Dear All, I’ve been going down a line of enquiry recently and wasn’t sure how to share it, but I think I’ve today reached an interesting insight. This entry is going to be a little more technical than some of the others, but hopefully I won’t lose you. Meanwhile, here’s a recording of me playing my keyboard tuned as discussed below, which you can listen to while you read (sounds better loud).

As you know, this website is based on my discovery of some odd, resonant audio behavior which I identified using an iPhone tone generator connected to Bluetooth headphones (video of this phenomenon is on the home-page, here). Here, I discovered that the frequencies 5.4 Hz (F), 7.2 Hz (B-flat) and 10.8 Hz (F again) are the point where a sub-audible “interference warble” on either side of these frequencies stops beating. 5.4 and 10.8 Hz are both the F note, an octave apart (5.4 Hz x 2 = 10.8 Hz), and 7.2 Hz is a B-flat precisely and mathematically related to the other two in what is known as a “perfect fifth” (do-so).

When I say these are the F and Bb notes, I mean in a new tuning based on these frequencies – rather than the 440 Hz, equal temperament standard we’re lumped with – and this site is dedicated to putting together a harmonic scale based on these “found” frequencies. So, so my initial assumption was that the lowest of these notes, the B-flat, would be the fundamental frequency from which we could derive a harmonic musical scale – and I’ve done that analysis on the homepage: calculating the 9th, 3rd, 5th, and 7th harmonic of these notes; and in turn the 9th, 3rd, 5th, and 7th of those harmonics, etc. until we’d covered all 12 notes of the western scale.

Well, then in the Summer of 2020, discovered here on the EarthPulse web-site that an **E-flat** (a perfect-fifth below our B-flat frequency (7.2 Hz / 3 x 2 = **9.6 Hz**)), is the frequency of the Earth’s magnetic field, as measured by Robert Becker (who wrote the book, The Body Electric) by driving poles into the ground and measuring the frequency.

(I have bought one of these EarthPulse devices to experiment with for sleep – and interestingly, the default setting is this **9.6** Hz frequency, which is how, by googling this frequency I found out about EarthPulse. But the best advice came from Sadhguru who advised sleeping East/West, rather than North/South!).

So, that’s a new bit of corroborating evidence for the Bb and F frequencies that I had found: that the Earth itself happens to generate a frequency precisely a perfect-fifth below my frequencies – indicating that it is the Earth itself which is responsible for that “interference” frequency which you can witness in the video – (or the Earth is following a universal frequency).

I had also previously reported in this blog entry about the ancient Hebrew and Babylonian measure of time known as a “Helek” – equal to 3.3333 recurring of today’s seconds. A Helek was determined in the ancient metrology as the time it takes the Earth to rotate 1/72nd of a degree as it turns on its axis! (There’s that number again, 72. Our Bb is 7.2 Hz, by the way.) It turns out, if you banged a drum once every Helek, that’s 1 beat every 3.3333 seconds = 1 / 3.3333 secs = **0.3 Hz**. And 0.3 Hz is a sub-octave of 9.6 Hz Eb (0.3 Hz x 32 = 9.6 Hz), the earth’s magnetic resonance. Makes sense that the vibration of the magnetic field would have a direct relationship to the speed of rotation of the earth.

(It’s also worth noting here that the “magical” number of **316.8** which John Michell documents in the The Dimensions of Paradise as appearing in Revelations, Plato’s Republic and in the dimensions of the Earth and Moon, turns out to be the **11**th harmonic of our 7.2 Hz B-flat tone (7.2 Hz x 11 x 4 = 316.8 Hz). And the “solfeggio tone” of 528 Hz turns out to be the **11**th harmonic of the G note that is a major-3rd harmonic of this E-flat frequency (9.6 Hz x 11 x 5 = 528 Hz!).) And you can find out more about the miraculous power of the 11th harmonic for destroying cancer in this video (although I don’t think they’re using my frequencies yet as their root frequency, but I have suggested it to them!)

So, to build a harmonic scale from these “found” frequencies we can keep going *up* in fifths (*multiplying* the frequency by 3) until we’ve got all 12 notes of the western musical scale, or we could also try going *down* in fifths (*divide* by 3) to see if there are other fundamental tones below the ones that presented themselves to me (the Bb and F frequencies).

Our E-flat is based on the rotation of the Earth (1 vibration per Helek) and gives us **0.3 **Hz. Divide this by three to go down a fifth to an A-flat (0.3 Hz / 3 = **0.1** Hz). It’s interesting to me how we’ve now gone from 3 to 1, in an almost biblical, Trinity sort of way. Is this what the Trinity was referring to, “first there was the word, and the word was [a vibration of 0.1 Hz]?! From this came the two (octave at 0.2 Hz) and the 0.3 Hz or Trinity of E-flat?

- A-flat:
**0.1**Hz - E-flat:
**0.3**Hz - B-flat:
**0.9**Hz - F:
**2.7**Hz - C:
**8.1**Hz

I think its interesting that however odd and discordant any frequency is that you might be playing, if 0.1 Hz is the A-flat building block from which all of the universe is constructed, then every subsequent harmonic will be made up of some multiple of 0.1 Hz vibrations. In terms of the “Aleph” at the beginning of Hebrew creation, it’s interesting that this note is an A, and an A-*flat *at that – as fundamental as you can get. In other words, the universe is fractal, built from this 0.1 Hz building block – and its harmonics.

Like the four fundamental musical tones of creation described by JRR Tolkien in the Silmarillion, (which I just started reading – funny how the poetic mind tends to be 100 years ahead of the scientific mind) even when over-reaching ambition makes us think we’re the centre of the universe and all reality emanates from our frequency, we cannot break the fabric of the universe, made up as it is in 0.1 Hz increments. The harmonic truth always rings through. Every evil plan is somehow botched by the goodness inherent in the system: Rockefeller also gave us mobility, Bill Gates also gave us computers. Anyway, enough of the realms of literature and tyrants 🙂

An additional interesting aspect of A-flat as the fundamental frequency at 0.1 Hz is that its octaves correspond to the doubling we’re familiar with from the binary scale (1, 2, 4, 8, 16, 32, 64, 128, 256, 512) except that because we’re starting with a decimal, the frequencies for the octaves of A-flat are 0.1, 0.2, 0.4, 0.8, 1.6, 3.2, 6.4, 12.8, 25.6, 51.2, 102.4, 204.8, 409.6 Hz, etc.

But keeping with the goal of delving ever downward to find that “fundamental of fundamental” (or holiest of holy) frequencies (the quarks of sound, let’s say) I tried then going down a fifth from our 0.1 Hz A-flat to **C#**. 0.1 Hz / 3 = **0.0333333333333333** recurring Hz. (Recurring numbers are always interesting, I think. And if as Nikola Tesla said, the universe is built of 3s, 6s, and 9s – this seems like a good sort of number to find at this point!) (The C# octave for this is 273.066666666666 recurring Hz.)

And a perfect 5th below that C# is **F#**: 0.0333333333333333 Hz / 3 = **0.0111111111111111 **recurring Hz. We’re back to “the one” again – and this corresponds to an F# at 364.08888 recurring Hz.

Next though is where the harmonic simplicity seems to stop: If we go one more perfect-fifth down, from F# to a B, we get: 0.0111111111111111 / 3 = **0.0037037037037037** recurring Hz. We’re no longer dealing with just 1s and 3s.

So, it’s *possible* that B, is the underlying frequency – the foundation of it all, but the numeric entropy we start to see from the 3s, 2s and 1s of E-flat, A-flat, C# and F# – devolving into 0.00370370370370 Hz for B, makes me think that B belongs more closely to the *top* of the cycle of fifths than the bottom. We know from the cycle-of-fifths, that we can go upwards or downwards to get to our destination. In this case, I think we’d go up – making the B the last ‘fifth’ before we get back to a starting point of F#. (I’ve positioned it in both places in the table below however, if you’d like to experiment)

( Now, it did occur to me to look at this B frequency in terms of Heleks: I just mention this because I think it’s interesting. I Googled this number, to see if it was significant. Interestingly, this “day calculator” tells us that (0.00370370370370 days happens to be 320 seconds. In Heleks, 320 seconds / 3.3333 seconds = 96 Heleks:

- If one Helek is the time it takes the Earth to rotate 1/72 nd of a degree
- Then, 96 Heleks = 96 – 72 = 1 degree and 24 Heleks
- 24 / 72 = 0.3333 recurring
- So, 96 Heleks = 1.3333 recurring; that’s 1 and-a-third 3 degrees of Earth’s rotation = 0.00370370370370 Hz = B, corresponding to 485.5 Hz )

So, if the fundamental note of our harmonic series is F# as 0.0111 recurring Hz, then our harmonic table of 5ths looks like this, (corresponding to an F# at 364.08888 recurring Hz):

(I’ve added the tuning “offsets” in cents from 432 Hz Equal Temperament and from 440 Hz Equal Temperament, incase you’d like to programme your keyboard to try these – e.g. to adjust to get an F# of 364.089 Hz, if you’re reference pitch in your software is A=432 Hz then you adjust by +3.755 Hz. Or if your reference pitch is A=440 Hz you’d adjust by minus 27.834 Hz, etc.)

Regarding the title, about black notes and white notes: if we make F# the starting point of our cycle-of-fifths, as shown in the table above, you notice that all the sharps (and flats) happen in the first four ‘hops’ of this cycle-of-fifths (F# to C#, C# to G#/Ab, G# to D#/Eb, and D# to A#/Bb. And then when we go from A#/Bb to F, it smooths out so that the remaining 5ths are are all “natural” notes, no sharps or flats.

Looking at the piano keyboard then, where we have the **black notes** and the **white notes**, isn’t it really interesting that the black notes are the *fundamental* building blocks from which our harmonic series (and perhaps the universe) is constructed; while the white notes are the later tones, more mundane, perhaps.

When constructing a piece of music, you could dip into the flats/sharps when you want to make those deeper connections to creation, and use the white notes when you’re dealing with things more in our every day experience. I’ll tell you, for me, playing these notes with my keyboard, using Apple Logic adjusted to these frequencies, I really *feel* it. And with the mind-set that when you’re playing the white notes your dealing with the more exoteric, *day-to-day *side of things, and when you’re playing the black notes your dipping into the more esoteric, *fundamental* side of things – it really gives a sort of quantum way of thinking about making music and what each note stands for and corresponds to in the “sonic geometry” of creation.

**Post-script:**

Well, I learned today (on Reddit) where the white notes and the black notes come from: It turns out that the medieval church organ keyboards were designed with only 8 keys, to only play the key of C-major (AKA mixolydian G, AKA only today’s white notes). The black-notes were added in later. When I was growing up, we had an 18th century piano in the house (tuned down so it wouldn’t break), and the first piece of music in the piano book was “I am C, middle-C, left-hand, right-hand middle-C!” – and I always wondered why it was “middle-C” – why not middle-D, which looks more like it’s in the middle?!. But one thing in all this I’ve noticed is that when we do arrange the cycle-of-5ths in the sequence as I have in the table above (where F-sharp is the fundamental from which all harmonics generate), C is indeed the middle key of all of that (6 5ths below C to get back to our starting frequency at F-sharp, and 6 fifths above C to return us to F-sharp (cycle-of-fifths – the lemma is fractal!). Maybe that’s why the Church favoured it. In my approach though, C is more a minor key than the “white-notes-only” C-major, having the Eb (earth frequency) as its minor-third, rather than the less fundamental E as the major-third.

**Technical Note**:

The astute will notice, hey your scale doesn’t have A = 432 Hz, or D = 288 Hz!

So, let’s just explore that for a moment. I have noticed when exploring the octaves of my “found” frequencies for Bb and F is that they reflect the magic numbers of 432 and 288 and 72 – but behind the veil of a *decimal point*! For example, the B-flat octaves are: 0.9, 1.8, 3.6, **7.2**, **14.4**, **28.8 **Hz. The magic numbers of 72, 144 and 288 are there, but as decimals.

Similarly with the octaves of F: 2.7, **5.4**, **10.8**, 21.6, **43.2** Hz. The magic “432” is there, along with 54 and 108, but as decimals.

Now, it’s a fact that the major-third interval can be found harmonically by multiplying a frequency by 10. So, 43.2 Hz as an F corresponds, when multiplied by 10, with an A of 432 Hz which is the major-third of F. And if you look at my home-page, those are the frequencies I gave for A (432 Hz), D (288 Hz), G (384 Hz), C# (270 Hz) and F# (360 Hz) – but these are all derived as *major-third* harmonics (of F, Bb, Eb, A and D, respectively), and they can make the overall scale less cohesive than when the frequencies are generated from perfect-fifths – in my perception.

In fact, using these 3rds-based frequencies basically renders portions of the harmonic series incompatible with the other half. And here’s why: When we’re dealing with 5ths, 4ths and 9th harmonics, these frequencies are all multiples of **3**: for 5ths we *multiply* by 3, for 4ths we *divide* by 3, and for 9ths we multiply 9. 3 and 9 (and 6) are all multiples of 3, and therefore any frequencies generated by using this multiplier will overlap and intersect when we go around the cycle-of-fifths (see my exploration of the cycle of fifths) – even when there is a gap (or “lemma”).

But, in terms of constructing a harmonic, musical scale that aligns with a fundamental frequency and reflects the power of that fundamental fully, I’ve come to the conclusion that it’s best to only use the perfect-5th and 9th harmonics. Because they are both based on 3, and therefore the symmetry of the pattern is not complicated by deriving notes using major-thirds (based on 5 or 10 as the multiplier). (Frequencies multiplied by 5 and 3 only coincide as multipliers at multiples of 15 – a bit like the Aztec calendar, they don’t harmonise very often! – whereas 3s coincide often at 3, 6, 9, 12, 15, etc.)

I tend to think, like Nikola Tesla, that 3, 6 and 9 are the cosmic numbers. Actually, I believe the cosmic numbers are just **1, 2, and 3** because you can make 3, 6 and 9 from 1, 2 and 3, as well as every other number. E.g. let’s say 1.3 Hz: harmonically it would be 0.3 Hz (Eb) x 2 x 2 + 0.1 Hz (from the Ab). And six is just an octave of 3 (times 2), and 9 is just a perfect-fifth of 3 (times 3). Meanwhile, in the Tarot, the number 5 is considered the human number – 5 senses, 5 limbs – it’s who we are, but as we know, we’re kind of out-of-kilter with the rest of creation – except at places where multiples of 5 and 3 coincide – such as 15, 45, 60, 90, 180, 360 (which might say something about geometry).

So, I’m thinking of harmonics derived from *major-thirds *as “satellite” frequencies – they compliment the music in a fractal sort of way, but cannot be used to generate other frequencies from. Therefore, I’ve released myself from the prejudice that my A has to be 432 Hz, and that my D has to be 288 Hz, etc. – even though harmonically those frequencies can be generated as major thirds from our “magic notes” of F at 10.8 Hz (10.8 Hz x 10 x 4 = 432 Hz), and Bb at 7.2 Hz (7.2 Hz x 10 x 4 = 288 Hz). With perfect-fifths, we still have the magical numbers of 432, 288, 72, 54 as *decimals* within the harmonic sequences or Bb and F (43.2, 28.8, 7.2, 5.4, as explained above).

In fact, this is where I think most attempts like this go off the rails because they don’t understand about the decimal point, so you see scales where C is defined as 256 Hz (generated as the major-third of A-flat (0.1 Hz x 5 = 0.5 Hz), with octaves at 1, 2, 4, 8, 16, 32 … **256 Hz)**, instead of our C of 259.2 Hz generated as the perfect-fifth from our F of 10.8 Hz). But, we do have the number **25.6** **Hz**, disguised as a decimal, as one of the octaves of Ab.

Nature is subtle, it understands decimal points! In fact, it’s almost as if the subtle roots of life *emerge* from the other side of the decimal point at A-flat = 0.1 Hz; and before that the origins of the C# and F# are tiny decimals, “lost in the mists of time”. Ha ha – perhaps that’s what that phrase really means!

It would be possible to construct a musical scale which included the major-3rds as well as the 5ths and even the 7ths, but we’d end up with the 11 notes each with their 3 harmonic “flavours”, so that’s 11 x 3 notes in an octave = 33 notes, which is probably the truth, but it makes making music on a keyboard or guitar, very, very ergonomically challenging! I had a guitar neck with 24 frets per-octave for a while, and in the end, I had to pull half of them out – the music actually ends up being more discordant because half the time you’ve accidentally played the wrong variant of the harmonic. Too much choice!

The good news is that most of the fundamental frequencies I had woven into a musical scale on the home-page and on the page on instrument design have not changed (what has changed are the F#, C#, D, A, and E) – and I have both tuning files in my Apple Logic, so I can go back to the old one if I want to. (I’ll add a link to the other one here, soon.) There is a different flavour between those two scales – but right now, I’m really liking this one, just based on the perfect-fifths.

And yes, I can only play in certain keys – but frankly, that doesn’t seem to be relevant because when I’m playing these notes, they feel so resonant with the fabric of reality – that I know it’s the right key!

Here’s a link to the Apple Logic project file with these offsets already in it. Hopefully it will download for you – and assuming you have Apple Logic. The other thing I’ve done is transpose the keyboard on each track so it’s playing 3 semi-tones higher. In this way, when it looks like I’m playing an F I’m really playing an Ab, a G is really a Bb, an A-minor is really a C-minor, etc. This is because I’m kind of new to the keyboard, and by transposing in this way I can play all the most sonorous chords and modes on the white notes (e.g Ab Lydian, Bb Mixolydian, C-minor, Eb major, F Dorian). Also, remember, this isn’t a *temperament* – I haven’t adjusted the frequencies from the cycle of fifths – so some keys will sound great, like the ones I mentioned above. Other keys won’t sound so good. After I worked out this harmonic series, I spent a day questioning all this and went back to my original mixed tuning using some major thirds, but in the end, this 5ths-based series just sounds more awesome!

I would be interested to hear what you think.