Decaononic: Difference between revisions

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'''~~Decaononic~~''' technique is the way of playing and composing where a ~~'''~~[[tone]]~~'''~~ is considered to be equal to ~~'''~~[[10/9]]~~'''~~.

The '''decaononic''' technique is the way of playing and composing where a [[tone]] is considered to be equal to [[10/9]]. It is a set of temperaments that may interpret this function differently.

It is a set of temperaments that may interpret this function differently.

== Origin ==

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== Theory ==

The name "decaononic" comes from Greek and Latin words for 10 and 9 respectively, and a letter o meaning "over", as in "[[otonal]]". In this system, one tone is set to be 10/9, about 182.4 cents, and other intervals may have multiple interpretations.

The name "decaononic", proposed by [[Eliora]], comes from Greek and Latin words for 10 and 9 respectively, and a letter o meaning "over", as in "[[otonal]]". In this system, one tone is set to be 10/9, about 182.4 cents, and other intervals may have multiple interpretations.

=== Whole tone scale ===

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=== Meantone ===

Meantone decaononic temperament assigns the perfect fifth to split the major ninth, as normal meantone would, in two. This therefore results in the fifth size of <math>\sqrt{20/9} = 1.490712...</math>, or about 691.2019 cents. The amount by which the fifth is flattened is equal to <math>\sqrt{81/80} = 1.0062...</math>, therefore this is effectively the same as ~~'''~~1/2-comma meantone~~'''~~.

Meantone decaononic temperament assigns the perfect fifth to split the major ninth, as normal meantone would, in two. This therefore results in the fifth size of <math>\sqrt{20/9} = 1.490712...</math>, or about 691.2019 cents. The amount by which the fifth is flattened is equal to <math>\sqrt{81/80} = 1.0062...</math>, therefore this is effectively the same as [[1/2 syntonic comma meantone|1/2-comma meantone]].

=== Devil's dozen ===

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-'''Decaononic''' technique is the way of playing and composing where a '''[[tone]]''' is considered to be equal to '''[[10/9]]'''.
+The '''decaononic''' technique is the way of playing and composing where a [[tone]] is considered to be equal to [[10/9]]. It is a set of temperaments that may interpret this function differently.
-It is a set of temperaments that may interpret this function differently.
 == Origin ==
@@ Line 9: / Line 7: @@
 == Theory ==
-The name "decaononic" comes from Greek and Latin words for 10 and 9 respectively, and a letter o meaning "over", as in "[[otonal]]". In this system, one tone is set to be 10/9, about 182.4 cents, and other intervals may have multiple interpretations.
+The name "decaononic", proposed by [[Eliora]], comes from Greek and Latin words for 10 and 9 respectively, and a letter o meaning "over", as in "[[otonal]]". In this system, one tone is set to be 10/9, about 182.4 cents, and other intervals may have multiple interpretations.
 === Whole tone scale ===
@@ Line 16: / Line 14: @@
 === Meantone ===
-Meantone decaononic temperament assigns the perfect fifth to split the major ninth, as normal meantone would, in two. This therefore results in the fifth size of <math>\sqrt{20/9} = 1.490712...</math>, or about 691.2019 cents. The amount by which the fifth is flattened is equal to <math>\sqrt{81/80} = 1.0062...</math>, therefore this is effectively the same as '''1/2-comma meantone'''.
+Meantone decaononic temperament assigns the perfect fifth to split the major ninth, as normal meantone would, in two. This therefore results in the fifth size of <math>\sqrt{20/9} = 1.490712...</math>, or about 691.2019 cents. The amount by which the fifth is flattened is equal to <math>\sqrt{81/80} = 1.0062...</math>, therefore this is effectively the same as [[1/2 syntonic comma meantone|1/2-comma meantone]].
 === Devil's dozen ===