Octaphore: Difference between revisions

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{{Infobox Interval|Name=~~Octaphore~~ comma, ~~Enneagari~~|Ratio=94450499584/94143178827|Monzo=14 -23 0 8}}

{{Infobox Interval

| Name = octaphore comma, enneagari comma

| Ratio = 94450499584/94143178827

| Monzo = 14 -23 0 8

}}

The '''octaphore comma''' is so named because it is the amount by which eight [[28/27]] third-tones exceed the [[4/3]] perfect fourth. It can also be found as the amount by which seven 28/27 third-tones exceed the [[9/7]] supermajor third, or as the sum of the ~~Garischisma~~ (33554432/33480783) and the ~~Septimal Ennealimma~~ (40353607/40310784).

The '''octaphore comma''', also known as the '''enneagari comma''', is a [[small comma|small]] [[7-limit]] (also 2.3.7-[[subgroup]]) [[comma]] measuring about 5.64 [[cent]]s. It is so named because it is the amount by which eight [[28/27]] third-tones exceed the [[4/3]] perfect fourth. It can also be found as the amount by which seven 28/27 third-tones exceed the [[9/7]] supermajor third, or as the sum of the [[garischisma|garischisma (33554432/33480783)]] and the [[septimal ennealimma|septimal ennealimma (40353607/40310784)]].

== Temperaments ==

Tempering out the ~~Octaphore~~ comma in the full 7-limit leads to rank-3 ~~Octophore~~ temperament (note the different spelling), and tempering it out in the 2.3.7 subgroup leads to the rank-2 ~~Actinide~~ temperament.

Tempering out the octaphore comma in the full 7-limit leads to rank-3 octophore temperament (note the different spelling), and tempering it out in the 2.3.7 subgroup leads to the rank-2 actinide temperament.

=== ~~'''~~Octophore~~'''~~ ===

=== Octophore ===

Subgroup: 2.3.5.7

[[Subgroup]]: 2.3.5.7

Comma ~~List~~: 94450499584/94143178827

[[Comma list]]: 94450499584/94143178827

Mapping~~: [⟨1 2~~ 2 4~~], ⟨0~~ -8 0 -23~~], ⟨0~~ 0 1 0]]

~~POTE tuning~~: ~28/27 ~~= 62.233~~, ~5~~/4 = 386.314~~

: mapping generators: ~2, ~28/27, ~5

~~Optimal ET sequence:~~ [[~~19edo|19~~]], [[~~39edo|39d~~]], ~~[[58edo~~|58]], ~~[[77edo|~~77]], ~~[[96edo|~~96d]], ~~[[135edo|~~135]]

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~28/27 = 62.233, ~5/4 = 386.314

=== Actinide ===

Subgroup: 2.3.7

[[Subgroup]]: 2.3.7

Comma ~~List~~: 94450499584/94143178827

[[Comma list]]: 94450499584/94143178827

Mapping~~: [⟨1~~ 2 4~~], ⟨0~~ -8 -23]]

~~POTE tuning~~: ~28/27 ~~= 62.233~~

: mapping generators: ~2, ~28/27

~~Optimal ET sequence:~~ [[~~19edo|19~~]], [[~~20edo|20d~~]], ~~[[39edo|39d]], [[58edo|58]], [[77edo|77]], [[96edo|96d]], [[135edo|135]]~~

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~28/27 = 62.233

=~~= See also ==~~

{{Optimal ET sequence|legend=1| 19, 20d, 39d, 58, 77, 96d, 135 }}

~~[[Small comma]]~~

@@ Line 1: / Line 1: @@
-{{Infobox Interval|Name=Octaphore comma, Enneagari|Ratio=94450499584/94143178827|Monzo=14 -23 0 8}}
+{{Infobox Interval
+| Name = octaphore comma, enneagari comma
+| Ratio = 94450499584/94143178827
+| Monzo = 14 -23 0 8
+}}
-The '''octaphore comma''' is so named because it is the amount by which eight [[28/27]] third-tones exceed the [[4/3]] perfect fourth.  It can also be found as the amount by which seven 28/27 third-tones exceed the [[9/7]] supermajor third, or as the sum of the Garischisma (33554432/33480783) and the Septimal Ennealimma (40353607/40310784).
+The '''octaphore comma''', also known as the '''enneagari comma''', is a [[small comma|small]] [[7-limit]] (also 2.3.7-[[subgroup]]) [[comma]] measuring about 5.64 [[cent]]s. It is so named because it is the amount by which eight [[28/27]] third-tones exceed the [[4/3]] perfect fourth.  It can also be found as the amount by which seven 28/27 third-tones exceed the [[9/7]] supermajor third, or as the sum of the [[garischisma|garischisma (33554432/33480783)]] and the [[septimal ennealimma|septimal ennealimma (40353607/40310784)]].
 == Temperaments ==
-Tempering out the Octaphore comma in the full 7-limit leads to rank-3 Octophore temperament (note the different spelling), and tempering it out in the 2.3.7 subgroup leads to the rank-2 Actinide temperament.
+Tempering out the octaphore comma in the full 7-limit leads to rank-3 octophore temperament (note the different spelling), and tempering it out in the 2.3.7 subgroup leads to the rank-2 actinide temperament.
-=== '''Octophore''' ===
+=== Octophore ===
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
-Comma List: 94450499584/94143178827
+[[Comma list]]: 94450499584/94143178827
-Mapping: [⟨1 2 2 4], ⟨0 -8 0 -23], ⟨0 0 1 0]]
+{{Mapping|legend=1| 1 2 0 4 | 0 -8 0 -23 | 0 0 1 0 }}
-POTE tuning: ~28/27 = 62.233, ~5/4 = 386.314
+: mapping generators: ~2, ~28/27, ~5
-Optimal ET sequence: [[19edo|19]], [[39edo|39d]], [[58edo|58]], [[77edo|77]], [[96edo|96d]], [[135edo|135]]
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~28/27 = 62.233, ~5/4 = 386.314
+{{Optimal ET sequence|legend=1| 19, 39d, 58, 77, 96d, 135 }}
 === Actinide ===
-Subgroup: 2.3.7
+[[Subgroup]]: 2.3.7
-Comma List: 94450499584/94143178827
+[[Comma list]]: 94450499584/94143178827
-Mapping: [⟨1 2 4], ⟨0 -8 -23]]
+{{Mapping|legend=1| 1 2 4 | 0 -8 -23 }}
-POTE tuning: ~28/27 = 62.233
+: mapping generators: ~2, ~28/27
-Optimal ET sequence:  [[19edo|19]], [[20edo|20d]], [[39edo|39d]], [[58edo|58]], [[77edo|77]], [[96edo|96d]], [[135edo|135]]
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~28/27 = 62.233
-== See also ==
+{{Optimal ET sequence|legend=1| 19, 20d, 39d, 58, 77, 96d, 135 }}
-[[Small comma]]