Factor 9 grid: Difference between revisions

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== Factor 9 Grid ~~temperament (495 & 666)~~ ==

== Factor 9 Grid temperaments ==

In an extremely ironic twist, this allegedly divine and enlightening scale is well-approximated by an evil satanic temperament of ~~[[666edo|~~666 equal divisions of the ~~octave]]~~. ~~If performed using general temperament theory, it results in the following 23-limit temperament:~~

In an extremely ironic twist, this allegedly divine and enlightening scale is well-approximated by an evil satanic temperament of 666 equal divisions of the 15/14 interval.

However, Eliora when trying to convert Factor 9 grid into a rank two temperament did not realize that x31eq.com resource takes first interval as the equivalence interval, and assumed that it is represented by [[666edo]] instead. "q666" in the temperament finder stands for 666ed15/14 as opposed to 666ed2.

This being said, 495 & 666 temperament will retain the name "Factor 9 grid", since music was already composed in the 666edo scale approximating Factor 9 grid. The corrected version will be named ''Real Factor 9 grid''.

If performed using general temperament theory, the first discovered temperament results in the following 23-limit temperament:

=== Factor 9 grid (495 & 666) ===

Subgroup: 2.3.5.7.11.13.17.19.23

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POTE Generator: 63.0631c (~28/27)

Vals: 171f, 495, 666

Vals: 171f, 495, 666.

The corrected version would be with 495ed15/14 & 666ed15/14, which corresponds to a 4973 & 6691 temperament in the 23-limit:

=== Real Factor 9 grid (4973 & 6691) ===

Subgroup: 2.3.5.7.11.13.17.19.23

Comma list: 52326/52325, 57477/57475, 89376/89375, 104329/104328, 392000/391989, 1382576/1382535, 4161311/4161114

Mapping: ⟨1 70 -149 -71 -648 1250 -461 73 -988], ⟨0 -203 449 219 1933 -3698 1380 -204 2945]

Optimal tuning (CTE): 404.4239c

Vals: 4973, 6691

== Mysticism and reality ==

@@ Line 46: / Line 46: @@
 |}
-== Factor 9 Grid temperament (495 & 666) ==
+== Factor 9 Grid temperaments ==
-In an extremely ironic twist, this allegedly divine and enlightening scale is well-approximated by an evil satanic temperament of [[666edo|666 equal divisions of the octave]]. If performed using general temperament theory, it results in the following 23-limit temperament:
+In an extremely ironic twist, this allegedly divine and enlightening scale is well-approximated by an evil satanic temperament of 666 equal divisions of the 15/14 interval.
+However, Eliora when trying to convert Factor 9 grid into a rank two temperament did not realize that x31eq.com resource takes first interval as the equivalence interval, and assumed that it is represented by [[666edo]] instead. "q666" in the temperament finder stands for 666ed15/14 as opposed to 666ed2.
+This being said, 495 & 666 temperament will retain the name "Factor 9 grid", since music was already composed in the 666edo scale approximating Factor 9 grid. The corrected version will be named ''Real Factor 9 grid''.
+If performed using general temperament theory, the first discovered temperament results in the following 23-limit temperament:
+=== Factor 9 grid (495 & 666) ===
 Subgroup: 2.3.5.7.11.13.17.19.23
@@ Line 55: / Line 62: @@
 POTE Generator: 63.0631c (~28/27)
-Vals: 171f, 495, 666
+Vals: 171f, 495, 666.
+The corrected version would be with 495ed15/14 & 666ed15/14, which corresponds to a 4973 & 6691 temperament in the 23-limit:
+=== Real Factor 9 grid (4973 & 6691) ===
+Subgroup: 2.3.5.7.11.13.17.19.23
+Comma list: 52326/52325, 57477/57475, 89376/89375, 104329/104328, 392000/391989, 1382576/1382535, 4161311/4161114
+Mapping: ⟨1 70 -149 -71 -648 1250 -461 73 -988], ⟨0 -203 449 219 1933 -3698 1380 -204 2945]
+Optimal tuning (CTE): 404.4239c
+Vals: 4973, 6691
 == Mysticism and reality ==