8 – we end up with the val {{val| 2 3 4 }} (2c mapping). This could be used to crush all of the 5 out of 5-limit music, and to then attempt to turn what remains into neo-Medieval harmony.

=== Additional curiosities ===

* [[99/70]] is [[Nearest just interval|a good rational representation]] of the square root of 2.

== Music ==