Fibonacci is a harmonic series

I believe that Phi (or the Fibonacci number) is not the magical ratio that drives nature, but that Phi reflects the real driver of nature, which is harmonic energy propagation – generated according to whole-number ratios from the Earth’s daily rotation.

Phi, also known as the Fibonacci number, is a ratio that appears throughout Nature: the ratio of last year’s twig growth vs this year’s; the length of one finger joint vs the next; the relative size of cells of a nautilus’ shell; the way that weather patterns evolve.

Phi reveals an essential beheavior across the fabric of the universe. And being that this web-site is dedicated to the notion that vibration is essential to that fabric, you’d think the two would go together.

But Phi doesn’t appear to be harmonic at first glance. Unlike harmonics, Phi is not a whole number multiplier. It’s a recurring ratio that approximates to 1.618 – and 1.618 does not generate harmonics.

Determining Phi

Phi is determined by starting with a number and then creating a new number by adding up the two previous numbers. So, for example, start with 1:
1 plus 1 is 2
1 plus 2 is 3
2 plus 3 is 5
3 plus 5 is 8
5 plus 8 is 13 – and you keep going.

As you keep going, the ratio of the current number to the one before it (e.g. 13/8) more and more precisely defines the value of Phi.

Normally, the Phi/Fibonacci series is started with a 1 – looking like the table below.

But what does 1.618 give us? Yes, it’s the “Golden Mean”; yes if you position objects in your painting to that proportion people will like it more; or have your plastic surgery done with this in mind – but can we get beyond the aesthetics and into a scientific understanding of what is underlying Phi?

Now, you don’t have to start the Phi series with 1. You don’t have to start with numbers at all – you could start with tomatoes, or rain drops, or wind – but numbers are a good way of quantifying our World, and it just so happens that music can be measured with numbers – specifically, the number of vibrations per second (Hertz, or Hz) for a musical note.

(Did you know that the ratio of the length and width of DNA is 34:21 angstroms? That’s the ratio of the 9th to the 8th position below. Amazing stuff.)

As you’ve probably noticed from this web-site, I’ve identified a strange phenomena around the notes of B-flat and F, specifically at the frequencies of 7.2 Hz (B-flat), and 5.4 Hz and 10.8 Hz (octaves of F), and their harmonic sequence. (See my video of this audio interference pattern, here.) – where these frequencies interact with the Earth’s geo-magnetic field resonance.

So, at first, I tried just multiplying one of my frequencies by Phi, e.g. F at 10.8 Hz x 1.618 = 17.4744 Hz. But the result isn’t in my musical scale at all. The nearest frequency is my D at 18 Hz. So, I couldn’t figure out what do with Phi for a few years.

Exploration

So then I thought, what happens if, instead of starting with 1, we start the Fibonacci series using a low frequency in the Earth Tone harmonic series, e.g. a B-flat sub-octave at 0.9 Hz, and see if this pattern generates other frequencies from the Earth Harmonic series. Here’s the result in the table below.

Note first of all that the Phi ratio for each position below is the same as In the table above, where we started with 1. It’s still a Fibonacci ratio based on adding up the last two numbers, but we’ve seeded it with 0.9 instead of 1…

The first six positions of Phi give two Octaves of B-flat, a third harmonic (F), a fifth harmonic (D) and another Octave. So far, so musical.

Then at the seventh position, we have a remainder: the Phi series has generated a tone of 11.7 Hz. But 11.7 Hz isn’t part of our harmonic series. A frequency that is close is 14.4 Hz – which is another B-flat (0.9 Hz x 2 x 2 x 2 x 2 = 14.4 Hz).

Okay, what’s the difference between the tone that the Fibonacci series generated (11.7 Hz) and the closest harmonic (14.4 Hz):
14.4 – 11.7 = 2.7 Hz.
And what is 2.7 Hz? It’s an F from the Earth Harmonic Series. (10.8 Hz divided by 4). So, the gap generated by the Fibonacci series and our closest note in the Earth harmonic series is itself one of the notes from the harmonic series.

They say, “the devil is in the details”. But I say, “God is in the gaps!” The gaps contain a mini reflection of the harmonic scale itself. Harmonics are fractal!

(By the way, it turns out 11.7 Hz is the 13th harmonic of our 0.9 Hz B-flat starter frequency: 0.9 Hz x 13 = 11.7 Hz. But, not to redesign western music just yet, let us surrender to only have 12 notes in the scale!).

Gaps above and below

A “difference” can be above or below the Fibonacci frequency. In this analysis, we chose 14.4 Hz because it’s the closest frequency in our harmonic series above the Fibonacci frequency. But it works just as well if you choose a frequency from the Earth harmonic series below the Phi frequency: 10.8 Hz is the harmonic F, below the Phi frequency of 11.7 Hz. So the difference between these two is:
11.7 Hz minus 10.8 Hz = 0.9 Hz.
And 0.9 Hz happens to be our fundamental B-flat frequency again!

So, whether you over-shoot or under-shoot, where there’s a gap between the frequency that the Fibonacci series lands on and our “closest living harmonic”, that gap will itself be one of our harmonics.

Starting our Fibonacci series with a “seed” number of 0.9 Hz, that gap between the 8th and 9th position is the ratio in angstroms of the length by the width of DNA.

The building block of biological life looks also to be harmonic Earth music!

You’ll also notice that at position 19 in the table above, the leimma (the gap) doesn’t resolve to one of our harmonics (indicated by a big red X). In this case we have a gap of 125.1 Hz. This isn’t one of the harmonics from the Earth harmonic series either (unless you count the 139th harmonic (0.9 Hz x 139 = 125.1). But our nearest harmonic in a 12-tone harmonic scale is 129.6 Hz (our C). So, in this case, we have a “double-leimma” (is that a “dilemma”? – ha ha!) where the gap is 4.5 Hz, which is a very low sub-octave of D.

Here’s someone’s YouTube beautifully animating the concept of fractal containment of the macro in the micro, and the micro in the macro:

As you are zoomed in, you see a little gap which you think might be something new, but then you realize it’s just another instance of the pattern you’ve encountered before – repeating like ripples in water. It appears that Nature uses gaps to maintain the harmonics of Nature without it becoming overpowered by its own resonance.

Moderns Western Science has problems with gaps. You can read my exploration of the harmonic “gap” in the cycle-of-fifths here. It was because of this gap that Western music adopted Equal Temperament so that the gap resulting from circling the cycle-of-5th harmonics could be spread out across all the notes in the scale and hopefully no-one would notice!

This allowed all a piece of music to be transposed to any musical key. But it broke the harmony of music . And we live on a planet generated by the rotation of Space Time, according to Nassim Haramein – a position we agree with.

The good news is that this also shows how we could restore our civilisation to its natural resonance.

Singing Creation into Existence:

So, I think of Phi differently. Not as a magical construct which guides Nature – as though 1.618 was some template emeshed into quantum physics; but more like a pea-pod full of harmonics.

Perhaps the nautilus is singing away happily to himself and builds the next chamber of its shell so it resonates with its predecessor. “Singing me back-home”!

Harmonic frequencies are generated in whole-number proportions to the original vibration – and these harmonics propagate further harmonics, with gaps that are themselves further harmonics.

Harmonic Dampening Through Fractal Gaps:

If there were no gaps in the cosmic harmonic propagation, then everything would be so spot-on harmonically that the universe would instantly resonate itself into oblivion. But, with the gap (which is a much quieter and less energetic version of the same harmonic), the harmony and energy is efficiently propagated without the universe shaking itself to bits: Little vortices of harmony spin off and create their own little harmonic microcosms – called Protons, and Planets. And all energy is inter-meshed with all other energy. And this might also supports Quantum Entanglement.

So, Phi is a way for us to measure from the outside, what’s going on inside – which is fractal harmonic propagation.

Some people might regard the early ratios of Phi (positions 1-6 above) as inaccurate – i.e. the early ratios of 1, 2, 1.5, 1.66666 are not 1.618. But these ratios precisely generate the octave, fifth and third harmonics – without leimmas. Phi doesn’t “get more accurate” – it’s always “doing its job” – accurately reflecting the next harmonic, or the next harmonic plus a leimma, where needed.

It would appear that it always does this, although I’ve stopped at position 26, but I expect it goes on forever. Someone can write a computer programme to check! As a matter of fact, to render the fractal harmonic propagation as a fractal image/video using my frequencies would be an awesome exploration. Someone should try it 🙂

Self-Correcting Barber-Shop:

Perhaps as a metaphor for the Phi fractal propagation of harmonics, we could think of a multi-voice choir which is set off with the first sound. The sound builds with different members of the choir singing along with harmonies. After a while, some of the choristers begin emitting strange, erratic noises and it seems like all is lost but, in combination with the sounds the rest of the choir is making, these aberrant sounds create “difference notes” – the difference between the “wrong” sound and the “right” sounds – combining to create a third note which is harmonic. If you’ve ever done throat singing with a group of people, you may have witnessed these strange whistling sounds which no-one is making but are the sum of the sounds they are making collectively.

Another interesting area where “difference notes” come into play seems to be the Solfeggio where the difference created by playing two or three of these notes simultaneously is generally spot-on with my harmonic series, even though the Solfeggio notes taken one at a time are not musical and cannot be used to construct a melody. See our exploration of this, here.

So, Nature is propagating harmonics in a Fractal way: there can be a gap/leimma between the generated Fibonacci tone and the note generated from the B-flat harmonic series – but that gap is itself a member of the B-flat harmonic series.

Being as we believe B-flat and F frequencies of 7.2 Hz, 5.4 Hz and 10.8 Hz are resonant still points against a background vibration of our World, then a Fibonacci series like the one above may be an important insight into how energy is propagated and how our World is structured.

Harmonics are the Templates:

I would propose that Nautilus shells and all the other reflections of Phi that we can see are actually built on this underlying common resonance – and that’s how it “knows” to construct itself that way, because that’s how the energy resonates and propagates. Perhaps this also relates to how bubbles in water “know” how to construct themselves into perfect spheres the way they do, as Buckminster-Fuller once remarked.

Phi appears to be a symptom of the underlying fractal harmonic propagation of energy – indicating that matter is really a harmonic extension of music. And music – harmony – is what keeps the universe together.