2edo: Difference between revisions

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If one attempts to use '''2edo''' as an actual scale, it would divide the octave into two equal parts, each of size 600 cents, which is to say sqrt(2) as a frequency ratio. It represents the [[3-limit]] [[consistent]]ly, and it can be used to give a skeletonized version of the 3-limit music such as was used in Medieval Europe, by mapping the fifth and therefore the fourth to 600 cents. That entails mapping 81/64 to the unison, and if we do the same for 5/4 we end up with the 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. The harmony that is found in 2edo can be said to revolve around Tonic-Antitonic contrast, with the note at 600 cents away from the Tonic having a function akin to 12edo's diminished fifth.

If we want to consider it to be a temperament, it tempers out [[9/8]], meaning that it supports [[Very low accuracy temperaments#Antitonic|antitonic]]- a temperament named based on the functionality of the 600 cent interval relative to the Tonic. However, as 9/8 is less than half the size of a single step, 2edo is therefore the first EDO to demonstrate 3-to-2 [[telicity]].

If we want to consider it to be a temperament, it tempers out [[9/8]], meaning that it supports [[Very low accuracy temperaments#Antitonic|antitonic]]- a temperament named based on the functionality of the 600 cent interval relative to the Tonic. However, the significance of 9/8 being less than half the size of a single step should not be underestimated, as because of this, 2edo is therefore the first EDO to demonstrate 3-to-2 [[telicity]].

== Factoids about 2EDO ==

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 If one attempts to use '''2edo''' as an actual scale, it would divide the octave into two equal parts, each of size 600 cents, which is to say sqrt(2) as a frequency ratio. It represents the [[3-limit]] [[consistent]]ly, and it can be used to give a skeletonized version of the 3-limit music such as was used in Medieval Europe, by mapping the fifth and therefore the fourth to 600 cents. That entails mapping 81/64 to the unison, and if we do the same for 5/4 we end up with the val &lt;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.  The harmony that is found in 2edo can be said to revolve around Tonic-Antitonic contrast, with the note at 600 cents away from the Tonic having a function akin to 12edo's diminished fifth.
-If we want to consider it to be a temperament, it tempers out [[9/8]], meaning that it supports [[Very low accuracy temperaments#Antitonic|antitonic]]- a temperament named based on the functionality of the 600 cent interval relative to the Tonic.  However, as 9/8 is less than half the size of a single step, 2edo is therefore the first EDO to demonstrate 3-to-2 [[telicity]].
+If we want to consider it to be a temperament, it tempers out [[9/8]], meaning that it supports [[Very low accuracy temperaments#Antitonic|antitonic]]- a temperament named based on the functionality of the 600 cent interval relative to the Tonic.  However, the significance of 9/8 being less than half the size of a single step should not be underestimated, as because of this, 2edo is therefore the first EDO to demonstrate 3-to-2 [[telicity]].
 == Factoids about 2EDO ==