Factor 9 grid: Difference between revisions

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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 represent the Factor 9 grid via a rank-2 temperament did not realize that x31eq.com resource takes the first interval in the number series as the equivalence interval, and assumed that it is represented by [[666edo]] instead. "q666" in the temperament finder, when 14:15:16:... typed out, 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''.

This being said, this temperament preserves more properties of the "Factor 9 Grid" than the corrected version, since it's period-9 and its period minus reduced generator interval also maps to the smallest interval in the Factor 9 Grid system, [[28/27]]. So in the end, 666edo does ironically represent the Factor 9 grid well. The corrected version would be with 495ed15/14 & 666ed15/14, which corresponds to a 4973 & 6691 temperament in the 23-limit, that has no structure resembling the initial factor-9 grid other than being made of two good edos in the 23-limit.

~~When viewed from a regular~~ temperament ~~perspective~~, the ~~first discovered temperament results in~~ the ~~following 23-limit temperament:~~

The 495 & 666 temperament is given the name ''enneasoteric'' by Eliora, since music was already composed in the 666edo scale approximating Factor 9 grid, while the name "factor 9 grid" to avoid ambiguity will be retained with the scale only.

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

=== Enneasoteric (495 & 666) ===

[[Subgroup]]: 2.3.5.7.11.13.17.19.23

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Vals: {{EDOs|171f, 495, 666}}.

This being said, this temperament preserves more properties of the "Factor 9 Grid" than the corrected version, since it's period-9 and its period minus reduced generator interval also maps to the smallest interval in the Factor 9 Grid system, [[28/27]]. So in the end, 666edo does ironically represent the Factor 9 grid well. 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 49: / Line 49: @@
 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 represent the Factor 9 grid via a rank-2 temperament did not realize that x31eq.com resource takes the first interval in the number series as the equivalence interval, and assumed that it is represented by [[666edo]] instead. "q666" in the temperament finder, when 14:15:16:... typed out, 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''.
+This being said, this temperament preserves more properties of the "Factor 9 Grid" than the corrected version, since it's period-9 and its period minus reduced generator interval also maps to the smallest interval in the Factor 9 Grid system, [[28/27]]. So in the end, 666edo does ironically represent the Factor 9 grid well. The corrected version would be with 495ed15/14 & 666ed15/14, which corresponds to a 4973 & 6691 temperament in the 23-limit, that has no structure resembling the initial factor-9 grid other than being made of two good edos in the 23-limit.
-When viewed from a regular temperament perspective, the first discovered temperament results in the following 23-limit temperament:
+The 495 & 666 temperament is given the name ''enneasoteric'' by Eliora, since music was already composed in the 666edo scale approximating Factor 9 grid, while the name "factor 9 grid" to avoid ambiguity will be retained with the scale only.
-=== Factor 9 grid (495 & 666) ===
+=== Enneasoteric (495 & 666) ===
 [[Subgroup]]: 2.3.5.7.11.13.17.19.23
@@ Line 64: / Line 64: @@
 Vals: {{EDOs|171f, 495, 666}}.
-This being said, this temperament preserves more properties of the "Factor 9 Grid" than the corrected version, since it's period-9 and its period minus reduced generator interval also maps to the smallest interval in the Factor 9 Grid system, [[28/27]]. So in the end, 666edo does ironically represent the Factor 9 grid well. 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 ==