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. It is best known as the equal-tempered version of the [[Bohlen-Pierce]] scale. 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.

== 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.

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

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]].

=== Harmonics ===

== Interval table ==

~~== Prime harmonics ==~~

[[Category:Macrotonal]]

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

[[Category:~~edt]]~~

~~[[Category:tritave]]~~

~~[[category:macrotonal~~]]

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 {{Infobox ET}}
+{{ED 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. It is best known as the equal-tempered version of the [[Bohlen-Pierce]] scale. 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.
+== 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.
-What it does introduce are flat pseudooctaves and sharp 3:2's, making it related to 5edo melodically.
+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]].
+=== Harmonics ===
+{{Harmonics in equal|8|3|1|}}
+{{Harmonics in equal|8|3|1|intervals=prime}}
 == Interval table ==
 {{Interval table}}
-== Prime harmonics ==
+[[Category:Macrotonal]]
-{{Harmonics in equal|8|3|1|intervals=prime}}
-[[Category:edt]]
-[[Category:tritave]]
-[[category:macrotonal]]