Kite's thoughts on antipodes: Difference between revisions

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* If the edo is even, the antipode is the half-octave. For example, 12edo's antipode is the tritone 6\12.

* If the edo is odd and the 4th is even, the antipodes are the half-~~fourth~~ and its octave complement, the half-12th. The antipodes are a perfect 5th apart. For example, [[19edo]]'s 4th is 8\19, and its antipodes are 4\19 (A2/d3) and 15\19 (A6/d7).

* If the edo is odd and the 4th is even, the antipodes are the half-4th and its octave complement, the half-12th. The antipodes are a perfect 5th apart. For example, [[19edo]]'s 4th is 8\19, and its antipodes are 4\19 (A2/d3) and 15\19 (A6/d7).

* If the edo is odd and the 5th is even, the antipodes are the mid-3rd (half-5th) and its octave complement, the mid-6th (half-11th). The antipodes are a perfect 4th apart. For example, [[17edo]]'s 5th is 10\17, and its antipodes are 5\17 and 12\17.

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== Applications ==

~~On a bosanquet-layout keyboard, in general the~~ antipodes is the most ~~awkward interval to play~~, in ~~the sense that~~ it ~~spans the greatest vertical distance~~.

The antipodes key is the least closely related key, and thus presumably the most shocking modulation. In 12edo, the antipodes of C major is F# major. But in 19edo, it's D# major or Bbb major.

The antipodes ~~key~~ is ~~the least closely related key~~, and ~~thus presumably~~ the ~~most shocking modulation. In 12edo~~, the antipodes ~~of C major~~ is ~~F# major. But~~ in ~~19edo,~~ it~~'s D# major and Bbb major~~.

The antipodes of D is where extended pythagorean notation might logically switch from sharps to flats. In [[31edo]], it's Gbb and Ax. Despite appearances, Gbb and Ax are a perfect 4th apart.

On a Bosanquet-layout keyboard like the [[lumatone]], in general the antipodes is the most awkward interval to play, in the sense that it spans the greatest vertical distance.

[[File:Lumatone 31edo 2.jpg|left|thumb]]

[[File:Lumatone antipodes for single-ring edos 12-53.jpg|none|thumb]]

~~The antipodes of D is where extended pythagorean notation might logically switch from sharps to flats. In [[31edo]], it's Gbb and Ax. Despite appearances, Gbb and Ax are a perfect 4th apart.~~

== Generalizations ==

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 * If the edo is even, the antipode is the half-octave. For example, 12edo's antipode is the tritone 6\12.
-* If the edo is odd and the 4th is even, the antipodes are the half-fourth and its octave complement, the half-12th. The antipodes are a perfect 5th apart. For example, [[19edo]]'s 4th is 8\19, and its antipodes are 4\19 (A2/d3) and 15\19 (A6/d7).
+* If the edo is odd and the 4th is even, the antipodes are the half-4th and its octave complement, the half-12th. The antipodes are a perfect 5th apart. For example, [[19edo]]'s 4th is 8\19, and its antipodes are 4\19 (A2/d3) and 15\19 (A6/d7).
 * If the edo is odd and the 5th is even, the antipodes are the mid-3rd (half-5th) and its octave complement, the mid-6th (half-11th). The antipodes are a perfect 4th apart. For example, [[17edo]]'s 5th is 10\17, and its antipodes are 5\17 and 12\17.
@@ Line 11: / Line 11: @@
 == Applications ==
-On a bosanquet-layout keyboard, in general the antipodes is the most awkward interval to play, in the sense that it spans the greatest vertical distance.
+The antipodes key is the least closely related key, and thus presumably the most shocking modulation. In 12edo, the antipodes of C major is F# major. But in 19edo, it's D# major or Bbb major.
-The antipodes key is the least closely related key, and thus presumably the most shocking modulation. In 12edo, the antipodes of C major is F# major. But in 19edo, it's D# major and Bbb major.
+The antipodes of D is where extended pythagorean notation might logically switch from sharps to flats. In [[31edo]], it's Gbb and Ax. Despite appearances, Gbb and Ax are a perfect 4th apart.
+On a Bosanquet-layout keyboard like the [[lumatone]], in general the antipodes is the most awkward interval to play, in the sense that it spans the greatest vertical distance.
+[[File:Lumatone 31edo 2.jpg|left|thumb]]
+[[File:Lumatone antipodes for single-ring edos 12-53.jpg|none|thumb]]
-The antipodes of D is where extended pythagorean notation might logically switch from sharps to flats. In [[31edo]], it's Gbb and Ax. Despite appearances, Gbb and Ax are a perfect 4th apart.
 == Generalizations ==