Octaphore: Difference between revisions

Line 15:

[[Comma list]]: 94450499584/94143178827

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

Line 23:

=== 2.3.7 Unicorn ===

==== Undecimal Octaphore====

By noticing that the interval at ⟨4 2 -2] is quite close to 11/8, we can add prime 11 to the mapping by tempering out the [[Reef comma]].

Subgroup: 2.3.5.7.11

Comma list: 94450499584/94143178827, 200704/200475

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

Optimal tuning (POTE): ~2 = 1\1, ~27/26 = 62.233, ~5/4 = 386.481

==== Tridecimal Octaphore ====

By noticing that two generators is extremely close to 14/13, we can add prime 13 to the mapping by tempering out the [[729/728|Squbema]], or equivalently by tempering out the [[28812/28561|Tesseract Comma]].

Subgroup: 2.3.5.7.11.13

Comma list: 729/728, 3584/3575, 660275/657072

Mapping: [⟨1 2 2 4 4 5], ⟨0 -8 0 -23 2 -25], ⟨0 0 1 0 -2 0]]

Optimal tuning (POTE): ~2 = 1\1, ~27/26 = 62.281, ~5/4 = 386.512

===2.3.7 Unicorn===

If we temper the octaphore in its minimal prime subgroup of 2.3.7, we get the 2.3.7-subgroup version of [[unicorn]], where it finds prime 5 by interpreting five gens as a flat [[~]][[6/5]] by tempering [[126/125]].

Line 39:

Line 61:

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

== See also ==

==See also==

* [[Unicorn family]]

*[[Unicorn family]]

* [[Unicorn comma]]

*[[Unicorn comma]]

[[Category:Commas named for how they divide the fourth]]

[[Category:Commas named for the intervals they stack]]

@@ Line 15: / Line 15: @@
 [[Comma list]]: 94450499584/94143178827
-{{Mapping|legend=1| 1 2 0 4 | 0 -8 0 -23 | 0 0 1 0 }}
+{{Mapping|legend=1| 1 2 2 4 | 0 -8 0 -23 | 0 0 1 0 }}
 : mapping generators: ~2, ~28/27, ~5
@@ Line 23: / Line 23: @@
 {{Optimal ET sequence|legend=1| 19, 39d, 58, 77, 96d, 135 }}
-=== 2.3.7 Unicorn ===
+==== Undecimal Octaphore====
-{{ See also | Unicorn }}
+By noticing that the interval at ⟨4 2 -2] is quite close to 11/8, we can add prime 11 to the mapping by tempering out the [[Reef comma]].
+Subgroup: 2.3.5.7.11
+Comma list: 94450499584/94143178827, 200704/200475
+Mapping: [⟨1 2 2 4 4], ⟨0 -8 0 -23 2], ⟨0 0 1 0 -2]]
+Optimal tuning (POTE): ~2 = 1\1, ~27/26 = 62.233, ~5/4 = 386.481
+==== Tridecimal Octaphore ====
+By noticing that two generators is extremely close to 14/13, we can add prime 13 to the mapping by tempering out the [[729/728|Squbema]], or equivalently by tempering out the [[28812/28561|Tesseract Comma]].
+Subgroup: 2.3.5.7.11.13
+Comma list: 729/728, 3584/3575, 660275/657072
+Mapping: [⟨1 2 2 4 4 5], ⟨0 -8 0 -23 2 -25], ⟨0 0 1 0 -2 0]]
+Optimal tuning (POTE): ~2 = 1\1, ~27/26 = 62.281, ~5/4 = 386.512
+===2.3.7 Unicorn===
+{{See also | Unicorn }}
 If we temper the octaphore in its minimal prime subgroup of 2.3.7, we get the 2.3.7-subgroup version of [[unicorn]], where it finds prime 5 by interpreting five gens as a flat [[~]][[6/5]] by tempering [[126/125]].
@@ Line 39: / Line 61: @@
 {{Optimal ET sequence|legend=1| 19, 20d, 39d, 58, 77, 96d, 135 }}
-== See also ==
+==See also==
-* [[Unicorn family]]
+*[[Unicorn family]]
-* [[Unicorn comma]]
+*[[Unicorn comma]]
 [[Category:Commas named for how they divide the fourth]]
 [[Category:Commas named for the intervals they stack]]