If F = 3 = G were true, where is still the distinction between both.

 Some points very very interesting. Some other points seem queer. If F = 3 = G were true, where is still the distinction between both. We are afraid to say that for some humans it sounds like a straight lie… When you can state the fifth G = 3×C as an overtone harmonic, shouldn't we get the fifth F = ⅓×C as its undertone harmonic. Since C can be, in its turn, as an overtone harmonic 3×F. Is this perhaps too simple. Please what's wrong with it?

yes thank you for thinking about this. The F is called the "phantom tonic" because the Perfect Fourth can not be created from the Overtone series by using the same root tonic of the C as the 1 since the denominator as 4/3 does not go into the 1 - so the F as the Perfect Fourth was created from the subharmonic Perfect Fifth of the C as the 1, so 2/3 as C to F, subharmonic. So using strings - you can not have a wavelength greater than the original frequency - so you need a double octave so that the F is created as 6/8 instead, using a different value of the 1 for the octave of 0 to 8. Then this is inverted for 8/6 as 4/3, the Perfect Fourth.

But now it is no longer frequency but instead it is geometric magnitude with the octave being 12 to 6. So then you get 8/12 as 2/3 with 3/2 frequency PLUS 8/6 as 4/3 frequency to create the very first LOGARITHMIC equation of Western science! So that as geometric magnitude then the PErfect Fifth PLUS the Perfect Fourth = the Octave as 8/12 plus 8/6 = 12/6. So this is never even questioned when Westerners learn music theory since most people learn by ROTE - so they don't notice that the "one" as the root tonic value got changed from 0 to 12 into 0 to 8.

This was recently discovered by Professor Richard McKirahan, translating Philolaus, with the realization that for the first time the word "magnitude" from geometry was then applied to music ratios in order to create a logarithmic equation, such that 9/8 cubed then equals the tritone interval as the square root of two value with 5/4 as the cube root of two. So this means the original "Doe a Deer" scale assumes a geometric magnitude value for the "x." Again the "F" of the Doe a Deer scale is derived from (2/3)x that is then "doubled" back into the same octave - with the WRONG assumption that it's the same value to the root tonic! So clearly a Perfect Fifth as subharmonic to the root tonic - as an "F" - has a different "pull" to the root tonic then the octave of that F as the Perfect Fourth above the root tonic.

And so the G as the 3/2 Perfect Fifth above the root tonic also has a different push to the octave - since it is a Perfect Fourth to the same Pitch of C in the octave. This is the "noncommutative phase" secret of music theory. Again this was completely covered up as the origin of Western science. Math professor Luigi Borzacchini calls it a "deep pre-established disharmony" that is the "guiding evolutive principle" of Western science. My blog has tons of research details on this. In contrast - China and India fully acknowledge and embrace the different geometry of 2/3 and 3/2 even though BOTH are a Perfect Fifth. So in other words since 2 does not go into 3 - then the Octaves can not be lined up as a logarithmic tuning.

The West went against the empirical reality of noncommutative phase and instead FORCED a logarithmic symmetric lie. This is why Archytas for his "Arithmetic Mean x Harmonic Mean = Geometric Mean Squared" logarithmic equation can ONLY use the frequencies with the numerator as a greater value than the denominator - in order to cover up this subharmonic origin of the 4/3 Perfect Fourth as "F" in the same octave music scale. Science calls this Fourier or Time-frequency uncertainty - assuming that a linear operator is necessary.

But science has recently proven that people can HEAR and LISTEN FASTER than Fourier Uncertainty (meaning when we listen, there is no need to convert the time-frequency noncommutative phase back into symmetric logarithmic math). So then Alain Connes, the Fields Medal math professor has rediscovered this noncommutative phase secret of music theory and says music theory provides the "formal language" for a unified field science - again based on this ANCIENT acoustics secret that is the empirical truth of reality (thus far covered up in order to create the standard symmetric logic of Western math from the Pythagorean Theorem as the Power Axiom Set).

So as Westerners we are all deeply brainwashed to think of time as a visual symmetric measurement when as Connes points out in fact Frequency is before geometry!! And so there is a "triple spectral" of frequency that is the 5th dimension (for each zero point of geometry). So for each zero point - there ALREADY is a noncommutative and non-local and nondual phase that is superluminal BECAUSE the Perfect Fifth is both F and G at the same time - the future and the past thus overlap. You can see my channel for more details with links to free pdfs and my blog, etc.

 Right  - this is what I got stuck at. David Hykes on Gurdjieff

The musical distances are identical, and of course the intervals are inverted (3/1 gives SOL, while 1/3, its inverse, gives FA).