Solfeggio Differences

 I never understood the Solfeggio.  They don’t make any kind of playable musical scale – they don’t seem to be harmonics of each other, you can’t create a melody out of them and they seem to have no relation to any other measured resonance.  Then in a video, I saw the image of two Solfeggio tones being subtracted from each other, and it occurred to me that the point of the tones (as Gregorian chants were supposedly their origin) was to create “difference notes” – a third note created by the unison singing or playing of two other notes.

Difference Tones

 With this idea in mind, I created a “difference table” to subtract every Solfeggio tone from every other, to see what those “difference notes” are:

Solfeggio difference

Down the left-hand column, you have the 5 Solfeggio tones and their frequencies – and above them, the same.  The area filled out in columns 4 through 8 are the results of subtracting the frequencies of each combination of Solfeggio frequencies – e.g. FA (at 639 Hz) minus UT at 396 Hz (in line 1) gives a new frequency of 345 Hz.  In the five right-most columns I’ve then compared this “difference note” to anything in the range of frequencies that I documented in the Harmonics of Nature page – based on two “magic” frequencies of B-flat (7.2 Hz) and F (5.4 Hz) which I discovered using a tone-generator to seemingly have a harmonic consonance with the background hum of our universe.  Take a look at the home-page, if you haven’t read that yet.

In the chart above, I was surprised to find that the frequencies for B, F and E that we had generated from our harmonic series for these B-flat and F “still points” (see Harmonics of Nature, section) exactly corresponded to the subtraction of one Solfeggio frequency from another.  These four are highlighted in yellow and red.  And four other frequencies are pretty close (highlighted just in red): G-sharp, A, C, B-flat.

  • MI minus UT = 264 Hz (4.8 Hz deviation from our C at 259.2 Hz)
  • FA minus UT = 243 Hz = (exactly a B, although B is a note I avoid playing) !
  • SOL minus UT = 345 Hz (0.6 Hz deviation from an F at 345.6) !
  • SOL minus RE = 324 Hz (exactly an E) !
  • SOL minus FA = 408 Hz (5.8 Hz from a G-sharp at 403.2)
  • LA minus UT = 456 Hz (4.8 Hz from a B-flat at 460.8 Hz)
  • LA minus RE = 435 Hz (3 Hz from an A at 432 Hz)
  • LA minus MI = 324 Hz (exactly an E) !
  • LA minus FA = 426 Hz (6 Hz from an A at 432 Hz)

Let’s just take a step back to marvel at that coincidence.  The harmonic frequencies based on my tone-generator’s “still-points” described here – a bunch of frequencies that could be just the random imaginings of my fevered brow – exactly  match the results of playing two Solfeggio tones at the same time and capturing the “difference tone” which they generate, in Hz.

The Solfeggio difference-notes which exactly match our harmonic series are:

  • B (FA minus UT): 243 Hz
  • F (Sol minus UT): 345 Hz
  • E (both LA minus MI and SOL minus RE): 324 Hz.

These do are not exactly matching frequencies from the Equal Temperament 440 Hz based modern musical spectrum – Why would they? – that wasn’t invented until the 1930s:

  •  B: 246 Hz
  • F: 349.2 Hz
  • E: 329.6 Hz)

The Solfeggio difference-notes are also not matching frequencies from the Just Intonation 440 Hz based modern musical spectrum:

  • B: 247.5 Hz
  • F: 347.7 Hz
  • E: 330 Hz

They don’t even match a “fifths based” Pythagorean series based on A=432Hz:

  • B: 243 Hz
  • F: 341.3 Hz
  • E: 324 Hz)

So, all you guys going on about A=432 Hz – that’s only half the story.  Yes, A=432 Hz is part of the harmonic series.  But it’s not the foundation of it.  In fact, it’s just the Third of a Fifth of B-flat; and even when a tuner is set to “Pythagorean Just” using A=432 Hz as the foundation, it throws the F off, significantly from 345.6 to 341.3!  (See calibrating your tuner, in the Appendix of the Home Page).

In fact, the difference-notes between the Solfeggio are exactly matching the harmonic series based on a B-flat of 7.2 Hz, as I had discovered with my tone-generator and calculated on the home-page:  B: 243 Hz, F: 345.6 Hz, E: 324 Hz

So, looking at the Solfeggio as “difference-notes” reinforces the correctness of the harmonic series I have documented in these pages.  And the harmonic series I had discovered reinforces the notion that the Solfeggio are “difference-notes”.  What are the chances of that?! 

I don’t hear anyone much talking about this on the internet – although obviously I’m not the first to surmise that the Solfeggio are intended to be “difference notes”.  The internet is jam-packed with various services playing these notes with nice production values – but generally, one at a time – which basically does nothing for you, and misses the point that they are supposed to be played – or sung – in combination.

Laying them out in sequence, the difference-notes generated by singing Solfeggio pairs together are:

  • A, B-flat/A-sharp, B, C (four semi-tones, all in a row, in fact
  • E, F, G-sharp (two semi-tones and a minor-third)

In relation to our harmonic series generated from the “magic” frequencies of 5.4 and 7.2 Hz – out of 15 possible Solfeggio “difference combinations”:

  • 4 Solfeggio combinations exactly match ours:  B, F and E (twice)
  • 5 Solfeggio combinations closely match ours: B-flat, A (three times!), and G-sharp
  • 4 Solfeggio combinations produce the same bungled approximation of B-flat (111 or 222 Hz)
  • There are no combinations of Solfeggio notes which create complete random noise, disparate from our harmonically generated keys based on still-points.

The natural frequency that is missed by the widest margin is our still-point note of B-flat.  The difference-frequencies show up by four different methods – but all giving either 111 or 222 Hz as the difference frequency.  That in itself is evidence of some heavy-duty encoding going on in the Solfeggio:

  • MI minus RE = 111,
  • FA minus RE = 222,
  • FA minus MI gives 111,
  • LA minus SOL gives 111.

Someone went to a lot of trouble to have 5 different Solfeggio frequencies (MI, RE, FA, LA, SOL)  which when played or sung together exactly produce the same difference-frequencies of 111 or 222.  These two frequencies are octaves of each other, but are not an actual note – at least not of the Western diatonic scale, falling exactly mid-point between an A and a B-flat in our harmonic scale.

To me, this rather simplistic number – 111 or 222 – looks like the work either of a simpleton trying to retrofit his/her idea of “symmetry” to the proceedings; or of a more intelligent person who has tampered with the frequencies in a way that would be obvious to people like ourselves – because we can see which notes are being exactly matched – and can surmise that B-flat at 460.8 (or octaves thereof) is the underlying frequency which is generating all of those harmonically related notes.  We can piece back together the correct Solfeggio note so that like the others, it falls within the harmonic scales generated from F and B-flat.  Because the other notes fit our harmonic series, and the most important note – our foundational B-flat note – is so obviously out of kilter with the harmonics generated from it, it’s easy to infer the correct frequency for B-flat and put the Solfeggio back together properly.

(Although there is one B-flat that seems to have survived largely unscathed, LA/UT – giving 456 Hz, which is pretty close to 460.8 Hz for our “still point” B-flat.)

It’s not clear to me how the Solfeggio frequencies were supposedly handed down through the centuries (or whether they originate from a much more ancient civilization), but perhaps our Gregorian monk ancestors (ok, not ancestors, as I guess they didn’t have children) didn’t have precise science, but were still trying to produce the same harmonic notes as difference-notes, held in secret and only made apparent through the act of actually singing the notes – and now being found to be close to our discovered, “magic” resonances of B-flat and F, at 7.2 and 5.4 Hz.


But we’re not done yet.  Let’s examine the “secret” aspect of all this.  I think it’s fascinating that F and B are almost exact hits.  345 Hz vs 345.6 Hz for an F, and 243 Hz for a B.  And, F and B are a tri-tone apart.

Yes folks, the “tri-tone” interval – the augmented 4th – the geometric mid-point measured along an octave – the very interval that the Christian church condemned as the “Devil’s interval” – is readily (and EXACTLY) accessible by having three Gregorian monks – two of them singing FA and UT (to make difference tone of a B), and one of them singing SOL (which combines with UT to give an F) – standing about looking innocent, singing tones that aren’t even a musical scale – but causing the tri-tone between F and B to be generated  from the frequencies they actually are singing.  Stick them in a nice, resonant church building and, voila – you’re in tri-tone heaven! (or perhaps, “Devil’s interval hell”) (humour).

Similarly, assuming that the Solfeggio were indeed “altered” when it came to B-flat – we would get a B-flat generated by two monks singing combinations of LA/UT, MI/RE, FA/RE, FA/MI, LA/SOL; and we get an E from SOL/RE, LA/MI and RE/UT.  Put the B-flat and the E together, and we get another tri-tone.

For a bunch of Gregorian monks protecting the harmonies of the sacred, there’s an awful lot of “Devil’s interval” in there.  In fact, that’s 8 of 15 combinations which generate the B-flat/E tri-tone, and 2/15 combinations that give us a F/B tri-tone.  That’s 10 out of 15 of the Solfeggio difference combinations produces tri-tones – and the two notes that are being consistently “tri-toned” are our B-flat and F notes!

Come on – this is not coincidence any more.  We are clearly on to something significant in terms of the power of harmonics – and why this kind of knowledge would have been encoded and passed down to us over the millennia!  We have discovered:

  1. When two Solfeggio frequencies are played simultaneously, they produce difference notes
  2. When the original pair of Solfeggio tones are combined with a third Solfeggio (or with another pair) – a tri-tone (augmented 4th, the “devil’s interval”) is generated – in 10 out of the 15 possible combinations
  3. And these turn out to be the tri-tone of B-flat (E), or the tri-tone of F (B)
  4. And B-flat and F just happen to be the two “magic” frequencies we discovered as having a harmonic, non-“beating” relationship to apparent sub-sonic, universal frequencies – as documented on the home-page

We are told that during the Medieval period, monks went to great lengths not to sing or play tri-tone intervals because to do so was a punishable offence.  The music of the day had great volumes of books dedicated on how to write to music that would avoid tri-tones – specifically.  And yet, here are a bunch of medieval monks doing everything possible to sing almost ENTIRELY in tri-tones, without ever actually singing a tri-tone – because the tones themselves are generated as the difference between the notes they are actually singing.  Clever, clever stuff.

When two sets of evidence triangulate to confirm each other, that’s a pretty exciting and significant thing.  In this case, my own casual discovery of B-flat and F as fundamental frequencies has a direct relationship to a body of knowledge that has been passed down secretly through the ages in the form of the Solfeggio; still thought by many to be a musical scale – but instead, apparently, a system of “difference notes” used to conceal and encode not just the frequencies that should be foundational to music, but also the tri-tones to these frequencies – which presumably have some kind of power if the monks saw fit to conceal them, and the Church saw fit to persecute anyone found to use them.

Sum Tones

And there’s more.  Similarly, instead of hearing the difference between notes, we can generate  “combination notes” through the summing of two notes to create a third note – which is heard but not sung.  When we add two Solfeggio frequencies, we get exact matches to our harmonic-series notes on B-flat, C, D, F (highlighted in red and yellow), and close matches on G-sharp (twice) and D (highlighted just in red).  And the remaining 7 “sum-notes” are not far off – as shown below:

Solfeggio sum

Playing or singing so as to produce sum notes with one pair of Solfeggio, and additional sum notes by playing or singing another pair of Solfeggio – we get the following tri-tones:

  • B-flat : E (e.g. UT/MI plus SOL)
  • D : G-sharp (e.g. SOL/LA plus RE)
  • C : F-sharp (e.g. UT/FA plus LA)

Again – our magic tone of B-flat figures in these tri-tones.

And considering that both difference-tones and sum-tones are all being generated at the same time – we would also be able to combine the F notes generated from the sum-notes above, with the B-notes generated from the difference-notes, further above.  So, the whole thing is tri-tone city, as far as I can tell.

So, were these Gregorian monks just a bunch of secret anarchists, getting off on generating the forbidden intervals, or were they the guardians of some sacred knowledge which they felt was worth protecting – and which held some power which was worth generating – all day and night?

9. Cancer and tri-tones

So, here’s a fascinating thing.  A group of researchers just discovered that by playing two hyper-frequencies (between 100,000 and 300,000 Hz), they can destroy up to 60% of cancer cells, so long as “the high frequency [is] exactly eleven times higher than the low”.

A frequency eleven times higher is, guess what?  The tri-tone.

To put this into the context, if my low note was 7.2 Hz (a B-flat), 11 x 7.2 Hz = 79.2 Hz.  An E happens to be 81 Hz.  That’s pretty close.  And an E is the tri-tone of a B-flat.  In other words, these scientists have discovered that, in the hyper audio range of 100,000 to 300,000 Hz, you can kill cancer cells by blasting them with tri-tones.

So, what exactly was the church protecting us from in the Medieval period?  The “devil” or something that can be used for health and well-being?  A lot of jazz, and the work of Richard Merrick is centered on the notion of the tri-tone.  Perhaps there is a power in them there tri-tones!

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