The wrong 528 Hz frequency and more


This subject has been around for many years and I’m still waiting for someone to correct many errors spread out on the internet and in many books. Wrong musical notes frequencies, notes associated with the wrong frequencies etc. It would be time to correct all those mistakes!

The 528 Hz frequency, known in the new age movement for its healing properties is not correct. 528 Hz is the frequency of C/Do based on the natural frequency of A/La 440 Hz. But 440 Hz is not a correct frequency, it is a modern frequency, but historically it’s never been the base frequency used for classical music!

Sicne millennia, instruments have been tuned with the A/La 432 Hz frequency. Using this frequency as a standard we get 518.4 Hz, not 528 Hz. As it can be seen clearly on the following tables:


La/A 432 Hz:

Freq. (Hz) Ratio Interval
La A 432 x1 Unison
La# A# 450 x25/24 = 1.0416 Minor second
Si B 486 x9/8 = 1.125 Major second
Do C 518,4 x6/5 = 1.2 Minor third
Do# C# 540 x5/4 = 1.25 Major third
Re D 576 x4/3 = 1.333 Perfect fourth
Re# D# 607.5 x45/32 = 1.40625 Diminished fifth
Mi E 648 x3/2 = 1.5 Perfect fifth
Fa F 691.2 x8/5 = 1.6 Minor sixth
Fa# F# 720 x5/3 = 1.666 Major sixth
Sol G 777.6 x9/5 = 1.8 Minor seventh
Sol# G# 810 x15/8 = 1.875 Major seventh



La/A 440 Hz:

Freq. (Hz) Ratio Interval
La A 440 x1 Unison
La# A# 458.33333 x25/24 = 1.0416 Minor second
Si B 495 x9/8 = 1.125 Major second
Do C 528 x6/5 = 1.2 Minor third
Do# C# 550 x5/4 = 1.25 Major third
Re D 586.66666 x4/3 = 1.333 Perfect fourth
Re# D# 618.75 x45/32 = 1.40625 Diminished fifth
Mi E 660 x3/2 = 1.5 Perfect fifth
Fa F 704 x8/5 = 1.6 Minor sixth
Fa# F# 733.33333 x5/3 = 1.666 Major sixth
Sol G 792 x9/5 = 1.8 Minor seventh
Sol# G# 825 x15/8 = 1.875 Major seventh



One thing that can be seen straight away with 432 as a standard is that all other frequencies are always exact, there are no irrational numbers as it happens when using 440 Hz giving 733.33333 or 586.66666 etc. This is true for any octave, frequencies are always exact.

I’ve been and still am trying to understand why 432 Hz was chosen (and the number in itself), I still never reached a clear cut conclusion, but there are very interesting things linked with this number. At least for music it is evident that using 432 Hz as a tuning pitch for all notes allows us to have exact frequencies for all notes.

For information, nowadays it’s the equal tempered scale that is the most used (for digital applications), because it’s an approximation of the exact scale to simplify it by dividing the octave in 12 equal chromatic intervals.
I won’t dwell into the details; in the equal tempered scale we switch from one semi-tone to the next by multiplying by 2^(1/12), 2^(2/12), 2^(3/12), 2^(4/12) etc.



La/A 432 Hz:

Freq. (Hz) Ratio Interval
La A 432 x1 Unison
La# A# 457.68806 x2^(1/12) = 1.05946 Minor second
Si B 484.90360 x2^(2/12) = 1.12246 Major second
Do C 513.73747 x2^(3/12) = 1.18921 Minor third
Do# C# 544.28589 x2^(4/12) = 1.25992 Major third
Re D 576.65082 x2^(5/12) = 1.33484 Perfect fourth
Re# D# 610.94026 x2^(6/12) = 1.41421 Diminished fifth
Mi E 647.26866 x2^(7/12) = 1.49831 Perfect fifth
Fa F 685.75725 x2^(8/12) = 1.58740 Minor sixth
Fa# F# 726.53450 x2^(9/12) = 1.68179 Major sixth
Sol G 769.73649 x2^(10/12) = 1.78180 Minor seventh
Sol# G# 815.50740 x2^(11/12) = 1.88775 Major seventh



La/A 440 Hz:

Freq. (Hz) Ratio Interval
La A 440 x1 Unison
La# A# 466.16376 x2^(1/12) = 1.05946 Minor second
Si B 493.88330 x2^(2/12) = 1.12246 Major second
Do C 523.25113 x2^(3/12) = 1.18921 Minor third
Do# C# 554.36526 x2^(4/12) = 1.25992 Major third
Re D 587.32953 x2^(5/12) = 1.33484 Perfect fourth
Re# D# 622.25398 x2^(6/12) = 1.41421 Diminished fifth
Mi E 659.25511 x2^(7/12) = 1.49831 Perfect fifth
Fa F 698.45646 x2^(8/12) = 1.58740 Minor sixth
Fa# F# 739.98884 x2^(9/12) = 1.68179 Major sixth
Sol G 783.99087 x2^(10/12) = 1.78180 Minor seventh
Sol# G# 830.60939 x2^(11/12) = 1.88775 Major seventh



Isn’t it ugly?… I wonder why we use this simplification, even in the past, when computers weren’t that powerful, it makes no sense, these logarithmic multiplications are way more complicated than the use of the perfect ratios, and on top of that, all the frequencies have decimals up to infinity…
There’s no doubt, for people who love maths, the choice of La/A 432 with perfect ratios gives the most beautiful results, and by far, all frequencies are perfect.

FYI: some people told me that the Do/C 528hz is based on a La/A 444hz… Yes, if we use this equal tempered scale, 444 x 2^(3/12) = 528.007959. But unlike using perfect ratios, it’s not an exact frequency and of no interest to me.

Visual spectrum:

The informations available on chakras and their relationship to musical notes all indicate the same. C/Do represents the root chakra, D/Re the navel chakra, E/Mi the solar plexus, F/Fa the heart chakra, G/Sol the throat chakra, A/La the third eye, B/Si the crown chakra. One thign I never understood is why C/Do was chosen as the note to start the octave? Because it could technically start from any note, octaves would still be correct, it wouldn’t change anything, so there must be a precise reason for starting at C/Do.. The only thing I observe is that C/Do is that famous note with a frequency of 518.4 Hz (mistakenly believed to be 528 Hz..)

Here’s a visual table associating chakras to the musical notes and to the visual color spectrum. What I’m also intrigued by, historically speaking, is: who chose to name musical notes that way? There are 7 precise notes par octave (Do/C, Re/D, Mi/E, Fa/F, Sol/G, La/A, Si/B) and historically speaking we’ve also always spoken of 7 chakras… I’m sure that there are some sacred mathematical relationships behind that choice!

chakrasvisu

One other interesting fact to note is that the visual spectrum that we are able to see as humans is almost exactly delimited by one musical octave. It’s somewhat simple and evident, but still, I’ve never had anything like that mentioned in any lectures while I studied at university, why us, why humans, why are we limited to almost exactly the equivalent of one musical octave as far as our visual perception is concerned? I would even say that our visual perceptions are exactly delimited by one octave of the electromagnetic spectrum (light), which is our visual octave. In older books, written prior to approx. 1950, scientists at the time often used that term of « visual octave », probably because at the time scientists were savants, they had knowledge not only in their specific field of study, but in all domains of terrestrial knowledge, including music. Whereas nowadays it’s generally not the case anymore..

To show that I have to transform the audio frequencies into a wavelength by choosing an appropriate and arbitrary velocity for the propagation of sound (very unlikely here, as it’s close to zero..) such that these wavelengths are in the range of the visual spectrum (~400-700 nm).

visusoundspectra

We can see that this arbitrary chocie gives us wavelength between 390 nm (used as the initial wavelength) and 731 nm, which is quite close to the real values of the visible spectrum, these limits are not even precisely defined… Sometimes we can read that our vision is between 380nm and 750nm, other times 360nm and 740nm, also 380nm and 720nm, etc. No one knows exactly, I would tend to believe that it starts around 360nm because our eyes can’t physically support shorter wavelength (and still, measurement vary depending on the human subjects). But here again, we have to take into account the photopic (good lighting conditions, diurnal vision) and scotopic (night vision), which are never determined to be exactly the same by different experiments. I’m sure that there is a mathematical way to perfectly determine the ideal visual octave for a human being.

I’ll put forward a somewhat crazy idea, which for me is evident! When we’ll discover the direct relationship between sound and light science will take a huge leap forward in many domains of research. For me it is evident that this link exists even though all I studied at university tried to convince me that this is not the case.

Without talking about sound frequencies, I’ll just leave you with the following image of the vescia piscis which is a well known geometry present in all human eyes! …I have no idea what to make of this as of yet…

Please note that √324 = 18 et √81 = 9 et √9 = 3. What attracts me a lot is this mirror numerology effect : 432 ~ 324 and 108 ~ 81. Which is also true with √972 √(3/4) = √729

Numerology:

Another very important detail in my opinion proving that the choice of 432 with perfect ratio is all but random, is that all frequencies become a 9 if reduced to a single digit following the rules of numerology, for any octave.

Let’s use a different octave that the one used in above examples, for example La/A 1728 Hz (4 x 432), two octaves above.

Freq. (Hz) Ratio Numerology
La A 1728 x1 1+7+2+8 = 18 = 1+8 = 9
La# A# 1800 x25/24 1+8+0+0 = 9
Si B 1944 x9/8 1+9+4+4 = 18 = 1+8 = 9
Do C 2073.6 x6/5 2+0+7+3+6 = 18 = 1+8 = 9
Do# C# 2160 x5/4 2+1+6+0 = 9
Re D 2304 x4/3 2+3+0+4 = 9
Re# D# 2430 x45/32 2+4+3+0 = 9
Mi E 2592 x3/2 2+5+9+2 = 18 = 1+8 = 9
Fa F 2764.8 x8/5 2+7+6+4+8 = 27 = 2+7 = 9
Fa# F# 2880 x5/3 2+8+8+0 = 9
Sol G 3110.4 x9/5 3+1+1+0+4 = 9
Sol# G# 3240 x15/8 3+2+4+0 = 9

You can play around with it for any octave, in any case it always comes back to 9, because changing octave just means multiplying or dividing by 2, when you do that, in numerology it always comes back to 9:
9 x 2 = 18 = 1+8 = 9
9 / 2 = 4,5 = 4+5 = 9

The musical choice of La/A 432 Hz with perfect ratios is the only one giving such a perfection in numerology for all frequencies.

As a more general rule, if the base frequency is a 9, any multiplication of that 9 by any of these ratios will alway give a 9. In fact we could use La/A 414, 423, 441 etc. But, no one ever spoke of such frequencies, this is just to explain some mathematical rules that apply to numerology. ;)

That being said, do note that not all fractions work, these ratios are very well chosen, for example 432 x (4/9) = 192 = 1 + 9 + 2 = 3, or 432 x (46/19) = 1045.894737… I repeat it again, the choice of these ratios, is all but random!