Tritone: Difference between revisions

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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.

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~~ generators for tuning systems analogous to flattone but substituting 11/8 for [[4/3]]; for instance, these are not ~~suitable~~ generators for 26edo with a whole-octave period, 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 valid generators for tuning systems analogous to flattone but substituting 11/8 for [[4/3]]; for instance, these are not valid generators for 26edo with a whole-octave period, because they instead produce [[13edo]].

== Temperaments that can use tritones as generators ==

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=== Temperaments that use 11/8 as a generator ===

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, for a temperament analogous to [[Injera]] but substituting 11/8 for 4/3.

In 13edo, 11/8 and 16/11 map to the tritones 6\13 and 9\13, respectively, and are valid generators for it. Furthermore, although 12\26 is not valid as a generator for 26edo with a whole-octave period, it ''is'' valid with a half-octave period, for a temperament analogous to [[Injera]] but substituting 11/8 for 4/3.

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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.
-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 generators for tuning systems analogous to flattone but substituting 11/8 for [[4/3]]; for instance, these are not suitable generators for 26edo with a whole-octave period, 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 valid generators for tuning systems analogous to flattone but substituting 11/8 for [[4/3]]; for instance, these are not valid generators for 26edo with a whole-octave period, because they instead produce [[13edo]].
 == Temperaments that can use tritones as generators ==
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 === Temperaments that use 11/8 as a generator ===
-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, for a temperament analogous to [[Injera]] but substituting 11/8 for 4/3.
+In 13edo, 11/8 and 16/11 map to the tritones 6\13 and 9\13, respectively, and are valid generators for it.  Furthermore, although 12\26 is not valid as a generator for 26edo with a whole-octave period, it ''is'' valid with a half-octave period, for a temperament analogous to [[Injera]] but substituting 11/8 for 4/3.
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