There’s a lot of discussion on the internet about A=432 Hz versus A=440 Hz – and, in my opinion, rightly so – because 440 Hz is an aberrant frequency with no grounding in nature. Whereas A = 432 Hz does show up as the Major 3rd harmonic of the Fifth (F) of our “magic frequency” of B-flat = 460.8 Hz (which we documented on the home page).
However, this argument also highlights another problem: the notion that the reference pitch – the foundational frequency of our harmonic series – should be an A.
As we’ve discussed, ancient instruments, and even today’s modern brass instruments, use F and B-flat as their reference pitch.
So, let’s see what happens when we generate the harmonic series using A=432 Hz as our foundation. Starting with A = 432 Hz, we generate the following harmonic frequencies by multiplying by 3, 5, 7, 9 – respectively:
So far, only G does not give us the frequency we received from the B-flat harmonic series as documented on the home-page. However, it’s worth noting that the notes we do match on (E, C-sharp and B) are all en-harmonic to the harmonic-series emanating from our B-flat “magic” frequency:
- E is a tri-tone of B-flat
- C-sharp is a minor 3rd, which contradicts the natural major 3rd harmonic of D
- B is a flattened 9th harmonic in relation to B-flat – which is highly dissonant to our “still point” frequency of B-flat, as well as being a dissonant tri-tone of F (our fifth).
This difference between the harmonic series generated from A=432 Hz versus B-flat=460.8 Hz could be ignored and shrugged off as a tale of he-said/she-said were it not for the empirical evidence I have seen with my tone generator where a perceived beating frequency came to a stop at 7.2 Hz – and how this same frequency seems to appear as the foundation of ancient musical instruments, cymatics and number theory. This “stop beating” phenomena does not occur at the relative sub-audio frequency for A – by the way.
So far, with the harmonic series we have generated from A = 432 Hz, we have only been able to produce frequencies that are in dis-harmony with the harmonic series of our magic note of B-flat = 460.8 Hz.
Let’s move on to the second generation of harmonics from A, starting with its third harmonic, a C-sharp:
As indicated in red, only B matches the frequencies generated from the harmonic series of B-flat. Even F – which should be an octave of our other magic frequencies of 5.4 and 10.8 Hz has been dis-figured from 345.6 (where it should be, and to which the ancient Chinese bells and cymatics were centered) to 337.5 Hz.
Things don’t improve when we generate the harmonics from the next fifth, G-sharp – and now even our B-flat has been mutilated from 230.4 Hz to 227.8 Hz:
Here’s a summary of all the notes generated harmonically from A = 432 Hz versus B-flat = 460.8 Hz. Besides the notes B, C-sharp and E (all of them en-harmonic with B-flat), every other frequency has been dis-figured slightly:
There’s no sleight of hand going on here. I’m multiplying the base frequency by the whole numbers 3, 5, 7, 9 each time. But, even though we’re using the correct frequency for A, at 432 Hz – we cannot treat it as the fundamental of the harmonic series. It is in fact the major 7th of B-flat – or the major third of F – a pretty tenuous harmonic – and that’s why using it as the foundation for a harmonic series seems to take us further from the sacred geometry we’re hoping to find. In fact, the harmonic series based on A produces a series of frequencies which are aberrant to the harmonic series we generated from our magic frequencies for B-flat and F.
Even though A=432 Hz is part of the harmonic series of B-flat and F – it’s not possible to go the other way and generate the correct harmonic frequencies for B-flat and F from an A.
This is further evidence that A should not be the reference pitch – just as we saw that the ancient Egyptian flutes didn’t even include the note A in their range.
Please read the home-page for information on how to correctly assemble a harmonic series that resonates with sacred geometry.