720edo: Difference between revisions

Line 13:

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{{clarify}}.

Since 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.

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.

== Regular temperament properties ==

=== Rank-2 temperaments ===

{| class="wikitable center-all left-5"

|+Table of rank-2 temperaments by generator

|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator

! Periods per 8ve

|-

! Periods per 8ve

! Generator*

! Cents*

! Associated Ratio*

! Associated Ratio*

! Temperaments

|-

Line 32:

Line 33:

|-

| 8

| 421\720 (61\720)

| 421\720 (61\720)

| 701.667 (101.667)

| 701.667 (101.667)

| 4/3 (36/35)

| 4/3 (36/35)

| [[Octant]]

|-

| 80

| 421\720 (7\720)

| 421\720 (7\720)

| 701.667 (11.667)

| 701.667 (11.667)

| 4/3 (?)

| 4/3 (?)

| [[Octogintic]]

|-

| 80

| 283\720 (4\720)

| 283\720 (4\720)

| 471.667 (6.667)

| 471.667 (6.667)

| 130/99 (?)

| 130/99 (?)

| [[Tetraicosic]]

|}

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

[[Category:Schismatic]]

[[Category:Octant]]

@@ Line 13: / Line 13: @@
 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{{clarify}}.
-Since 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.
+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.
 == Regular temperament properties ==
 === Rank-2 temperaments ===
 {| class="wikitable center-all left-5"
-|+Table of rank-2 temperaments by generator
+|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
-! Periods<br>per 8ve
+|-
+! Periods<br />per 8ve
 ! Generator*
 ! Cents*
-! Associated<br>Ratio*
+! Associated<br />Ratio*
 ! Temperaments
 |-
@@ Line 32: / Line 33: @@
 |-
 | 8
-| 421\720<br>(61\720)
+| 421\720<br />(61\720)
-| 701.667<br>(101.667)
+| 701.667<br />(101.667)
-| 4/3<br>(36/35)
+| 4/3<br />(36/35)
 | [[Octant]]
 |-
 | 80
-| 421\720<br>(7\720)
+| 421\720<br />(7\720)
-| 701.667<br>(11.667)
+| 701.667<br />(11.667)
-| 4/3<br>(?)
+| 4/3<br />(?)
 | [[Octogintic]]
 |-
 | 80
-| 283\720<br>(4\720)
+| 283\720<br />(4\720)
-| 471.667<br>(6.667)
+| 471.667<br />(6.667)
-| 130/99<br>(?)
+| 130/99<br />(?)
 | [[Tetraicosic]]
 |}
-<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
+{{orf}}
 [[Category:Schismatic]]
 [[Category:Octant]]