User:Eliora/Concoctic scale: Difference between revisions

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which simply becomes

<math>a^2 \equiv 1\mod N</math>.

<math>a^2 \equiv 1\mod N \hspace{4cm} (1)</math>.

There are also paraconcoctic scales, or chroma-negative concoctic scales. The formula for such a scale is

<math>a^2 \equiv -1\mod N</math>.

<math>a^2 \equiv -1\mod N \hspace{4cm} (2)</math>.

Since octave-inverting the MOS generator has no impact on the scale, paraconcoctic scales are identical to their usual, orthoconcoctic counterparts. However, the difference is pronounced in keyboard making - in terms of chroma direction, the white keys' generator will be the amount of black keys and vice versa.

=== Example ===

12edo keyboard layout predominantly in use in the world today features 7 white keys and 5 black keys. ~~The~~ diatonic scale of 7 keys is obtained by stacking the generator, 7\12 fifth 7 times. Likewise, the pentatonic of black keys is obtained by stacking it 5 times.

12edo keyboard layout predominantly in use in the world today features 7 white keys and 5 black keys. In direction-conscious manner, the diatonic scale of 7 keys is obtained by stacking the generator, 7\12 fifth 7 times. Likewise, the pentatonic of black keys is obtained by stacking the 5\12 perfect fourth 5 times. And such scale is generated with the first formula.

On the other hand, in [[25edo]], stacking 18\25 will lead to maximum evenness scale of 7 note "black keys", and stacking 7\25 will result in a 18-note scale of "white keys". This is the EDO that only has the scale through the second formula.

== List ==

@@ Line 14: / Line 14: @@
 which simply becomes
-<math>a^2 \equiv 1\mod N</math>.
+<math>a^2 \equiv 1\mod N \hspace{4cm} (1)</math>.
 There are also paraconcoctic scales, or chroma-negative concoctic scales. The formula for such a scale is
-<math>a^2 \equiv -1\mod N</math>.
+<math>a^2 \equiv -1\mod N \hspace{4cm} (2)</math>.
 Since octave-inverting the MOS generator has no impact on the scale, paraconcoctic scales are identical to their usual, orthoconcoctic counterparts. However, the difference is pronounced in keyboard making - in terms of chroma direction, the white keys' generator will be the amount of black keys and vice versa.
 === Example ===
-edo keyboard layout predominantly in use in the world today features 7 white keys and 5 black keys. The diatonic scale of 7 keys is obtained by stacking the generator, 7\12 fifth 7 times. Likewise, the pentatonic of black keys is obtained by stacking it 5 times.
+edo keyboard layout predominantly in use in the world today features 7 white keys and 5 black keys. In direction-conscious manner, the diatonic scale of 7 keys is obtained by stacking the generator, 7\12 fifth 7 times. Likewise, the pentatonic of black keys is obtained by stacking the 5\12 perfect fourth 5 times. And such scale is generated with the first formula.
+On the other hand, in [[25edo]], stacking 18\25 will lead to maximum evenness scale of 7 note "black keys", and stacking 7\25 will result in a 18-note scale of "white keys". This is the EDO that only has the scale through the second formula.
 == List ==