25edo: Difference between revisions
No need to remind readers of what a regular temperament is everywhere Tag: Undo |
→Theory: Add note about harmonic entropy (like 24edo and 26edo); add notable superset 50edo |
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If 5/4 and 7/4 are not good enough, it also does 17/16 and 19/16, just like 12edo. In fact, on the [[k*N subgroups|2*25 subgroup]] 2.9.5.7.33.39.17.19 it provides the same tuning and tempers out the same commas as 50et, which makes for a wide range of harmony. | If 5/4 and 7/4 are not good enough, it also does 17/16 and 19/16, just like 12edo. In fact, on the [[k*N subgroups|2*25 subgroup]] 2.9.5.7.33.39.17.19 it provides the same tuning and tempers out the same commas as 50et, which makes for a wide range of harmony. | ||
Its step of 48{{c}}, as well as the octave-inverted and octave-equivalent versions of it, holds the distinction for having very [[harmonic entropy]] and thus is, in theory, the second-most dissonant (second-closest to the peak at 46.4{{c}}, after neighboring [[26edo]]), assuming the relatively common values of ''a'' = 2 and ''s'' = 1.01. This property is shared with all edos between around 20 and 30. Intervals smaller than this tend to be perceived as unison and are more consonant as a result; intervals larger than this have less "tension" and thus are also more consonant. | |||
=== Possible usage in Indonesian music === | === Possible usage in Indonesian music === | ||
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=== Odd harmonics === | === Odd harmonics === | ||
{{Harmonics in equal|25}} | {{Harmonics in equal|25}} | ||
=== Subsets and supersets === | |||
Since 25 is 5 x 5, 25edo is the smallest composite EDO that doesn't have any intervals in common with [[12edo]]. Doubling 25edo to get [[50edo]] produces a good [[meantone]] tuning. | |||
== Intervals == | == Intervals == | ||