440 or 432 Hz? It’s just a matter of… hoaxes!

In this short article, I wish to clarify (which, by the way, has already been done extensively by many scientists) what is true about the alleged benefits of a 432 Hz pitch compared to the modern standard of using an A at 440 Hz. Without unnecessary preamble, I can already anticipate that the pseudo-scientific theories supporting the 432 Hz are, as is almost always the case, the product of people who wish to invent conspiracies and all other forms of collective lies to satisfy an ego not much gratified by daily life.

In short, they are just blatant hoaxes that, like chakras and various cosmic energies, go to fill the pages of books that, alas, sell more than Tolstoy’s War and Peace. As we shall see, the very idea on which such alleged truths base their foundations is fallacious, belied by history, and lacking any experimental or physico-theoretical support.

But what are we going to do about it? Then again, the earth is flat, the South Pole, demarcating the boundaries of the circle, is controlled by hundreds of millions of American soldiers (why only Americans?) and, even the poor clouds, when they form what meteorology formally calls “cirrus clouds,” are by force elected to “chemtrails,” whose purpose, unknown and mysterious, would be to prove… (ed. please come to my aid!)… normality!

First point: why (if there is a reason) is A tuned to 440 or 432 Hz?

What would you say if I asked you why an electromagnetic wave at a frequency of 520 THz is called “yellow”? Conventionally! The visible spectrum is a continuous range from the upper limit of infrared to the lower limit of ultraviolet. For neuroscientific reasons, our visual perception leads us to distinguish what we call “colors,” which have been given proper names for various reasons.

Then, if we want to be nitpicky, there is no such thing as “yellow” either since a range of about 10 THz contains all shades of what is collectively called yellow. Of course, a linguist could trace the origin of a noun, but this would only serve to understand by what association of ideas a specific noun was defined instead of another. Nothing more.

Similarly, the names of musical notes are entirely conventional and not even that stable over time. Aside from tuning issues that I cannot discuss here, during the Baroque, the A had a frequency roughly around 415 Hz, understanding that there were no precision instruments and if a tuning fork produced a sound at 416 Hz, no one would pay attention. This brings us to the second point, which features Mozart, who connoisseurs of this occult discipline cite as an advocate of 432 Hz.

Mozart at 432 Hz… or 420… or maybe 421 Hz?

Let us start with a historical truth: A in Mozart’s time was generally tuned to a higher frequency than in the Baroque period. More or less at 420 Hz. But why “more or less”? I repeat: there were no precision instruments, and the most negligible errors were not detectable in virtually any way. Suppose, for example, that the candidate frequency was 420 Hz; this means that the upper octave is at 840 Hz, and therefore, using equal temperament, the first semitone had a base frequency of 420 * 1.05945 ≈ 445 Hz, i.e., about 25 Hz higher than the reference note. This means that A# would have a frequency of 445 Hz.

Do you think that 1 / 25 semitone was distinguishable? Mozart was gifted with an over-ear, but here we talk about deviations that electronic tuners often fail to detect! So if, in an orchestra, it was decided to tune to the fateful frequency of 432 Hz, do you think that all the instruments could have produced an A at that frequency? The most obvious result would have been an interval centered around 432 Hz, with an amplitude as small as the director’s ear accurate.

In other words, the idea that one could tune an instrument with infinitesimal precision to 432 Hz is simply ridiculous. However, proponents of the theory do not give up so quickly and claim that slight deviations are acceptable. Well, let me ask a question: how small? Since we are talking about math, we can use numbers, so let’s do it!

Tuning (approximately) to cosmic frequencies (inaccurate)

Let’s repeat the experiment from before. If the octave is 432 Hz wide, the first semitone has a frequency of 432 * 1.05945 ≈ 457.7, and its amplitude is about 25.7 Hz. The quarter tone is about 12.65 Hz wide; The eighth tone is about 6.28 Hz wide, etc. So, the sound that is a quarter semitone above A has a frequency of about 438.3 Hz. Assume a deviation of 3 Hz, thus moving from the magical frequency to the nefarious frequency of 435 Hz. The same microtonal sound as before will now have a frequency of about 441.33 Hz. The deviation is 3.03 Hz, which, in relative terms, becomes 3.03 / 435 ≈ 0.7%.

This level of inaccuracy is concrete and measurable. It could have severe consequences if a value is needed to send a rocket into orbit. Still, in the case of music, the receptor is the human ear, which at best can perceive quartertones at frequencies that are not too low (remember that the amplitude of the octave is proportional to the frequency of the fundamental) but would have serious difficulty distinguishing more minor variations.

Some great performers indeed noticed sonic imperfections that are generally overlooked by most. Still, these were often “dirt” due to mechanical malfunctions or similar structural problems (e.g., a faulty bow or a rusty string). As a classical guitarist, I can perceive when a sound “scratches” because the fingernail is not perfectly smooth, but that doesn’t mean I can distinguish a 3 Hz deviation in an A at 435!

Also, it is good to remember that in the case of orchestras, many instruments rarely play in isolation. Therefore, if early violins have tuners ranging from 430 to 435 Hz, the overall effect of an A will be perceived more or less as a sound centered on the frequency of 432.5 Hz.

432 Hz vs. 440 Hz: cosmic frequencies vs. … (you fill in the dots)

The period of revolution of the Earth around the Sun is about 31556928 seconds (equivalent to 365 days, 5 hours, 48 minutes, and 48 seconds). This number has nothing to do with 432. Similarly, for the period of Earth’s rotation and a thousand other physical phenomena. The human heart rate varies roughly from 1 to 2 Hz (60 to 120 bpm).

Human gestation lasts about 9 months, or an average of 270 days. Not to mention the myriad of irrational numbers found in nature. Pi, Nepero’s number, the golden section, etc. Nothing can easily lead to this beautiful integer value of 432, which may appear (perhaps followed by a string of decimals) precisely like many other numbers.

Conclusions

The choice to tune A to 440 Hz is purely conventional and based only on the need for a shared reference that avoids arbitrary choices and thus makes the sound result of the music equal. The frequency of 432 Hz or 435, 442, etc., could have been adopted. None of this is of any importance or consequence except to hear the same tracks at slightly lower or higher frequencies, nothing more.

Alleged health benefits are baseless inferences to be stigmatized without hesitation. Instead of taking refuge in vaticins imbued with sacred doctrines as fanciful as they are arbitrary, I strongly recommend the healthy conventional study, made up of sacrifices, work, difficulties, and far more solid certainties. Happy listening to all!

If you like this post, you can always donate to support my activity! One coffee is enough! And don’t forget to subscribe to my weekly newsletter!

Share this post on: