User:Eliora/Concoctic scale: Difference between revisions

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12edo 5L2s diatonic scale, the predominantly used scale in the world's music today, is an example.

== Mathematical ~~definition~~ ==

== Mathematical derivation ==

The length of a maximum evenness scale's generator can be determined through a '''modular multiplicative inverse''' of the note amount and the tuning size<ref>https://individual.utoronto.ca/kalendis/leap/index.htm</ref>:

The length of a maximum evenness scale's generator can be determined through a '''modular multiplicative inverse''' of the note amount and the tuning size<ref>https://individual.utoronto.ca/kalendis/leap/index.htm</ref>.

<math>ax \equiv 1\mod N</math>,

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<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

A scale is called '''orthoconcoctic''', if the generator corresponding to note amount is the chroma-positive generator, for example - the 12edo diatonic scale is. There are also '''paraconcoctic''' scales, or chroma-negative concoctic scales. The formula for such a scale is

<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~~.

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 terms of modal brightness.

=== Example ===

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|[[15625/15552]]*

|

|Forms the [[Hanson]] (11b & 15)

|*Forms the [[Hanson]] (11b & 15)

|-

|16

@@ Line 3: / Line 3: @@
 edo 5L2s diatonic scale, the predominantly used scale in the world's music today, is an example.
-== Mathematical definition ==
+== Mathematical derivation ==
-The length of a maximum evenness scale's generator can be determined through a '''modular multiplicative inverse''' of the note amount and the tuning size<ref>https://individual.utoronto.ca/kalendis/leap/index.htm</ref>:
+The length of a maximum evenness scale's generator can be determined through a '''modular multiplicative inverse''' of the note amount and the tuning size<ref>https://individual.utoronto.ca/kalendis/leap/index.htm</ref>.
 <math>ax \equiv 1\mod N</math>,
@@ Line 16: / Line 16: @@
 <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
+A scale is called '''orthoconcoctic''', if the generator corresponding to note amount is the chroma-positive generator, for example - the 12edo diatonic scale is. There are also '''paraconcoctic''' scales, or chroma-negative concoctic scales. The formula for such a scale is
 <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.
+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 terms of modal brightness.
 === Example ===
@@ Line 131: / Line 131: @@
 |[[15625/15552]]*
 |
-|Forms the [[Hanson]] (11b & 15)
+|*Forms the [[Hanson]] (11b & 15)
 |-
 |16