Factor 9 grid: Difference between revisions

(2 intermediate revisions by the same user not shown)

Line 4:

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.

Line 75:

== 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 ==

@@ Line 4: / Line 4: @@
 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.
@@ Line 75: / Line 75: @@
 == 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 ==