As William Blake, said, “to hold the universe in a grain of sand, and eternity in an hour!” Well, indeed Nature is fractal, and it seems the fundamental frequency of our harmonic scalar explorations just happens to be a Day. Bold claim – which I’ll explain below. All the vibrations and music we make naturally are sub-harmonics of that fundamental beat. The World turns, and we sing.
That’s not how the generally accepted, Western, A = 440 vibrations-per-second, non-harmonic, Equal Temperament scale works. And that’s why ultimately when we listen to nearly all commercial music, the message we’re actually receiving is one of dissonance with Nature.
Back to the Day. It makes sense – we live on a rotating vortex of energy which emits an electro-magnetic and gravitation field, (which I just happened to detect while using a frequency generator in 2016) at the frequencies of 5.4 Hz (F), 10.8 Hz (F) and 7.2 Hz (B-flat).
And it turns out that the 3rd harmonic below that B-flat is an E-flat which corresponds to one beat every ancient “Helek”. The ancient Hebrew measure of time (the Helek) was 3.333 recurring of today’s seconds – which is the time it takes the Earth to rotate 1/72nd of a degree. One beat per Helek corresponds to 0.3 vibrations-per-second (also known as Hertz (Hz)). And 0.3 Hz just happens to be an E-flat, exactly the 3rd harmonic below this same B-flat.
(What do I mean by “3rd harmonic below”? Basically, the frequency that is 3 times slower than the B-flat. So, if B-flat is 7.2, then 7.2 divided by 3 = 2.4 Hz. And the octaves of E-flat are 0.3 Hz -> 0.6 Hz, 1.2 -> Hz -> 2.4 Hz). And there is a measured peak in the Earth’s electro-magnetic field at 9.6 Hz (octaves 2.4 Hz -> 4.8 Hz -> 9.6 Hz)).
So, we have 3 frequencies we can be pretty sure are emanations of the physical energy field of the Earth.)
Let’s keep going because we haven’t talked about the Day yet: The frequency of one Earth rotation every 24 hours (or 1 vibration every 86,400 seconds).
Based on this notion that a Day – the rotation of the Earth itself – might be the origin of these harmonics – I extrapolated the frequencies, by starting with the number of seconds in a day, (in the lower-left corner in the diagram above):
- 60 seconds x 60 minutes x 24-hours = 86,400 seconds per day (= 43,200 secs in 12 hours, for those who like to see the number 432)
- So, one beat per day = 1/86,400 seconds = 1.15740740 x 10-5recurring vibrations per second (Hz)
- Which, if you octave it up a lot (multiply by 2, many times) = 388.36148148 recurring Hz.
Let’s take a quick recap of the harmonic and mathematical tools available to us:
- Octaves: The ear hears double the frequency of a note as an “octave”, e.g. perceptively the same note, only lower or higher. Multiply the frequency of your note by 2 to get an octave above, divide by 2 to get the octave below. For those of us old enough to remember, the bass-lines of My Sharona, and Thank You (Falettinme Be Mice Elf Agin) – or Some-Where Over the Rainbow.
- 3rd harmonics:
- Like it says on the tin, if you multiply the frequency by 3, you get the 3rd harmonic above. With a guitar string, this is what happens when you touch it 1/3 of the way along its length – it vibrates in 3 nodes, each vibrating 3 times faster than the original notes.
- The 3rd harmonic corresponds with going Do-Re-Mi-Fa-So, which is the 5th note in the Western major scale so they call it the “Perfect 5th” – which is confusing, but there you go. e.g. Twinkle-Twinkle Little Star. Conversely, dividing by 3 gives the 3rd harmonic below
- 5th harmonics:
- And if you touched your vibrating guitar string 1/5th of the way along, you would get 5 nodes each vibrating 5 times faster than the original. Multiply your frequency by 5 . This 5th harmonic corresponds to Do-Re-Mi, and is therefore called the “major 3rd” interval in Western music – ‘cos its the 3rd one.
So, these are our harmonic building blocks. Yes, harmonics form at the 7th, 9th, 11th harmonic – actually on all whole numbers (that’s why Eddie Van Halen can get micro-harmonics all over his guitar neck), but they get progressively weaker, so the harmonics we hear primarily are the octaves, 3rd and 5th harmonics. And it’s this basic sonority that we seek in a musical scale: if these harmonics are clashing with one another, we’re going to feel that dissonance quite strongly.
So, let’s use these 3 harmonic tools to explore the harmonics of a Day.
As calculated above, we have our Day as equivalent to a G of 388.36168168 recurring Hz (1 beat per 86,400 seconds and octaved up by multiplying by 2 lots of times):
The 3rd harmonic is the strongest after the octave.
- The “3rd harmonic of a Day” = 24 hours / 3 = 8 hours;
- The frequency is 3-times faster. So, multiply a G of 388.36 Hz by 3 gives us the 3rd-harmonic above (=1,165.08504504 Hz, which if we divide by 4 to go down a few octaves = D of 291.27111 Hz.
- This D is illustrated in the chart above, as the D directly above the G in the lower left-hand corner.
- Because in harmonics, dividing or multiplying by 2 gives you an octave, this D frequency for 8 hours can be octaved down to 4-hours, 2-hours, 1-hour, half-an-hour, 15 minutes, and still be this D.
Obviously, a Day corresponds to a complete turn of the Earth: 360 degrees. So, in the chart above I’ve also included the number of degrees, and the portion of the day in minutes which each musical harmonic represents.
In this way, we can find “geo-harmonic”, 3rd-harmonics in the left-hand column: G, D, A, E. I call these the “Geometric frequencies” because they’re all directly based on our rotating Earth.
Then, the other strong harmonic is the 5th-harmonic (central columns). Let’s see what happens when we take the 5th harmonic of “a Day”:
- The 5th harmonic of G is B (do-re-mi)
- 388.36 Hz x 5 = 485.452 Hz (after octaving it down)
So? Well, as it happens, when we extrapolate downwards in 3rd harmonics from the “phenomenal frequencies” (from the B-flat and E-flat we know, down through E-flat, to A-flat, C-sharp, F-sharp to B, going down in 3rd harmonics (divide by 3), as shown in the centre column, above, this is the exact same frequency that we get for B based on the geo-harmonic G in the left column (485.452 Hz). They exactly connect!
So, there it is Ladies and Gentlemen – the “phenomenal” frequencies that I experienced (as shown in the middle column) directly connect with the frequency of the Earth rotating once a day.
In other words, this confirms that the B-flat and F frequencies I had found are electro-magnetic resonances of the Earth’s rotation and its magnetic field.
And going the way other way,, the “geometric” frequencies generated from a Day exactly meet up with the harmonic series from the “phenomenal frequencies” (F, B-flat, E-flat). Seamlessly!
Coincidence? Well, no. Clearly, there are electro-magnetic, harmonic, vibrational “nodes” that emanate from our planet’s daily rotation, and which produce the harmonics I measured for B-flat and F.
In the chart above – I’ve shown the 3rd-harmonics, going vertically – and the 5th harmonics, going sideways – and this includes a 3rd column where, by the way, we get another A at 432 Hz, and another D at 144 or 288 Hz. We’ll talk about those later.
The remaining trick then is to know which notes we are pulling from where in this harmonic matrix and to construct musical scales that resonate with specific aspects of the divine geometry.
e.g. Do you take the E from the first/Earth column (327.68 Hz), or from the second/magic column, or from the 3rd/heavenly column?
If we create our binaural beats based on these frequencies, our brains will be attuned – give this one I created a try, or this. Binaurals rely on headphones or stereo-speakers to deliver two different frequencies to your left and right ears, and your brain has to assimilate this information. I wonder if it will help remedy migraine headaches.
- I sometimes sleep with a 9.6 Hz magnetic resonator under the mattress, corresponding to E-flat, above. It brings on lucid dreams, and muscular relaxation!
- If our music and discourse are made against this fabric of sonority, we will be in-sync with the bird- and animal-song; we will hear what they are saying in the context of what it is – a hymn to the creative wonder that gives us life every moment of the Day!
When I took this following recording of Beethoven’s Moonlight Sonata which I tuned on my computer to play only these exact frequencies, out into the fields, it seemed like the Birds and the Sheep were just singing along all the time: I just happened to show up with a piece of music which was based on the same musical scale they were singing to already!
A day is a day. That may be the only thing left in our lives which cannot be re-construed, twisted and theoriticised by propaganda (I’m sure the Establishment would like us to live permanently in the Meta-Verse (AKA Matrix) where they can manipulate time itself, but that’s not going to happen). Take this piece of music out into the fields, and enjoy!
- In the right-column, we can generate alternative frequencies for G, D, A, E and B. And I’ve tried to highlight these “alternative flavours”in the same colour – e.g. E in purple. Potentially, for micro-tonal music, you could have an instrument with more than 12 notes per octave, and have multiple versions of these notes – and probably that’s what singers do. But for instruments with frets or hard-tuning like the pinch it’s a lot easier to keep it simple with just 12 notes per octave – and on the guitar, that’s what bends are for!
- Note, that these “upper” frequencies for G, D, A, E correspond to Zarlino’s frequencies in the 1500s, and the frequencies which enthusiasts for music based on A = 432 Hz generally espouse.
A Is Not 432 Hz
In the recording above, A is 436.90666 Hz – taken from the first column of 3rd-harmonics of the Day. In this next recording, the A is taken from the 3rd column above, two 5th harmonics away from the first column. You can decide which you prefer.
Seconds and Helekim and Geometry
Just one thing to note is that some of these numbers are familiar, “cosmic” numbers in the Vedas, the New Jerusalem, Plato’s Magnesia, John Michell’s Dimensions of Paradise, etc., but I want to mention that there’s a hidden prejudice in our modern thinking, which is that we think everything is about the Second: Hertz is vibrations per Second. But, for the ancient Hebrews and Babylonians who developed the sexagesimal counting system – the unit of time was the Helek – equal to 3.333 recurring of today’s seconds; and not the second.
So, does the number 432 appear in Earth harmonic scale anyway even if we don’t make A=432 Hz? Yes, it does:
- 432 beats per Helek = 432 / 3.33333 seconds = 129.6 Hz. And what note is 129.6 Hz? It’s not an A, it’s an octave of C at 259.2 Hz
- Also, as it happens, there are 25,920 Heleks in a day (3.3333 seconds x 25,920 = 86,400 seconds (there’s that 432, 864 number again). So, 432 is important, but it may refer to C rather than A.
(John Michel is an excellent, readable source for information about the amazing coincidences of size, distance and proportion which mean that Pi can be derived from the ratio of the Earth to the Moon, how the Moon is sized and distanced so perfectly in relation to the sun that it precisely blocks it out in an eclipse, etc.; and amazing coincidences of how the same harmonic numbers we see here translate to the numbers of stades, furlongs and Egyptian feet necessary to span the Earth’s equator. Evidence of the harmonics of balance being foundational to our universe, and something never taught in today’s schools! )
We mentioned that there are 25,920 Heleks in a Day. There are also 25,920 years in the Great Year (the time it takes the precession of the Earth’s equinox to complete the tour of all 12 areas of the zodiac). So, the significance of 432 viewed with the ancient metrology of the Helek instead of the Second, shows itself more in the C-note as being of cosmic significance, than the A.
- Similarly for 288: Instead of 288 beats per second as a D, 288 beats per Helek = 288 / 3.33333 seconds = 86.4 Hz. And what note is 86.4 Hz? It’s not a D, it’s an octave of our magic F at 345.6 Hz
It’s not for nothing that the size of the “enclosures” at Gobekli Tepe, and the distances reported for moving stone with sound correspond to the wavelengths of the frequencies for B-flat, F and C. They are “sacred” resonances because they align with the very tissue of our conscious planet, and our experience of it.
Guitars are tuned like the Day!
Funnily enough, the open notes on a guitar are tuned to the 3rd harmonics emanating from the Day/G in the lower left-hand corner of the diagram. G D A E B. (tuned as E A D G B E). Even more interesting is that we derived all of these as 3rd harmonics, except for the G to B, which is 5th harmonic (going horizontal on the diagram above); and on standard guitar tuning, G to B is the only string relation based on the 5th harmonic. Perhaps there is something fundamental in the way a guitar is tuned that has somehow been passed down through the ages.
- At C-sharp in the diagram, it corresponds to both 1-minute, and 1-degree.
- B-flat corresponds to 1.11 seconds. There is an increasing number of people who find that most of the time when they look at a digital clock it is showing 11 minutes, 22 minutes, 33, 44, 55 minutes past the hour. Perhaps then this is a harmonic event making itself known.
60-based counting, vs 64-based counting:
The ancient Babylonians worked out our 60-based counting system. 5 x 12 is 60; 12 can be derived from 3, 4, 6, etc. In the guitar-string example it works well, because when you touch your finger at various whole-number divisions of the length of the string, you hear the harmonics that make up the fundamental sound of the string played open. And the strongest harmonics are divisions at 2, 3, 4, 5, 6, 7, 8, 9 of the string length.
But some have posited that the Ancients got it wrong: there are, for example, 64 codons in DNA, 64 hexagrams in the I-Ching, and, of course, 64 is a binary number: 2, 4, 8, 16, 32, 64. One extension to this idea is that C should be 256 Hz (because 64, 128, 256), instead of 259.2 Hz from the middle column as the 3rd harmonic of F. (Whereas C at 256 Hz can be derived as the 5th harmonic of our Ab frequency (0.1 Hz x 5 = 0.5 Hz, which if you multiply by 2 gives you octaves of 1 Hz, 2, 4, 8, 16, 32, 64 Hz, etc.)
Notice though that, when viewed as vibrations per Helek, E-flat can be one vibration per Helek – or one vibration per 64 Heleks as it’s octave (1, 2, 4, 8, 16, 32, 64). E-flat, as one vibration per the Ancient unit of time provides that binary aspect to the sonic pattern, without having to distort C as 256 Hz.
As DNA has 64 codons, perhaps there is an interesting health opportunity with the use of E-flat as a healing frequency. As I mentioned, I use an electro-magnet under my mattress, set to E-flat (at 9.6 Hz) and I do seem to wake up refreshed. (The one I use, programmes in an hour of B-flat (14.4 Hz) at the end, so you are bought out of deep gamma. If I get up before that part of the programme, I’m pretty groggy!)
So, go to this section on Harmonic Instrument Design in order to play your music with these “Earth” harmonic frequencies.