Decaononic: Difference between revisions

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

In 5-limit just intotation and most of the music theory that comes with it, 10/9 is viewed as a secondary tone as opposed to [[9/8]]. In general, when the [[81/80|difference]] between the two is eliminated, what it really means is that the "tone" is set to equal to 9/8 and the tuning completely misses 10/9. This is primarily because 9/8 and an octave are equal to a stack of two perfect fifths. 10/9 therefore in this paradigm only occurs as a side product of 9/8, and it isn't an interval of its own.  

While there are temperaments which use 10/9 as a generator for various purposes (such as [[Porcupine]]), decaononic means that 10/9 is ''the tone,'' and 9/8 is not as emphasized.

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.  

=== Whole tone scale ===

{{Main|10/9ths equal temperament}}

Decaononic temperaments can be represented in EDOs which compress the 12edo scale to get the major second to be equal to 10/9. In [[79edo]], for example, a whole tone itself contains a mini-12edo keymap inside it, and the final 7 notes are a truncated tetrachord. If played naively, this produces a rather flat fifth of 638.413c just, or 637.974c (79edo). In an effect this makes for a [[Glacial7]]-type scale.

=== 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} = 1.490712...</math>, therefore this is effectively the same as '''1/2-comma meantone'''.  

=== Devil's dozen ===

* [[Minortone]]