Tritone: Difference between revisions
Move semioctave tritones table up; add example of a tuning system having a semioctave that is not equal to its tritones; convert "TBD" to {{todo|complete section|inline=1}}. |
Left out some words -- fixed this; also added the possibility for 11/8 as a generator with a half-octave period. |
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However, it is possible for a tuning system to have an even number of notes and a pair of tritones that is not the same as the semioctave. | However, it is possible for a tuning system to have an even number of notes and a pair of tritones that is not the same as the semioctave. | ||
An example of a tuning system having an even number of notes and a pair of tritones that is not the same as the semioctave is [[26edo]]. In [[flattone]] tuning systems such as 26edo, 11/8 is C-F♯, which is the lesser tritone mapping to 12\26 (not the semioctave 13\26); 16/11 is C-G♭, which is the greater tritone mapping to 14\26. Note that these tritones are not necessarily suitable substitute generators for flattone; for instance, these are not suitable generators for 26edo, because they instead produce [[13edo]]. | An example of a tuning system having an even number of notes and a pair of tritones that is not the same as the semioctave is [[26edo]]. In [[flattone]] tuning systems such as 26edo, 11/8 is C-F♯, which is the lesser tritone mapping to 12\26 (not the semioctave 13\26); 16/11 is C-G♭, which is the greater tritone mapping to 14\26. Note that these tritones are not necessarily suitable substitute generators for flattone; for instance, these are not suitable generators for 26edo with a whole-octave period, because they instead produce [[13edo]]. | ||
== Temperaments that can use tritones as generators == | == Temperaments that can use tritones as generators == | ||
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=== Temperaments that use 11/8 as a generator === | === Temperaments that use 11/8 as a generator === | ||
In 13edo, the tritones | In 13edo, 11/8 and 16/11 map to the tritones 6\13 and 9\13, respectively, and are suitable generators for it. Furthermore, although 12\26 is not suitable as a generator for 26edo with a whole-octave period, it ''is'' suitable with a half-octave period, as in [[Injera]]. | ||
{{todo|complete section|inline=1}} | {{todo|complete section|inline=1}} | ||