8edt: Difference between revisions

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~~{{todo|clarify|comment~~ = ~~why~~ is ~~8edt~~ the analog of 10edo? 8edt ~~does not support 4L 5s (~~3~~/1-equivalent)~~.}}

== Theory ==

As the double of [[4edt]], it is the analog of [[10edo]] being the double of [[5edo]]. However, the full 3:5:7 triad is already present in 4edt which is unlike the situation in 10edo where 4:5:6 gains a new better approximation than the sus4 triad in [[5edo]]. More precisely, 8edt is [[enfactoring|enfactored]] in the 3.5.7 subgroup.

~~As a double of~~ [[~~4edt|4edt~~]], it is the ~~analog of~~ [[~~10edo]] for [[4L 5s (~~3/1~~-equivalent)|Lambda~~]]~~-based systems. However~~, the ~~full~~ 3~~:5:7 triad is already present in 4edt~~ which ~~is unlike~~ the ~~situation in 10edo where 4:5:6 gains a new better approximation than~~ the ~~sus4 triad in~~ [[~~5edo]]. More precisely, 8edt is [[enfactored~~]] ~~in the 3.5.7 subgroup~~.

What it does introduce are flat [[2/1]] pseudo-octaves and sharp [[3/2]] perfect fifths, making it related to 5edo melodically. It is equivalent to 5edo with the [[3/1]] made just, by compressing the octave by 11.3 cents, which has the side effect of bringing the step size slightly closer to [[8/7]].

What it does introduce are flat [[2/1]] pseudo-octaves and sharp [[3/2]] perfect fifths, making it related to 5edo melodically. It is equivalent to 5edo with the [[3/1]] made just, by compressing the octave by 11.3 cents.

=== Harmonics ===

== Harmonics ==

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[[Category:~~edt]]~~

[[Category:Macrotonal]]

~~[[Category:tritave]]~~

~~[[category:macrotonal~~]]

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 {{Infobox ET}}
-{{EDO intro}}
+{{ED intro}}
-{{todo|clarify|comment = why is 8edt the analog of 10edo? 8edt does not support 4L 5s (3/1-equivalent).}}
+== Theory ==
+As the double of [[4edt]], it is the analog of [[10edo]] being the double of [[5edo]]. However, the full 3:5:7 triad is already present in 4edt which is unlike the situation in 10edo where 4:5:6 gains a new better approximation than the sus4 triad in [[5edo]]. More precisely, 8edt is [[enfactoring|enfactored]] in the 3.5.7 subgroup.
-As a double of [[4edt|4edt]], it is the analog of [[10edo]] for [[4L 5s (3/1-equivalent)|Lambda]]-based systems. However, the full 3:5:7 triad is already present in 4edt which is unlike the situation in 10edo where 4:5:6 gains a new better approximation than the sus4 triad in [[5edo]]. More precisely, 8edt is [[enfactored]] in the 3.5.7 subgroup.
+What it does introduce are flat [[2/1]] pseudo-octaves and sharp [[3/2]] perfect fifths, making it related to 5edo melodically. It is equivalent to 5edo with the [[3/1]] made just, by compressing the octave by 11.3 cents, which has the side effect of bringing the step size slightly closer to [[8/7]].
-What it does introduce are flat [[2/1]] pseudo-octaves and sharp [[3/2]] perfect fifths, making it related to 5edo melodically. It is equivalent to 5edo with the [[3/1]] made just, by compressing the octave by 11.3 cents.
+=== Harmonics ===
-== Harmonics ==
 {{Harmonics in equal|8|3|1|}}
 {{Harmonics in equal|8|3|1|intervals=prime}}
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 {{Interval table}}
-[[Category:edt]]
+[[Category:Macrotonal]]
-[[Category:tritave]]
-[[category:macrotonal]]