Factor 9 grid: Difference between revisions

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== 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 ==

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 == 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 ==