## Music based on the 3 and 5

The “cycle of fifths” is actually a spiral, where in you start with a frequency and go to its third-harmonic, and its third harmonic, in-turn until you get around to the note you started at, but as it turns out, there’s a gap between your starting frequency and your ending frequency. This presents a problem for anyone believing that nature is based on fundamental frequencies because, “where is the beginning?”

We do know a couple of fundamental frequencies which are resonant with the Earth, being an F at 5.4 and 10.8 vibrations per second (Hz), and a B-flat at 7.2 Hz. As it happens, we also know that an Eb, at 9.6 Hz, is a third harmonic below the Bb and corresponds to the time it takes the Earth to rotate 1/72nd of a degree (3.3333 seconds, called a “helek” by the ancient Hebrews and Babylonians. See the home-page for how I found these frequencies, their behavior and even the fact that those numbers are regarded by ancient cultures as sacred.

But, we don’t know if E-flat is the “foundational frequency”, or if there’s a frequency below that which generates E-flat, or a frequency below that which generates that? Is it “turtles all the way down”?

The strongest harmonics are the octave (multiply or divide by 2, or touch your guitar string half way along its length to hear that octave harmonic); and the second strongest harmonic is the 3rd harmonic (multiply or divide by 3, or touch your guitar string 1/3rd along its length). Bb is already a third-harmonic below F, so we know nature is using those harmonics – but how far down do we go? The third harmonic below Bb is Eb, then Ab, then C#, then F#, then B, then E. But, where do we stop? Which frequency is the fundamental – that we can say is the “harmonic root” of all the vibration we experience – before we start repeating ourselves with each 3rd harmonic, e.g. E goes down to A, down to D, to G, to C, to F, etc. And the problem being, that when you get back to the frequencies you started with using the cycle of 3rd harmonics, the frequency you start and end at are not octaves of each other, even though they both should be. There’s a gap because in going around the cycle you actually overshoot your mark. 3rd harmonics are a little aggressive, you might say.

Now, another interesting phenomena is that the next strongest harmonic is the 5th harmonic (AKA our musical major-third intervaldo-re-mi, see I told you the intervals were a confusing way to think of it, which is why i refer to the harmonics instead). And where the 3rd harmonic generally overshoots the starting point in the cycle of 3rd harmonics, the 5th harmonic generally falls short.

So, these two harmonics give us something to work with: one overshoots, the other falls short. Perhaps in some combination we could devise a harmonic scale where the ending note and the starting note are octaves of each other, or close enough for our human bodies to perceive.

With this in mind, I’ve read with interest the work of Ernest Macclain, Musical Theory and Ancient Cosmology. In Plato’s Critias he refers to “Poseidon and his five pairs of twin sons”, and McClain interprets this to refer to a harmonic series where Poseidon “begets” the other frequencies. Which frequency is “Poseidon” then, is the question!

So, long story short, I’ve used McClains’s idea to try to derive which our fundamental frequency would be, and to also construct a harmonic scale that doesn’t make war with itself at both ends (e.g. the starting frequency being dissonant with the ending frequency).

Poseidon is of course the God of the deep, the ocean, the abyss. It doesn’t hurt that my hypnotised synesthesia characterised the note B as Black, the abyss, the void. So, I’m going to combine art and science here and you can all hate me for it!

So, just to go with the idea that “Poseidon” is B for a moment, then the “twins” from the circle above are:

1. F# and C#
2. Ab and Eb
3. Bb and F
4. C and G
5. D and A

And (their “mother” presumably) would be E. Interestingly, my synesthesia for E also gave it void-like energy (gray or white).

Now, we discovered Bb and F together, so those seem like pairs; and I would say the others form good pairs as well based on the synesthesia colours and my own aesthetics. But besides the subjectivity of my synesthesia, is there some other further evidence that B is the fundamental frequency of the Abyss? Well, let’s look at the numbers of these derived harmonic frequencies themselves:

There is a body of thought, which John Michell probably led, or perhaps Ernest McClain, that the numbers themselves have meaning, regardless of whether they’re vibrations per second, cubits, feet, furlongs, degrees of earth’s rotation, etc. The theory is that the ancient metrology which agreed how many degrees in a circle, how many cubits around the equator, etc., were based on an understanding of an interdependency of rotation and distance in physics (a “unified field theorem” we are yet to re-discover) where the Babylonian 60-digit counting system was the key.

With this in mind, I constructed the following table, just to look at the numbers associated with each musical note, as we go down in third harmonics from Bb (7.2 or 0.9 Hz) to Eb (0.3 Hz) etc. going in 3rd harmonics:

(I’m concerned that table may not be readable (try to zoom in), so I may re-create it, or you can ask me for the original table in Excel). Assuming you can read it, starting with the first row of data we have:

1. Vibrations per second
2. Vibrations per helek (1 ancient helek = 3.333 recurring moderns seconds)
3. Earth degrees of rotation per vibration (e.g. we know that Eb is 1 beat every 3.333 rec seconds which is the time it takes the earth to rotate 1/72nd of a degree
4. Number of seconds per vibration (for the really low vibrations)
5. Number of Halakim per vibration – why not?

Here we are using the lens of harmonic numbers to identify the frequency that is the root of our harmonic series. Certain numbers, at various “octaves” and ignoring decimal points, seem to be fundamental and “sacred”. So, by looking at the numbers only, not only for Hz but also for the corresponding degrees of earth’s rotation for that frequency etc., this may help us use the points where the “magic numbers” begin and end as a way to determine the harmonic fundamental frequency which drives them all. Simply by dividing by 3 from our E-flat frequency these number patterns emerged in the table above. I’ve colour-coded the number types to help spot the patterns, e.g.

• 1234567901234579 recurring
• 37037037 recurring
• 11111111 recurring
• 33333 recurring
• 1: 8, 16, 32, 64, 256
• 3: 6, 12, 24, 48, 96
• 9: 18, 36, 72
• 27: 54, 108, 216, 432
• 81: 162, 324

Conclusions of numeric examination:

Using 3rd harmonics, the harmonic number range in the table above seems to start with low B, but goes no lower; and seems to end with C or G and go no higher. (e.g. 0.0012345679 is part of low B and high G, and this is an interesting number as it encompasses all the digits in sequence, except 8, and is recurring, and generated simply as a sub-harmonic of E-flat).

Also, if we notice, Eb is 1/72nd of a degree. The third harmonic below that (Ab) would be 1 divided by 72 divided by 3 = 1/24 degrees. And as harmonics and octaves, 1/24 is equivalent to 1/12, 1/6, 1/3 degrees.

A third-harmonic below that (C#) would be 1/1 = 1 degree. A 3rd harmonic below that (F#) would be 3 degrees; and a 3rd harmonic below that (B) would be 9 degrees of the Earth’s rotation.

9 degrees is harmonically equivalent to 18, 36, 72 degrees, as octaves. And 360 degrees divided by 72 = 5. So, what is the frequency that is 5 times slower than the B? It’s a G with a frequency of 0.0037037 rec / 5 (or 10) = 0.00037037 recurring Hz. And, octaved up, that is a G of 388.36148148 rec. Hz.

So, a day, 360 degrees, is an extremely low G which correspond to a higher G of 388.36148148 rec. Hz. And the good news is that this is very close to the G of 388.8 Hz generated as the 5th harmonic from E flat at 307.2 Hz.

So, we can start our scale at B, knowing that it’s equivalent to the time it takes the Earth to turn 9 degrees, (and also 18, 36, and 72 degrees as sub-octaves.) And if we build our scale in this way, our G for a day, and our G of 388.8 Hz match up. We have symmetry – and minimal discernible dissonance, plus it all aligns with the rotation of the only clock we know is true – the Earth’s rotation.

“Shut up and play your guitar!” Alright, well this is not guitar but here’s some music I created using this scale in Apple Logic:

It turns out the differentiation between the black notes and the white notes is quite handy because with 7 white notes, and 5 black notes, we can arrange it so that most of those 3rd harmonic (white) notes get a pure 5th harmonic (black) note to give them that “major third” interval:

• Eb has G
• F has A
• Ab has C
• Bb has D
• C could have E

And here’s how I’ve arranged the notes on my Apple Logic keyboard, where I can transpose by minus-6, like this. This puts the notes that were generated with 5th harmonics (G, A, C, D, E) as black notes, where they can be accessed from their corresponding white notes to form perfect major chords for Eb, F, Ab, Bb, respectively). (In the smallest text below, you can see the cent adjustments for each note (compared to an equal temperament scale where A is 432 Hz)).

(Note: on the Cents adjustments, I originally used this utility to calculate them from the desired Hz frequency. http://www.sengpielaudio.com/calculator-centsratio.htm. What I’ve found though is that the theoretical adjustment doesn’t produce the exact frequency – so the cent adjustments you see above are what I ended up with after using the “Oscillator” in Apple Logic which handily allows you to play every note of the scale and tells you frequency it’s playing, based on the off-sets you had put in the File -> Project Settings -> Tuning. And remember, I use a master offset of -31.8 cents to make my A = 432 Hz first, instead of A = 440Hz which is the default. )

If minus 6 is too extreme of a keyboard transposition for you, I can understand, here’s a plus 1 transposition, so you still get the benefit of the 5th harmonics being on most of the black notes.

One thing I didn’t mention is that last year I bought John Michell’s final book “How The World Is Made” and on page 11 he talks about how the geometry of 5 and 10 pertains to life. And I thought, well, we don’t want a harmonic scale based purely on 3,6,9 that is so sterile it misses out our biological essence! There’s quite a nice video about the 5 and 6 in geometry and music, here by Jain 108:

And also in John Michell’s book he references a print by Albrecht Dürer which seeks to encompass the hexagon and the pentagon into a combined geometry.

Anyway, all this is meaningless if it doesn’t sound good, so, hopefully you clicked on my SoundCloud link above and are enjoying the frequencies, if not necessarily my musicality!

1. Playing the white notes only – they all sound great together!
2. Playing the black notes only – they all sound great together!
3. Wait for it, yes – picking our black notes to go with the white notes for “major thirds” – also sounds great!

Having “major 3rds” in a chord that are harmonically aligned to the tonic of the chord has been a goal of tuning temperaments from Bach and Mozart to the microtonalists of the present day. The trouble is, that unless you have an instrument with more than 12 notes per octave, your D as a major-3rd in a Bb chord, can’t be the “perfect 5th” in a G chord as well, as that D is slightly too low, and it sounds bad with the G. But by playing chords where the tonic or root of the chord is one of the white notes shown above, those “major-3rds” (pure 5th harmonics) are sequestered as black notes and can therefore be played only to give harmonic colour to a chord, rather than to be the tonic or 5th of that chord.

The other challenge of course is, can you play a harmonic scale in any key with this harmonic scale? Usually the answer is “no”, you can generally play in about 3 related keys in a harmonic scale, and then things start to go awry. Frankly, I’ve been trying to play harmoniously, so I haven’t explored if there’s a discordant side to this, but this scale is in harmony with our rotating earth and it’s magnetism, and our “low” 3rd-harmonic E is essentially the same as our high 5th-harmonic E – so it sounds consonant and good.

Being that the modern western scale at 440Hz for A is too high, this is an interesting solution to the problem: we should all transpose our keyboards up a semi-tone, and tune down to these magic frequencies. This would be the true way to “raise our vibration” – by raising it and lowering it!

Long story short, this is the sweetest scale I’ve produced – or heard. It feels more natural in my body. When I play with this tuning, it seems like the birds congregate to sing happily outside my window! It’s a good feeling. Life is good.

And because the low E below our starter B (323.635 Hz) and the high E (derived as the 5th harmonic of C) as 324 Hz, are pretty much the same, the scale is cyclical: there is no “war at the ends of the scale” – so it doesn’t really matter if E is “high” based on 5th harmonics, or low as our starting point for 3rd harmonics – it all gels.

The key sacred numbers are accounted for, as well:

1. The frequencies I found on my tone generator (7.2 Hz for Bb, and 5.4 and 10.8 Hz for F)
2. E-flat as 9.6 Hz or 0.3 Hz as a measure of the earth’s rotation
3. C# as the time it takes the earth to rotate 1 degree
4. Ab with a frequency of 0.1 Hz or 10 seconds per vibration, which has been thought by some to be the frequency of heart/brain coherence (e.g. Greg Braden)
5. Plus we have A as 432 Hz – which everyone loves, and D as 288 Hz – both related to the dimensions of the planet.
6. Our B is also the frequency of 72 degrees of rotation of the Earth;
7. And a day is a G, the 5th harmonic below that B! – although we’re keeping our G as the 5th harmonic of Eb because it is a harmonic, and it sounds sweeter with the rest of the scale.

Plus, playing it, I feel like a child again, where everything is in tune.

I feel that western music has been so bastardized in every way: (the wrong frequency for A, the fact that A shouldn’t even be the reference note (e.g. probably should be E or B as the harmonic foundation, as we’ve discovered); plus we’ve been lumped with equal temperament – pretending that harmonic propagation doesn’t need to start with a common root. So, I figure if want to flip the black notes and white notes so that it’s more playable, that seems like a good thing. That said, playing the now black notes (the 5th-harmonic derived notes) all sounds great as I mentioned – so you don’t have to do the transposition if you don’t want to although you’re more likely to get combinations of notes that don’t gel quite perfectly.

So, now we have harmonic propagation from our fundamental B “word” of 0.0037037037 recurring Hz, using both the 3rd harmonic and the 5th harmonic: the numbers of sacred geometry and sacred biology.

By the way, I really recommend John Michell’s books if you’re interested in sacred geometry. The correlation between the numbers of geometry, ancient metrology, and now music can probably only be explained by a correlation between mass, gravity, electro-magnetism rotation and frequency. If you think about it, we’ve found that the Eb frequency of 9.6 Hz which corresponds to the Earth’s magnetic field is also an octave of 0.3 Hz which is the time it takes the Earth to turn 1/72nd of a degree (3.3333 recurring of today’s seconds, referred to as a ‘Helek’ in ancient Babylon). I suspect that all “vibration”, whether at the macro level like our planet, or the quantum level like electrons, is all really just rotation as a function of mass (or energy, as Einstein pointed out).

So, “energy has rotation” is basically the formula. Some clever mathematician will come up with the “holy-grail” unified field theory at some point proving that mass, rotation speed, gravity, and electromagnetism are directly related mathematically, but it’s clear that all we’re really doing here is rediscovering truths about the fabric of our universe which were also known by the ancient Babylonians and Hebrews when they developed geometry and their units of measurement. Somehow they incorporated these numbers into how they measured the rotating earth, their concept of time, and how they measured distance – and how they blew their walls down with trumpets!

And in the interim, the loss of this knowledge which we’re now re-assembling, has been at the heart of the horrible way we’ve treated each other, ourselves and our planet for the past few thousand years. But now we’ve got this harmonic knowledge back (or pretty darn close to it, I would say!) and are once more coherent, so we can feel good – music can be restored – our bond with nature and the conscious cosmos can be strengthened – and we can live natural lives in harmony with our natural world and each other!

Happy resonating!

## Music and the fabric of time

Well, I just came across this article where the author goes back to the ancient Hebrew divisions of time and overlays musical frequencies in keeping with these time divisions and – lo and behold – comes up with the exact same frequencies for the complete musical scale that I did, based on the phenomena of the “resonant still points” which I demonstrate on my homepage.

https://ethnographicsblog.wordpress.com/2019/04/19/a-horological-and-mathematical-defense-of-philosophical-pitch/

The Hebrew measure of time was the “helek” which equates to 3.333333 (recurring) seconds. Gives you more time to think, I suppose.

This measure of time was devised by dividing each of the 360 degrees by which the Earth turns every day into 72 parts to give a total of 25,920 helakim (plural of helek) per day.

First off, my frequency (and his) for C is 259.2. (By the way, each time you multiply a frequency by 10 you’re getting the Major Third of the original – so 25,920 also suggests a frequency for G# (C-D-E, E-F#-G#).

As the author points out, 25,920 also equates to the number of years in the Great Year – the time it takes for the world’s axial “wobble” to precess through 360 degrees, going through the twelve Ages – one for each of the Astrological signs. And it takes 72 years for the equinox to precess by one degree.

Two hours is 25,920/12 = 2160 helakim, and 2,160 years is the length of an Age. And this suggests a microcosm/macrocosm thing where we enjoy a tiny Age, or change of astrological sign, every two hours of the day.

And every day is, in effect, a mini Great Year as our position on the planet passes through all 12 astrological signs.

The Earth rotates 1 degree on its axis every 4 minutes (72 helakim x 3.333 seconds = 240 seconds = 4 minutes.) (3.333 recurring is a favourite number of the Free Masons but perhaps their big secret is simply the Helek. By the way, this video beautifully presents much of this.)

Every day, we turn 360 degrees, 4 minutes per degree = 1,440 minutes which is a number the author equates to F# as 1,440 Hz, which is an octave of 360 Hz – which is also the frequency I’ve found for F#.

Dividing the hour into seconds suggests B at 60 Hz.

He makes the root frequency for his scale 108 Hz because 360 degrees divided by 3.3333 seconds per helek = 108. 360 represents the full daily and annual rotation of the planet on its axis and around the zodiac. Now, 108 Hz is a sub-octave of 216 and 432 Hz – so that’s the frequency for A. Same as mine. So he sort of encompasses a whole year into A as the root note.

He then derives the harmonic series from this A using the “5-Limit” harmonic approach (which is simply deriving 5ths (multiply the frequency by 3) and the major third (multiply by 5).

The author also considers beats per minute as a starting point – so that the rhythm of the music and the music itself are aligned with the fabric of time.

He works into this a division of time (in seconds or helakim) by whole numbers: 2, 3, 5, 7, 9.

So he divides the day into seconds (60 seconds times 60 minutes times 12 hours) = 86,400 seconds, (a number which relates to A=432 Hz). He also starts with a notion of C at one cycle per second where its octaves would be 2 Hz, 4, 8, 16, 32, 64, 128, 256 Hz, etc.

And with one helek = 3.333-seconds, a minute is 18 helakim – which relates to D at 9, 18, 36, 72, 144, 288 Hz

As he says, “Using 5 Limit Tuning with the root set to A (at 216) rather than C, the frequencies of notes C4 (256), G4 (384), E4 (320), D4 (288), and B4 (240) are reducible to, respectively: 1, 3, 5, 9, and 15“. Meaning that 1, 3, 5, 9 are sub-octaves of the given frequencies, e.g. 9 x 2 x 2 x 2 x 2 x 2 = 288 Hz = D.

If, as I believe, the phenomenon I can demonstrate on my tone generator is indeed the phenomenon of sound interacting with the fabric of the universe, then what more powerful evidence than to find that these frequencies all tie back to a natural way of measuring time – at least on our Earth. Do check it out: https://ethnographicsblog.wordpress.com/2019/04/19/a-horological-and-mathematical-defense-of-philosophical-pitch/

## The Cygnus Key

So, I’ve been reading Andrew Collins’ fascinating book, the Cygnus Key – which gets into the common astro-alignment of Gobekli Tepe and the pyramids of Giza, and the acoustic qualities of both. The author talks about how the inner sanctuary as these “temples” (or shall we call them studios?!) was 20 cubits by 30 cubits.

The ancient measure of a cubit has been determined from the pyramid at Giza to be 21 inches.  So, a room that is 30 cubits long (using the Royal Cubit of 21 inches) is 52.5 ft.  And the frequency for a wavelength that is 52.5 ft long is 21.5 Hz (use this tool to calculate: http://www.1728.org/freqwavf.htm using an air temperature of 20 degrees centigrade) – and in my world of magical frequencies, an F is 21.6 Hz!!  That’s just 0.1 Hz off!  So, the inner sanctuary that the author mentions on page 262 would be actually tuned almost exactly to an octave of the magical F frequency of 10.8 Hz (10.8 Hz x 2) which I discovered as a “still node” of vibrational consonance and have documented on this web-site!

The other dimension of that inner sanctuary, at 20 cubits, at 21 inches per cubit is 35.0 feet.  And the frequency corresponding to a wavelength of 35.0 ft is 32.2 Hz.  And, the frequency for a C, as a harmonic 5th of my F frequency, is 32.4 Hz!  So, just 0.2 Hz off!
So, the inner sanctum of these ancient temples, using dimensions first identified in 9,600 BC were more than for creating a fifth/fourth resonance – it was designed to produce resonance specifically to the “magical” frequencies that I discovered for F and C.
That is an incredibly strong piece of corroborating evidence for both of our theories.
For the later sanctuaries, where the long dimension was extended to 90 cubits (page 277): at 21 inches per cubit is 157.5 feet.  And the frequency corresponding to a wavelength of 157.5 feet is 7.15 Hz.  And my frequency for the fundamental, magical tone of B-flat is 7.2 Hz !!  B-flat is the lowest note from which the fifth is F, and the fifth of F is C.
So, allowing for temperature, these rooms are designed specifically to generate B-flat, F and C – and not the modern, 440 Hz version of these notes, but the specific frequencies of these notes which I was able to discover of 7.2 Hz for B-flat, and 10.8 Hz for F, and their Octaves and harmonics, as I have documented on my web-site.
Clearly, the ancient Egyptians, and the ancient Anatolians before them, knew what these frequencies were and knew they were fundamental, sacred resonances at the foundation of creation!
Once again, this theory of sacred resonance has been re-inforced, this time by the ancient geometry of Gobekli Tepe and the ancient Egyptian temples that came after it!

## A video of the sonic “still-points” phenomena that I discovered with a tone generator

Best listened to with headphones: The phenomena I discovered in which very low frequencies emit a waving, purring oscillation sound which comes to a halt at precisely 10.8 Hz, 7.2 Hz and 5.4 Hz. These frequencies correspond to a very low F, B-flat and low lower octave of F, respectively. And they are exactly a musical fifth interval apart (7.2 x 3/2 = 10.8).

I interpret the cause of this phenomena to be a sonic “interference pattern” between the generated tone and some background vibration which is essential to reality but which we don’t hear. Interestingly, NASA has provided recordings of black holes emitting a very low B-flat note and I have found evidence of these frequencies from a range of ancient bells and flutes and other phenomena which I have documented at http://www.HarmonicsOfNature.com

Interestingly, the harmonic scale generated from these frequencies produces A = 432 Hz, thought by many to be the correct reference pitch instead of the current “standard” of A = 440 Hz.

The implications to music are profound, indicating that music should rightfully be played in scales based on these frequencies for B-flat and F in order to align with the fabric of the universe. The healing potential for these frequencies and their harmonics needs to be further explored for health, happiness and spiritual alignment.

Interestingly, 72, 54 and 108 are all ancient sacred numbers – which I didn’t realize when I first found this phenomena.