8edt: Difference between revisions

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'''8 equal divisions of the tritave''' ('''8edt''') is the [[nonoctave]] [[tuning system]] derived by dividing the [[tritave]] (3/1) into 13 equal steps of 237.744 [[cent]]s each, or the eighth root of 3. As the double of [[4edt|~~4edt]], harmonically, 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~~.

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

What it does introduce are flat ~~pseudooctaves~~ and sharp 3:2's, making it related to 5edo melodically.

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.

== Harmonics ==

== Interval table ==

~~== Prime harmonics ==~~

~~{{Harmonics in equal|8|3|1|intervals=prime}}~~

[[Category:edt]]

[[Category:tritave]]

[[category:macrotonal]]

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 {{Infobox ET}}
+{{EDO intro}}
-'''8 equal divisions of the tritave''' ('''8edt''') is the [[nonoctave]] [[tuning system]] derived by dividing the [[tritave]] (3/1) into 13 equal steps of 237.744 [[cent]]s each, or the eighth root of 3. As the double of [[4edt|4edt]], harmonically, 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.
+{{todo|clarify|comment = why is 8edt the analog of 10edo? 8edt does not support 4L 5s (3/1-equivalent).}}
-What it does introduce are flat pseudooctaves and sharp 3:2's, making it related to 5edo melodically.
+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.
+== Harmonics ==
+{{Harmonics in equal|8|3|1|}}
+{{Harmonics in equal|8|3|1|intervals=prime}}
 == Interval table ==
 {{Interval table}}
-== Prime harmonics ==
-{{Harmonics in equal|8|3|1|intervals=prime}}
 [[Category:edt]]
 [[Category:tritave]]
 [[category:macrotonal]]