8edt: Difference between revisions

(7 intermediate revisions by 5 users not shown)

Line 1:

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

== Theory ==

If you view things from the perspective of the [[4L 5s (3/1-equivalent)|4L 5s<3/1>]] Bohlen-Pierce MOS scale, then 8edt could be seen as an analog of [[10edo]], since 8edt is a double of [[4edt]] (the collapsed form of the 4L 5s<3/1> scale, while 10edo is the double of [[5edo]] (the collapsed form of the [[5L 2s]] diatonic scale). 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 ==

Line 15:

Line 14:

[[~~Category:edt~~]]

== See also ==

[[Category:~~tritave]]~~

* [[Alpha, beta, and gamma family of equal divisions]]

~~[[category:macrotonal~~]]

[[Category:Macrotonal]]

@@ Line 1: / Line 1: @@
 {{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).|inline=1}}
+== Theory ==
+If you view things from the perspective of the [[4L 5s (3/1-equivalent)|4L 5s<3/1>]] Bohlen-Pierce MOS scale, then 8edt could be seen as an analog of [[10edo]], since 8edt is a double of [[4edt]] (the collapsed form of the 4L 5s<3/1> scale, while 10edo is the double of [[5edo]] (the collapsed form of the [[5L 2s]] diatonic scale). 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}}
@@ Line 15: / Line 14: @@
 {{Interval table}}
-[[Category:edt]]
+== See also ==
-[[Category:tritave]]
+* [[Alpha, beta, and gamma family of equal divisions]]
-[[category:macrotonal]]
+[[Category:Macrotonal]]

8edt: Difference between revisions

CompactStar (talk | contribs)