432Hz – An open, fair and critical examination

432Hz! Is it a fact or a myth? Well, spoiler alert, it is complicated, but I will give you an open, fair, and also critical examination which is also quite thorough. I don’t want to fight or disprove anyones believes in the matter, but much more help anyone who is interested to not use arguments which make no sense in order to defend or promote 432Hz. After reading this the subject of 432Hz is down to what really matters, without all the doubletalk. It is distilled 432Hz, for anyone to use and listen to, but based in fact, not obvious misdirections.

But before we dig in. Let me tell you where I come from: I come from a very spiritual, rather esoteric, family but then I have learned a scientific profession (electronician) and later became a, among other subjects, physics teacher. Furthermore for one of my diplomas I have written about the physical difference between tempered tuning, just intonation and pythagorean tuning, which is very interesting in it self not mattering which base Frequency of  “A” you start from.

I give you this information as a starting point so that you can understand that I’m always interested and open for the supernatural, but I’m also a scientist at heart. I have many believes but I will never hold on to a silly believe if it can be clearly disproven by science. My believes are in the places where science has no answers and in my opinion no believe system should ever try to justify itself with layman-science. If anyone is into “believing” instead of “knowing” he should just own it and say: “It’s a believe” and not to try to justify it with pseudo-science. Yet anyone holding on to believes should of course be open to the believes being proven wrong by science and be ready to let the believe go at any time.

So knowing that much about me, it should be clear, that naturally if I hear something like that 432Hz tuning thing I’m both very interested but I also look at the scientific logic behind the matter. So after my first couple of hours of reading I have read mostly all those blogs and texts that look at it from a spiritual point of view. Which is fine, there are many interesting benefits listed ranging from a cure for cancer to a means for world peace. But I’m a science guy and while I sure want to believe that this magial frequency should do all those things I simply ask, like a scientist AND a child: Why?

Why should 432Hz have those benefits?

And those spiritual blogs try to give scientific arguments.
Basically it all comes down to a tuning based on “A” 432Hz is supposed to produce more beautiful and round numbers for the frequencies of all the other notes and / or resonate with all sorts of other natural stuff.

A little bit of knowledge is needed before hand. I make it quick, and the knowledge is very useful anyhow.
First: a frequency in Hz (Herz) is a measure of how many vibrations per seconds a soundwave does.

Second: So that musicians can play in tune together it has become common practice to define the frequency of the 4th “A” to 440Hz and develop all other notes from there. The 3th “A” is at 220Hz the 5th “A” is at 880Hz. Every octave doubles the frequency. The other 11 Notes we use are in between and all have their own frequencies and Octaves.

Third: 432Hz propagates to use 432Hz instead of 440Hz for the 4th “A”.

Fourth: In theory the frequencies of the other notes are derived from mathematical relations to 440Hz. Think of a string, pull it, it vibrates 440 times a second, there is your “A”. Now half that string with your finger, it will vibrate 880 times a second, there is the next “A”. Now you can also use 9/8 of the string, 5/4, 4/3, 3/2, 5/3, 15/8 and it happens to sound very pleasant to human ears. Like that you get 7 notes, you can get more notes, if you start from a different note, but those will not be in perfect harmony with the ones before. There is no way, mathematically, that you get all 12 notes in perfect harmony. The fact, that we actually use 12 notes is due to a compromise nobody knows of. It is called “tempered tuning” which is what pretty much ALL of the music you have ever heard has been using. In this tempered tuning it is allowed to diverge from this perfect “just” tuning of perfect fractions, in order to allow for more notes. Why do I tell you this? Well just to let you in on the fact, that no matter if you use 440Hz or 432Hz as a starting point, pretty much all common instruments will have a tempered tuning and thus not produce mathematically perfect harmonic notes.

If you want to know more about he difference between different tunings. There is a lot to take away from that alone because the some tunings are purely mathematical and are definitly more harmonic than the “allrounder” the tempered tuning.

432Hz, mathematically more beautiful and part of natural sequences? Depends and sometimes true, but it doesn’t matter.

Most authors on the subject of 432Hz play around with the numbers of the frequencies of the notes and do some nice arithmetic which is totally nice to see and makes also sense in it self. It’s math after all. However they are usually completely ignoring if the scale they are talking about is “pythagorean”, “just” or “tempered”. But this makes a big difference in the resulting numbers because the tempered tuning will always tend to produce weird fractions and the just intonation and pythagorean tuning will always tend to produce whole numbers. If you do math with the frequencies of the just intonation or pythagorean tuning it will always work out nicer than with the tempered tuning and it doesn’t matter if you start from 432hz or 440hz. In the following table you can see the frequencies of the notes in either base and in pythagorean, just intonation and tempered tuning. You can see easily that because of it’s purely mathematical properties (see ratios) the just and the pythagorean tuning produce more integer numbers for the frequencies of the tones.

Frequencies of notes in Just Intonation, Pythagorean tuning and tempered tuning.

Note that the just intonation is in terms of harmony between the notes the most perfect of the three tunings. The just intonation produces more integer numbers in the 440Hz base, while the pythagorean tuning produces more integer numbers in the 432 Hz base. So, if you are after “integer frequency tones” it depends which tuning you talk about.

Many musicians are not aware of the fact that setting the base A to 432 Hz alone does not make them play the beautiful integer frequencies of the pythagorean tuning. Anyone who truly wants to take advantage from any supposedly mystical properties of 432Hz has only the 7 notes C, D, E, F, G, A, B at his disposal and needs to tune all those notes to the according frequencies. Simply setting synths or music software to 432Hz or pitch shifting existing music to 432 Hz will produce the frequencies of the tempered tuning and you can see above how far they are from a pythagorean tuning.

The problem with the time unit the “second”

This is the key problem of all the numerical arguments for the 432Hz base: All frequencies are based on the time unit the “second”. Herz is defined as: “The number of vibrations per second”. And this is where the problem lies: The length of the second is just an invention of mankind and could be longer or shorter which would make the frequency different. If we had chosen a different length for the second 432Hz would mean a faster or slower vibration.

The second was defined as ¹⁄_86,400 (that is, 1/24 × 60 × 60) of a mean solar day from the year 1000 until 1960. 1960 It was defined as the fraction 1/31,556,925.9747 of the tropical year. The redefinition of the second in 1960 changed the length of the second and therefore changed also the number of vibrations per time corresponding to a certain frequency in Hertz. Since 1960 432Hz is not the same 432Hz as it was before 1960. It is slower now.

So any “number-games” with that 432Hz tuning are dismissed by that. What ever you throw into the discussion, be it golden means or fibonacci or whatever. I will always say: for which length of the second are we talking? And: Why should mankinds crazy idea of dividing the day into 24 hours and the hour into 60 minutes and the minute into 60 seconds have ANY relevance with some magical, universal frequency? What if we had just divided the day into 100 hours and the hour into 100 minutes and the minute into 100 seconds? Or if we had used some fibonacci sequence to divide the day? The second would be different and there for the resulting number for the same velocity vibrations would be different.
Arythmetic reasoning for 432Hz doesn’t work because it’s all relative to the second and the second has changed and also it is a relatively “new” invention. Before the year 1000 it was not known at all. 

Maybe it’s not about the number, but about the vibration?

So, after dismissing all arguments that 432Hz is better than 440Hz because of numerical tricks that you can make with its number  I went on and assumed the following: 432Hz is just THE number of vibrations per OUR new 20century second that is special. I could accept that. But then I ask: Why?

More beautiful patterns in pools and on plates that vibrate at 432Hz and 440Hz. Myth.

There are videos with those more beautiful patterns on plates or in pools which I completely dismiss because it depends on the dimensions of the plate or pool. You can chose any dimension that creates beautiful patterns with any frequency. You can make a vibrating plate that makes nice patterns with 440Hz or with 432Hz you just have to chose the length and width of the plate so that it’s according to the wavelengths of either frequency. If the length and/or width of the plate is a multiple of the wavelength of the frequency it will of course bounce back from the borders more nicely than if it isn’t. Besides, what’s more beautiful or not is also in the eye of the beholder.

The resonance frequency of the water molecule. Myth.

There is the very interesting argument with water reacting to that frequency more than to 440Hz and humans being practically filled with water. That would be amazing! Wouldn’t it? But I checked the physical resonance frequencies of the water molecule. I only found some info on water vapour. The lowest resonance of the water molecule seems to be 22235000 Hz. In the following table you can see that this number is neither a multiple of 440Hz nor 432Hz, but also that 22235000Hz is such a ridiculously high frequency that multiples of both 432Hz and 440 come very close in terms of percentage. Multiples of both frequencies actually come within 40Hz of 22235000Hz. That water vapor resonance frequency is just a middle though. Depending on various other conditions it changes in nature. So it could be that either base is spot on with the water molecule in some conditions.

Finding definitive numbers for the resonance frequency of water is not so easy either. Is it known at all? The idea of 432Hz being a better frequency for resonating the water molecule can neither be completely debunked nor confirmed at this time. However it is certain that it is very very high as this is normal for things happening on the nano-scale or beyond. Since it is that high, the slightest deviations would completely mess up any resonance from 432 or 440hz and therefore it is unlikely that 432Hz is always better, but far more likely that both frequencies are sometimes perfect.

432Hz is supposedly a multiple of the Schuman Frequency. Myth.

I have also heard claims that the 432Hz would be better because of the frequency of “C” being multiples of 8hz which again is said to be the resonant frequency of the earth. The schuman frequency. However there are two problems with that.

First: The tempered scale with 432Hz base doesn’t put C at those multiples of 8Hz. See in the table above, the values of C are not integer numbers at all. This would only work in a pythagorean tuning.

Second: The Schuman Frequency is not one frequency but three (14.3, 20.8, 27.3 and 33.8) and none of them is 8hz, in fact the lowest is 7.83Hz. If you take this as a base for “C” it puts c5 at 501Hz, wheras the 432Hz in pythagorean scale puts c5 at 512Hz. 12Hz difference is even more than the difference between 440Hz and 432Hz. The 440Hz scale puts c5 to 523Hz though. So if there really is something going on with that frequency then we would need to make it multiples of 7.83Hz, not 8Hz. The other schuman frequencies are 14.1Hz and 20.8Hz. 14.1 x 31 is 437Hz which sits even closer to 440Hz than 432Hz. And also those frequencies are only means, they fluctuate.

432 Hz in sync with the fundamental frequency of the sun? Myth.

I came across information that supposedly astronomers at stanford found the Suns fundamental frequency to be at 144Hz and that 432Hz is the 3d harmonic of 144Hz. Which well would be true, but the researchers at stanford did NOT put the fundamental frequency of the sun at 144Hz! The measured over a period of 144 days and they found a frequency in the microHz range. Some guys once read that wrong in the original paper and from then on it has been misquoted all over the internet. A good example why you should always remain critical an check the sources of such claims.
http://quake.stanford.edu/~sasha/PAPERS/diam_3.pdf

The relation to the “cosmic octave” – here it gets interesting! Fact!

The cosmic octave or the planetary frequencies is the idea of giving the revolutions of a planet around its own axis or around the sun a frequency. In other words: How many times a second does the earth revolve around itself or around the sun? Of course the result is a very very small number, since the rotation is very slow. Nevertheless if the source of the time meassurements is correct the results are independent from the definition of the second and very real to a point. To a point because the roation of the earth around its own axis fluctuates.

Planetary Frequencies

The frequencies are calculated by dividing 1 by the number of seconds it takes for a revolution. (This is how frequencies are always calculated). For the earth day it divides 1/86400. The result is then 24 times doubled until it hits 194.18Hz. If this note would be assumed as C-sharp the resulting A would be 435.9 Hz. A That isn’t quite a hit, but it also doesn’t make sense because there are various ways to look at the earths rotation. One revolution until it faces the sun again? Synodic day. Until if faces the same stars again? Sideric day. If you think a day has truly passed when you look again at the same stars then A at 440Hz would be close enough with 437Hz.

If you take the rotation around the sun as a point of meassure however it gets interesting. Because if you divide 1/31556925.54 which is the time the earth needs to rotate around the sun the resulting frequency is: 0.00000003168 Hz. If you double this 32 times the resulting frequency is 136.10Hz which (see table above) is pretty exactly C-sharp in the tempered tuning of the 432Hz base! So there really is one undisputable connection of a natural phenomenom to 432Hz! 

I do have some reservations though. Its because a year is very very very long and I believe that one could argue that IF we can feel a connection to that super low frequency we would probably feel the super low frequency of earths rotation more because it is faster AND not in sync with the super low frequency of the rotation around the sun. If you look at this precisely there is even a dissonance between those two frequencies. So one could argue that we are under constant stress because two major frequencies, that of earths own rotation and that of earths rotation around the sun are NOT in sync during all our lives. That raises a big question mark. Because it means that if there is any relevance to those frequencies, which needs to be for it to make it necessary to tune instruments according to it, then it also means that we live on a planet with a major dissonance happening all the time.

There is more, brace yourselves: Why not “tune to the moon”? It might be even better. The moon rotates around the earth in 2351134.08 seconds. 1/2351134.08 resulting in a frequency of 0.000000425326658Hz. This results in an A-sharp at 228.34Hz which is actually pretty close to A-sharp in the 432Hz base tempered scale which is 228.83. That is pretty cool indeed!

It’s important to note that both frequencies, sun and moon, sit on the tempered tuning. Which means that all theories who advocate 432Hz through “number games” with integer numbers in the pythagorean tuning are NOT in sync with the cosmic octave.

The supposed historic relevance of 432Hz. Myths.

A frequency must be meassured with a clock

I checked for historic frequencies of “A” and found that it changed countless times and there was no standard for centuries. Also I couldn’t find any evidence that there was the consensus that is presented to us today by those advertising the 432Hz base in India and Tibet. I have found countless websites who “claim” to know, but no historic evidence was presented anywhere. Claims that classic violins being tuned to 432Hz or famous composers using it in their work are all mere inventions with no backup. The opposite is true. Violins and composers are reported to have used various frequencies all over the place. Sometimes 432 was among them just as any other possible frequency.

There is a reason why nobody can present historic evidence of monchs using 432Hz tuning 2000 years ago. It’s simple there is a much bigger problem here: How would the Indians or Tibetians know the frequency from 1000 years ago if they didn’t have clocks to measure frequencies? So it is very obvious that the frequency definitly couldn’t have been delivered through time in writing. Also bowls or instruments would have suffered from aging and change their frequency because of that.

There is no way of knowing what they tuned their instruments to 1000s of years ago. Measurements of frequencies were only possible in the last 2-300 years or so. Everybody knows that clocks, let alone precise clocks weren’t even a thing more than 400 years ago. You could never know a frequency without a clock.

Is it possible to teach a tuning in perfect sync over 1000s of years?

The teachers could have shown it to their students and other teachers. Or they could just magically “feel” it.

But Think about it: Do you believe that a purely intuitive delivery of a frequency through time has remained spot on and today, with our modern 20th century definition of the second, magically sits exactly on that 432Hz a number that is also funny to do math with? Well. I don’t, but I can understand if one wants to.

For me that would be a lot of coincidence. Even if we assume all those musicians have the ability to intuitively feel the magic frequency, If we had defined the length of the second differently the “number” of that frequency would be different and all the funny math wouldn’t work anymore. But it could of course just all have “fallen into perfect place” when they changed the length of the second in 1960… yet. again then the funny math and the numbers only works with the pythagorean tuning and exactly that tuning doesn’t work with the cosmic octave… big contradiction there.

The truth is the frequency of “A” has probably changed all over the world as it did in europe where A has ranged from 300hz up to 470 or something within the last 300 years alone.

That Nazi controlled frequency thing… of course Myth!

And, uhm, yes, that thing that 440Hz was invented by the NAZis in order to make people more aggressive and obedient is very probably not really true, or at least there is no evidence that it is. All you can find are people claiming it to be true but there is not a single shred of evidence, not a single paper or research that I could find. Today, because of historic documents, we even know that Hitlers penis was deformed and a lot about cruel experiments with disabled people done by the Nazis. So I believe we would be able to find some evidence for those theories too. But I haven’t found any. Also 440Hz wasn’t even first proposed by the Nazis as it is often claimed. The American music industry reached an informal standard of 440 Hz in 1926 way before the Nazis were significant, and some began using it in instrument manufacturing. In 1936 the American Standards Association recommended that the A above middle C be tuned to 440 Hz.

So, sorry folks, no Nazis in this one either. Except if you accept people just saying it is true as evidence that is. If you look closely you can only find many people quoting each other without anyone having any prove other than their opinion. That is not good enough for me to base a believe on.

Lets sum the facts part up

So what really is left after a lot of reading is that there is:
– no historic (it changed so many times!) evidence
– almost no scientific evidence, most is just pointless funny math, but one truly nice and science based connection to the time earth needs to revolve around the sun and a close match to the rotation of the moon around the earth.

The only thing that is left is of course is the most important thing of it all:

How does it feel?

Maybe it doesn’t need ANY explanation at all. Fuck history, fuck science! Maybe it just feels right!

This is thing where all discussion should be centered around. Nobody should try to advocate the 432Hz base through science or history, it fails. If you want to talk about 432Hz, talk about how it feels.

… and that is the truly tricky thing… because the mind tricks us heavily and if we WANT to believe we easily feel what we want to believe. Especially if there are such “logical” theories behind it as with the 432Hz theory. Are we tricking ourselves in feeling it?

We have to let go of all supposedly logical theories (they are not even logical, see above) and we need to be honest to ourselves: Only blind tests can give us some degree of objectivity.

I checked if there are studies on the matter. Some tests have been made and the results where that mostly people didn’t prefer any frequency. But that doesn’t mean anything since we are all used to 440Hz tunings and might therefore prefer it just out of habit.

Never trust a study that you didn’t manipulate yourself. What really counts: how does it feel to me? To me most 432Hz things I heard on its own sounded fine. In direct comparison between a piece in 432Hz and 440Hz I always prefered the 440Hz tuning. But that could of course also be because I’m used to it. So it’s even trickier.

After all: It is a matter of believe. Do you believe in 432Hz? Do you believe in reincarnation?

You believe in it and make 432Hz music? Well, I think it’s completely ok to believe such a thing but it should be clear to the person that this really is mostly BELIEVE. Allmost all science behind it can be debunked by science so it is not science. It’s like believing in god, the bible, jesus, elves, santa clause. There is no prove that any of it is wrong but there is no fact behind it either. No one needs to try to prove jesus with science or history, 432Hz proponents shouldn’t try too much either, because it mostly fails. Any explanations but one fail. However if this connection is important it means we all live in a constant state of the dissonance between the frequency of the day and the frequencies of the moon and the sun. And if that dissonance matters it might not really matter how we tune our music.

If you are among those who believe that the connection of 432Hz to the length of the year and the length of the “moon” is of importance you should be aware that this might not be the case for everyone, since others would rather  “tune to the day”. Maybe not one tuning is right, but you can pick any natural frequency, tune your instruments to it and make your music appeal to whoever also loves that natural phenomenon. Tune to the day. Tune to the moon, tune to schuman frequency, maybe all have other effects on different people. 432Hz is certainly not the “one for all” that much is completely clear just by running the numbers.

Nevertheless: I will try it myself sometime and check how it feels! It was interesting research. And that thing with the sun and the moon… well it makes me thinking. I love the moon! Would you rather tune to the day? Which one? Full rotation or looking at the same star again?

What do you think? Do you have any links to real research and true science? I’m not interested in spiritual talk, but in the physical connection to the world: the real thing.