Factor 9 grid: Difference between revisions

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== Attempts at representing the scale through regular temperament theory ==

~~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~~.

Within regular temperament theory, the Factor 9 grid admits close approximations through equal divisions of just intervals, and is well-supported by any tuning system that either represents the [[23-limit]] intervals well, or the direct intervals mentioned in the scale.

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~~.

Though, in particular, it is worth noting that it can be represented by 666 equal divisions of the 15/14 interval (666ed15/14), which directly models its harmonic structure, as well as by 666edo, which supports a related regular temperament with similar properties, which is a very ironic aspect of the scale.

The scale, often justified by proponents through numerological arguments emphasizing purity and the special status of certain numbers, is located in close correspondence with equal temperament systems involving the number [[wikipedia:666 (number)|666]], which is a value widely regarded in popular numerological traditions, and Western popular culture as a whole as [[wikipedia:the Number of the Beast|the Number of the Beast]] or satanic. Thus, within the proponents’ own framework, where numerical symbolism is treated as musically or metaphysically significant, this association with 666 directly contradicts the stated rationale for privileging the scale over conventional tuning systems.

[[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, 666edo, more specifically, the 495 & 666 23-limit temperament, regular 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 scale, [[28/27]]. So in a limited way, 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, however that temperament has no structure resembling the initial factor-9 grid other than closely approximating its constituent intervals.

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.

@@ Line 51: / Line 51: @@
 == Attempts at representing the scale through regular temperament theory ==
-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.
+Within regular temperament theory, the Factor 9 grid admits close approximations through equal divisions of just intervals, and is well-supported by any tuning system that either represents the [[23-limit]] intervals well, or the direct intervals mentioned in the scale.
-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.
+Though, in particular, it is worth noting that it can be represented by 666 equal divisions of the 15/14 interval (666ed15/14), which directly models its harmonic structure, as well as by 666edo, which supports a related regular temperament with similar properties, which is a very ironic aspect of the scale.
+The scale, often justified by proponents through numerological arguments emphasizing purity and the special status of certain numbers, is located in close correspondence with equal temperament systems involving the number [[wikipedia:666 (number)|666]], which is a value widely regarded in popular numerological traditions, and Western popular culture as a whole as [[wikipedia:the Number of the Beast|the Number of the Beast]] or satanic. Thus, within the proponents’ own framework, where numerical symbolism is treated as musically or metaphysically significant, this association with 666 directly contradicts the stated rationale for privileging the scale over conventional tuning systems.
+[[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, 666edo, more specifically, the 495 & 666 23-limit temperament, regular 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 scale, [[28/27]]. So in a limited way, 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, however that temperament has no structure resembling the initial factor-9 grid other than closely approximating its constituent intervals.
 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: Difference between revisions

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