Factor 9 grid - Revision history

Eliora: /* Theory */

2026-04-01T22:44:53Z

Theory

← Older revision		Revision as of 22:44, 1 April 2026
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	The scale is an isoharmonic sequence consisting of the following frequencies (in Hz): 126, 135, 144, 153, 162, 171, 180, 189, 198, 207, 216, 225, 234, 243, and their octave equivalents. This sequence forms an arithmetic progression with a constant difference of 9, which gives rise to the name "Factor 9 grid". It hence is identical to the [[14ado]] scale spanning the 14th through 28th harmonics, and since 14ado is a [[23-limit]] just intonation system, Factor 9 grid correspondingly is a part of of [[23-limit]] just intonation.		The scale is an isoharmonic sequence consisting of the following frequencies (in Hz): 126, 135, 144, 153, 162, 171, 180, 189, 198, 207, 216, 225, 234, 243, and their octave equivalents. This sequence forms an arithmetic progression with a constant difference of 9, which gives rise to the name "Factor 9 grid". It hence is identical to the [[14ado]] scale spanning the 14th through 28th harmonics, and since 14ado is a [[23-limit]] just intonation system, Factor 9 grid correspondingly is a part of of [[23-limit]] just intonation.

	More precisely, the "Factor 9 grid" refers to a specific mode of [[14ado]] whose tonic is placed on the step corresponding to 432 Hz and its octave equivalents, such as 216 Hz or 864 Hz, which is the 11th step of 14ado itself. It is this particular modal alignment that is commonly associated with "A = 432 Hz" conspiracy theories, where the emphasis is placed on organizing the scale around 432 Hz as a tonic.		More precisely, the "Factor 9 grid" refers to a specific mode of [[14ado]] whose tonic is placed on the step corresponding to 432 Hz and its octave equivalents, such as 216 Hz or 864 Hz, which is the 11th step of 14ado itself. It is this particular modal alignment that is commonly associated with "A = 432 Hz" conspiracy theories, where the emphasis is placed on organizing the scale around 432 Hz as a tonic. Proponents of the "Factor 9 grid" manly present it as the more consonant or acoustically "healthier" alternative to the prevailing [[12edo\|12-tone equal temperament]], often accompanied by references to the symbolic or "sacred" significance of the number 12.

	Proponents of the "Factor 9 grid" manly present it as the more consonant or acoustically "healthier" alternative to the prevailing [[12edo\|12-tone equal temperament]], often accompanied by references to the symbolic or "sacred1 significance of the number 12. However, descriptions of the scale, as they are presented in the video, contain several internal inconsistencies. The underlying structure of the grid, as mentioned above, corresponds to [[14ado]], which by definition contains 14 distinct steps per octave rather than 12, thus conflicting with the initial claims that the scale is 12-note or is a replacement for 12edo.		However, descriptions of the scale, as they are presented in the video, contain several internal inconsistencies. The underlying structure of the grid, as mentioned above, corresponds to [[14ado]], which by definition contains 14 distinct steps per octave rather than 12, thus conflicting with the initial claims that the scale is 12-note or is a replacement for 12edo.

	Furthermore, in the cited material, the sequence appears to omit the frequency 243 Hz (and its octave equivalents), despite it being a member of arithmetic progression that constitutes the scale. This omission appears to be motivated by an attempt to align the number of pitches with the 12-note framework of standard Western notation, as the presentation maps the resulting tones onto conventional note names. However, the rationale for excluding specifically 243 Hz and its octave displacement, as opposed to any other member of the sequence, is not explicitly addressed. No criteria are provided for why this particular step is removed while the remaining tones are retained, leaving the adjustment unexplained within the context of the scale’s stated arithmetic construction.		Furthermore, in the cited material, the sequence appears to omit the frequency 243 Hz (and its octave equivalents), despite it being a member of arithmetic progression that constitutes the scale. This omission appears to be motivated by an attempt to align the number of pitches with the 12-note framework of standard Western notation, as the presentation maps the resulting tones onto conventional note names. However, the rationale for excluding specifically 243 Hz and its octave displacement, as opposed to any other member of the sequence, is not explicitly addressed. No criteria are provided for why this particular step is removed while the remaining tones are retained, leaving the adjustment unexplained within the context of the scale’s stated arithmetic construction.

Eliora: /* Mysticism and reality */

2026-03-31T03:29:29Z

Mysticism and reality

← Older revision		Revision as of 03:29, 31 March 2026
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	However, claims that specific tuning systems (such as just intonation or particular frequency standards like 432 Hz) have direct effects on public health, social cohesion, or global conditions are not supported by empirical evidence. While differences in tuning can influence perceived consonance, timbre, and listener preference, these effects operate at the level of auditory perception and musical aesthetics rather than large-scale societal outcomes.		However, claims that specific tuning systems (such as just intonation or particular frequency standards like 432 Hz) have direct effects on public health, social cohesion, or global conditions are not supported by empirical evidence. While differences in tuning can influence perceived consonance, timbre, and listener preference, these effects operate at the level of auditory perception and musical aesthetics rather than large-scale societal outcomes.


	Furthermore, from a mathematical perspective, it is not possible to simultaneously achieve the exact rational interval relationships of just intonation and the structural evenness of equal temperament. The irrationality inherent to equal divisions of the octave has been recognized since antiquity, most commonly through proofs such as the irrationality of √2. For example, if there were an exact just intonation fraction corresponding to the 600-cent tritone, its numerator and denominator would be required to satisfy mutually incompatible conditions — [[wikipedia:Square root of 2#Proof by infinite descent\|being both even and coprime]]. Similarly, if a stack of pure fifths (3/2) were to close exactly at the octave, the resulting comma {{Monzo\|-X Y}} would have to equal 1. In this number, numerator X must be a power of 2 and the denominator Y a power of 3, thus implying the existence of an even power of 3, which is not possible.		Furthermore, from a mathematical perspective, it is not possible to simultaneously achieve the exact rational interval relationships of just intonation and the structural evenness of equal temperament. The irrationality inherent to equal divisions of the octave has been recognized since antiquity, most commonly through proofs such as the irrationality of √2. For example, if there were an exact just intonation fraction corresponding to the 600-cent tritone, its numerator and denominator would be required to satisfy mutually incompatible conditions — [[wikipedia:Square root of 2#Proof by infinite descent\|being both even and coprime]]. Similarly, if a stack of pure fifths (3/2) were to close exactly at the octave, the resulting comma {{Monzo\|-X Y}} would have to equal 1. In this number, numerator X must be a power of 2 and the denominator Y a power of 3, thus implying the existence of an even power of 3, which is not possible.

Eliora: /* Mysticism and reality */

2026-03-31T03:28:39Z

Mysticism and reality

← Older revision		Revision as of 03:28, 31 March 2026
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	== Mysticism and reality ==		== Mysticism and reality ==
	The motivation behind the scale, ~~or any kind of~~ esoteric just intonation ~~proposal~~, is that the irrational pitch ~~standard~~ of equal temperament ~~has an~~ acoustically unpleasant ~~effect~~, ~~that subsequently allegedly spreads~~ to ~~the~~ subconscious ~~levels of the mind~~ and ~~results in deterioration of the quality of~~ human ~~life~~.		The motivation behind the scale, as with many esoteric just intonation proposals, is the claim that the irrational pitch relationships of equal temperament produce acoustically unpleasant effects which, in turn, are said to propagate into subconscious perception and negatively affect human well-being.

	However, ~~it is not possible to have both the rationality of~~ just intonation ~~and evenness of equal temperament at the same time. The irrationality of equal temperament has been known since ancient times by various names~~, ~~the most common being the proof~~ by ~~infinite descent of the square root of two~~. ~~If there was an exact JI interval fraction which corresponds to the 600 cent tritone~~, ~~it's numerator and denominator would have to be both even~~ and ~~coprime~~, ~~which cannot happen. Another example is that if a stack of fifths (3/2) were to close~~ at the ~~octave, the resulting comma {{Monzo\|-X Y}} would be equal to 1, while having X be a power~~ of 2, and ~~Y be a power of 3. This would imply the existence of an even power of 3, which is nonsense~~.		However, claims that specific tuning systems (such as just intonation or particular frequency standards like 432 Hz) have direct effects on public health, social cohesion, or global conditions are not supported by empirical evidence. While differences in tuning can influence perceived consonance, timbre, and listener preference, these effects operate at the level of auditory perception and musical aesthetics rather than large-scale societal outcomes.

	~~If there~~ is ~~credible scientific evidence that playing~~ just intonation ~~music~~ through ~~public loudspeakers~~, in ~~soundtracks~~, or ~~other~~ public ~~venues will increase peace~~ and ~~quality~~ of human ~~life~~, ~~it must be~~ presented ~~properly, without~~ occultist ~~context~~.
			Furthermore, from a mathematical perspective, it is not possible to simultaneously achieve the exact rational interval relationships of just intonation and the structural evenness of equal temperament. The irrationality inherent to equal divisions of the octave has been recognized since antiquity, most commonly through proofs such as the irrationality of √2. For example, if there were an exact just intonation fraction corresponding to the 600-cent tritone, its numerator and denominator would be required to satisfy mutually incompatible conditions — [[wikipedia:Square root of 2#Proof by infinite descent\|being both even and coprime]]. Similarly, if a stack of pure fifths (3/2) were to close exactly at the octave, the resulting comma {{Monzo\|-X Y}} would have to equal 1. In this number, numerator X must be a power of 2 and the denominator Y a power of 3, thus implying the existence of an even power of 3, which is not possible.

			More broadly, while differences in tuning systems can affect perceived consonance, beating, and timbral character, these effects remain within the domain of auditory perception and musical aesthetics. There is no established physiological or cognitive mechanism by which specific frequency ratios could influence complex outcomes such as public health, social stability, or quality of life at scale. Such phenomena are determined by a wide range of economic, environmental, and social factors, none of which have demonstrated dependence on musical tuning standards.

			Accordingly, claims that particular tuning systems produce measurable improvements in human well-being would require empirical verification under controlled conditions. In the absence of such evidence, assertions of this kind remain unsupported, particularly when presented within numerological or occultist frameworks rather than scientific methodology.

	== External links ==		== External links ==

Eliora: /* Attempts at representing the scale through regular temperament theory */ do the same, expand

2026-03-31T03:17:28Z

Attempts at representing the scale through regular temperament theory: do the same, expand

← Older revision		Revision as of 03:17, 31 March 2026
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	== Attempts at representing the scale through regular temperament theory ==		== 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.		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.

Eliora: /* Theory */

2026-03-31T03:04:59Z

Theory

← Older revision		Revision as of 03:04, 31 March 2026
Line 6:		Line 6:
	More precisely, the "Factor 9 grid" refers to a specific mode of [[14ado]] whose tonic is placed on the step corresponding to 432 Hz and its octave equivalents, such as 216 Hz or 864 Hz, which is the 11th step of 14ado itself. It is this particular modal alignment that is commonly associated with "A = 432 Hz" conspiracy theories, where the emphasis is placed on organizing the scale around 432 Hz as a tonic.		More precisely, the "Factor 9 grid" refers to a specific mode of [[14ado]] whose tonic is placed on the step corresponding to 432 Hz and its octave equivalents, such as 216 Hz or 864 Hz, which is the 11th step of 14ado itself. It is this particular modal alignment that is commonly associated with "A = 432 Hz" conspiracy theories, where the emphasis is placed on organizing the scale around 432 Hz as a tonic.

	Proponents of the "Factor 9 grid" manly present it as the more consonant or acoustically "healthier" alternative to the prevailing [[12edo\|12-tone equal temperament]], often accompanied by references to the symbolic or "~~sacred”~~ significance of the number 12. However, descriptions of the scale, as they are presented in the video, contain several internal inconsistencies. The underlying structure of the grid, as mentioned above, corresponds to [[14ado]], which by definition contains 14 distinct steps per octave rather than 12, thus conflicting with the initial claims that the scale is 12-note or is a replacement for 12edo.		Proponents of the "Factor 9 grid" manly present it as the more consonant or acoustically "healthier" alternative to the prevailing [[12edo\|12-tone equal temperament]], often accompanied by references to the symbolic or "sacred1 significance of the number 12. However, descriptions of the scale, as they are presented in the video, contain several internal inconsistencies. The underlying structure of the grid, as mentioned above, corresponds to [[14ado]], which by definition contains 14 distinct steps per octave rather than 12, thus conflicting with the initial claims that the scale is 12-note or is a replacement for 12edo.

	Furthermore, in the cited material, the sequence appears to omit the frequency 243 Hz (and its octave equivalents), despite it being a member of arithmetic progression that constitutes the scale. This omission appears to be motivated by an attempt to align the number of pitches with the 12-note framework of standard Western notation, as the presentation maps the resulting tones onto conventional note names. However, the rationale for excluding specifically 243 Hz and its octave displacement, as opposed to any other member of the sequence, is not explicitly addressed. No criteria are provided for why this particular step is removed while the remaining tones are retained, leaving the adjustment unexplained within the context of the scale’s stated arithmetic construction.		Furthermore, in the cited material, the sequence appears to omit the frequency 243 Hz (and its octave equivalents), despite it being a member of arithmetic progression that constitutes the scale. This omission appears to be motivated by an attempt to align the number of pitches with the 12-note framework of standard Western notation, as the presentation maps the resulting tones onto conventional note names. However, the rationale for excluding specifically 243 Hz and its octave displacement, as opposed to any other member of the sequence, is not explicitly addressed. No criteria are provided for why this particular step is removed while the remaining tones are retained, leaving the adjustment unexplained within the context of the scale’s stated arithmetic construction.

Eliora: /* Theory */ streamline the writing, make it more formal, read like a proper reading of a source not a claim about F9G

2026-03-31T03:04:40Z

Theory: streamline the writing, make it more formal, read like a proper reading of a source not a claim about F9G

← Older revision		Revision as of 03:04, 31 March 2026
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	== Theory ==		== Theory ==
	The scale is an isoharmonic sequence ~~that consists~~ of the following ~~notes,~~ in ~~Hertz~~: 126, 135, 144, 153, 162, 171, 180, 189, 198, 207, 216, 225, 234, 243~~, (octave)~~, and their octave ~~displacements. Therefore this is equivalent to [[14ado]] scale, running from 14th to 28th harmonic~~. This is an arithmetic progression with ~~the~~ difference of 9, ~~hence why this scale was named~~ "Factor 9 grid". ~~Since~~ the ~~largest prime present in~~ the ~~intervals~~ is 23, ~~this makes~~ Factor 9 grid a part of [[23-limit]] just intonation.		The scale is an isoharmonic sequence consisting of the following frequencies (in Hz): 126, 135, 144, 153, 162, 171, 180, 189, 198, 207, 216, 225, 234, 243, and their octave equivalents. This sequence forms an arithmetic progression with a constant difference of 9, which gives rise to the name "Factor 9 grid". It hence is identical to the [[14ado]] scale spanning the 14th through 28th harmonics, and since 14ado is a [[23-limit]] just intonation system, Factor 9 grid correspondingly is a part of of [[23-limit]] just intonation.

	~~The scale~~, ~~as proposed in~~ the ~~video, contains a major inconsistency - it has 14 notes, while it claims~~ to ~~be supposedly~~ a ~~better replacement towards~~ the ~~current 12-note system~~ and ~~makes references towards~~ the ~~sacrality~~ of ~~the number 12. In addition, the table presented features a 13-note scale where G# and Ab are not enharmonic~~. ~~Also, the scale in the video skips number 243 for an unknown reason, given~~ that ~~126~~ = ~~9 × 14~~, ~~and you need 14 notes to count to~~ the ~~octave displacement, if you are using an arithmetic difference of 9. This page will consider~~ the ~~full 14:15:…:28 otonal sequence~~.		More precisely, the "Factor 9 grid" refers to a specific mode of [[14ado]] whose tonic is placed on the step corresponding to 432 Hz and its octave equivalents, such as 216 Hz or 864 Hz, which is the 11th step of 14ado itself. It is this particular modal alignment that is commonly associated with "A = 432 Hz" conspiracy theories, where the emphasis is placed on organizing the scale around 432 Hz as a tonic.

	~~Since~~ the ~~esoteric affliction towards~~ the note A being ~~432~~ Hz is ~~usually considered~~, the scale is ~~supposed to be played starting~~ with A, ~~which leaves a wide semitone inside~~ the ~~octave~~.		Proponents of the "Factor 9 grid" manly present it as the more consonant or acoustically "healthier" alternative to the prevailing [[12edo\|12-tone equal temperament]], often accompanied by references to the symbolic or "sacred” significance of the number 12. However, descriptions of the scale, as they are presented in the video, contain several internal inconsistencies. The underlying structure of the grid, as mentioned above, corresponds to [[14ado]], which by definition contains 14 distinct steps per octave rather than 12, thus conflicting with the initial claims that the scale is 12-note or is a replacement for 12edo.

			Furthermore, in the cited material, the sequence appears to omit the frequency 243 Hz (and its octave equivalents), despite it being a member of arithmetic progression that constitutes the scale. This omission appears to be motivated by an attempt to align the number of pitches with the 12-note framework of standard Western notation, as the presentation maps the resulting tones onto conventional note names. However, the rationale for excluding specifically 243 Hz and its octave displacement, as opposed to any other member of the sequence, is not explicitly addressed. No criteria are provided for why this particular step is removed while the remaining tones are retained, leaving the adjustment unexplained within the context of the scale’s stated arithmetic construction.

			Additionally, the accompanying table distinguishes between G♯ and A♭ as separate pitches, resulting in a 13-note scale rather than either 12 or 14. This is not explained in the video as well, and further complicates the stated aim of aligning the system with a 12-note framework, particularly in light of the emphasis placed on the number 12 in the associated commentary.

	== Intervals ==		== Intervals ==

BudjarnLambeth at 06:37, 8 October 2024

2024-10-08T06:37:04Z

← Older revision		Revision as of 06:37, 8 October 2024
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	'''Factor 9 grid''' is a type of musical scale which was first proposed for esoteric reasons as a supposed replacement to [[12edo]]. The scale also became notable in music theory when esoteric properties of the scale were subsequently refuted by the famous YouTuber, bassist, and composer Adam Neely.		'''Factor 9 grid''' is a type of musical scale which was first proposed for esoteric reasons as a supposed replacement to [[12edo]]. The scale also became notable in music theory when esoteric properties of the scale were subsequently refuted by the famous YouTuber, bassist, and composer [[Adam Neely]].

	== Theory ==		== Theory ==

BudjarnLambeth: Undo revision 138035 by BudjarnLambeth (talk)

2024-03-03T12:09:10Z

Undo revision 138035 by BudjarnLambeth (talk)

← Older revision		Revision as of 12:09, 3 March 2024
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	* [https://www.youtube.com/watch?v=ghUs-84NAAU Testing 432Hz Frequencies and Temperaments] - refuting by Adam Neely		* [https://www.youtube.com/watch?v=ghUs-84NAAU Testing 432Hz Frequencies and Temperaments] - refuting by Adam Neely

	[[Category:23-limit~~]][[Category:14afdo~~]]		[[Category:23-limit]]

BudjarnLambeth: Added category 14afdo

2024-03-03T12:08:21Z

Added category 14afdo

← Older revision		Revision as of 12:08, 3 March 2024
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	* [https://www.youtube.com/watch?v=ghUs-84NAAU Testing 432Hz Frequencies and Temperaments] - refuting by Adam Neely		* [https://www.youtube.com/watch?v=ghUs-84NAAU Testing 432Hz Frequencies and Temperaments] - refuting by Adam Neely

	[[Category:23-limit]]		[[Category:23-limit]][[Category:14afdo]]

BudjarnLambeth: /* Attempts at representing the scale through regular temperament theory */ Added link to name Eliora

2024-03-03T12:06:17Z

Attempts at representing the scale through regular temperament theory: Added link to name Eliora

← Older revision		Revision as of 12:06, 3 March 2024
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	== Attempts at representing the scale through regular temperament theory ==		== 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.		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, 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.		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.