Tritone: Difference between revisions
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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}}. |
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Note that sometimes, tritones ''are'' used as generators, utilizing the small commas between the tritone pairs to approximate some other interval. The two simplest tritones, 11/8 and 7/5, also happen to be rather far from the semioctave, and as such are rather useful for this purpose: | Note that sometimes, tritones ''are'' used as generators, utilizing the small commas between the tritone pairs to approximate some other interval. The two simplest tritones, 11/8 and 7/5, also happen to be rather far from the semioctave, and as such are rather useful for this purpose: | ||
== Tritones as approximations of the semioctave == | == Tritones as approximations of the semioctave == | ||
The following table compares selected JI tritone pairs that approximate the half-octave and the commas separating them: | In some tuning systems having an even number of divisions of the octave (equal or well-tempered), the tritone (defined as three whole tones) is the same as the half-octave; if the divisions of the octave are equal and the octave is tuned pure, the tritone will therefore be exactly the square root of 2. The following table compares selected JI tritone pairs that approximate the half-octave and the commas separating them: | ||
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| [[1682/1681]] | | [[1682/1681]] | ||
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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 substitute generators for flattone; for instance, these are not suitable generators for 26edo, because they instead produce [[13edo]]. | |||
== Temperaments that can use tritones as generators == | |||
=== Temperaments that use 11/8 as a generator === | |||
In 13edo, the tritones are 6\13 and 9\13, and are suitable generators for it. | |||
{{todo|complete section|inline=1}} | |||
=== Temperaments that use 7/5 as a generator === | |||
{{todo|complete section|inline=1}} | |||
== In moment-of-symmetry scales == | == In moment-of-symmetry scales == | ||