720edo: Difference between revisions

Line 11:

=== Subsets and supersets ===

720edo is the 14th [[superabundant edo]], and also the 6th factorial edo (720 = 1 × 2 × 3 × 4 × 5 × 6 = 6!), which means it contains a massive amount of subsets, limited modes of transposition, and fraction-octave [[mos]]ses. With 720edo, it is better to use various vals mimicking smaller edos instead of the patent val, because it sounds as if the patent val is ''creating'' commas, not tempering them out (for example, the 421\720 patent val fifth vs. the 420\720 fifth stemming from [[12edo]]).

720edo is the 14th [[superabundant edo]], and also the 6th factorial edo ({{nowrap|720 {{=}} 1 × 2 × 3 × 4 × 5 × 6 {{=}} 6!}}), which means it contains a massive amount of subsets, limited modes of transposition, and fraction-octave [[mos]]ses. With 720edo, it is better to use various vals mimicking smaller edos instead of the patent val, because it sounds as if the patent val is ''creating'' commas, not tempering them out (for example, the 421\720 patent val fifth vs. the 420\720 fifth stemming from [[12edo]]).

Since {{nowrap|720 {{=}} 72 × 10}}, its possible to conceptualize it as a superset of [[72edo]] and [[10edo]], which are interesting in their own right. However, the patent val's 5/4 of 720edo comes from [[90edo]], and not 72edo.

Line 50:

| [[Tetraicosic]]

|}

<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if ~~it is~~ distinct

<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct

[[Category:Schismatic]]

[[Category:Octant]]

@@ Line 11: / Line 11: @@
 === Subsets and supersets ===
-edo is the 14th [[superabundant edo]], and also the 6th factorial edo (720 = 1 × 2 × 3 × 4 × 5 × 6 = 6!), which means it contains a massive amount of subsets, limited modes of transposition, and fraction-octave [[mos]]ses. With 720edo, it is better to use various vals mimicking smaller edos instead of the patent val, because it sounds as if the patent val is ''creating'' commas, not tempering them out (for example, the 421\720 patent val fifth vs. the 420\720 fifth stemming from [[12edo]]).
+edo is the 14th [[superabundant edo]], and also the 6th factorial edo ({{nowrap|720 {{=}} 1 × 2 × 3 × 4 × 5 × 6 {{=}} 6!}}), which means it contains a massive amount of subsets, limited modes of transposition, and fraction-octave [[mos]]ses. With 720edo, it is better to use various vals mimicking smaller edos instead of the patent val, because it sounds as if the patent val is ''creating'' commas, not tempering them out (for example, the 421\720 patent val fifth vs. the 420\720 fifth stemming from [[12edo]]).
 Since {{nowrap|720 {{=}} 72 × 10}}, its possible to conceptualize it as a superset of [[72edo]] and [[10edo]], which are interesting in their own right. However, the patent val's 5/4 of 720edo comes from [[90edo]], and not 72edo.
@@ Line 50: / Line 50: @@
 | [[Tetraicosic]]
 |}
-<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
+<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
 [[Category:Schismatic]]
 [[Category:Octant]]