25ed4: Difference between revisions

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 {{Infobox ET}}
-'''25ed4''' is the [[Ed4|equal division of the double octave]] into 25 parts of exactly 96 [[cent|cents]] each (every second step of [[25edo]]).
+'''25ed4''' is the [[Ed4|equal division of the double octave]] into 25 parts of exactly 96 [[cent|cents]] each (every second step of [[25edo]]). It corresponds to 12.5edo and is notable as a type of compressed [[12edo]].
 == Theory ==
-We could have 12edo with a quarter note, like with 1.5edo, where the 2nd note is the same as the 3rd in 4edo or we could squish the notes and fit in something else.
+On the surface, 25ed4 seems fairly similar to [[12edo]]. Its step is 96¢, its perfect 5th is actually quite flat at 672¢ (but still 7 steps), but it has an excellent [[5/4]] at 4 steps (384¢). However, try to map this to a 12edo keyboard and you will run into multiple issues. First, the octave is WAY out. 12\25ed4 is 1152¢. Second, the best fifth of 25edo is only found up an octave. Third, 24≠25, so double octaves don't work unless you use some isomorphic keyboard.
+Here are some important ratios and their relative errors in 25ed4.
+/1: 18.8%
+/2: -31.2%
+/3: -18.8%
+/4: -2.4%
+== Intervals ==
+{{Interval table}}
+== Harmonics ==
+{{Harmonics in equal
+| steps = 25
+| num = 4
+| denom = 1
+}}
+{{Harmonics in equal
+| steps = 25
+| num = 4
+| denom = 1
+| start = 12
+| collapsed = 1
+}}
 {{stub}}