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Would you believe that there is a conspiracy theory about the way we tune musical instruments? And that this theory even involves the Nazis, chakras, and whatnot? No? Then sit down and enjoy perhaps the most ridiculous conspiracy theory of all times.

To understand what all the fuss is about, we need a little bit of historical background. As you probably know, musical instruments need to be tuned. When you turn a tuning peg on a string instrument or adjust the length of the tube of a wind instrument, it makes it sound a little bit higher or lower.

For different instruments (and even different strings of one instrument) to sound good together, they all have to produce the same tone (same pitch) when they play the same musical note (e.g. A).

The usual way to specify a tuning is to give the frequency of the note A 4 . The modern standard is A = 440 Hz, where Hz is a unit meaning “per second”, so “440 Hz” refers to 440 vibrations per second (such as those of a string). To tune to this frequency, a musician would either listen to a tone played by some tuning device and tune by ear or use an electronic tuner.

The 432 Hz conspiracy

If you Google “432 Hz”, you will find a tremendous number of articles and YouTube videos about the tuning A = 432 Hz and its presumed healing and soothing properties. If you dig a little bit deeper, you will also find an “explanation” of this phenomenon. Presumably, the 432 Hz tuning is in some way tuned to the vibrations of nature itself, whereas the 440 Hz tuning was introduced by Joseph Goebbels, the Nazi minister of propaganda.

Yes, that’s right. There are millions of people in the world who believe that Goebbels introduced the tuning to make people feel more anxious.

Now, why should 432 Hz be so great? According to proponents of the theory, the number 432 has special properties. And, indeed, it is an interesting number. It is a sum of four consecutive primes: 103 + 107 + 109 + 113. It is exactly three gross, where gross = 144 is a traditional unit. An equilateral triangle whose area and perimeter are equal has the area of exactly the square root of 432.

Then you will find many mystical arguments, such that there are 432 Buddha statues on Mount Meru, or that it is somehow related to the location of chakras. There is even a claim that scientists at Nike found out that the best golf balls have 432 dimples…

Why the numerological explanations of 432 Hz are all nonsense

I cannot say with certainty that there is no difference in the psychological effects of A = 432 Hz and A = 440 Hz, but I suspect there is no significant difference, since orchestras around the world used to tune to anywhere from 400 Hz to 470 Hz, and if 432 Hz were some kind of a sweet spot, someone would have noticed by now. Any psychological effect of the tuning is likely caused by the simple fact that 432 Hz is different from what we are used to and would be pretty much the same as the effect of 440 Hz if the standard were 448 Hz.

What I can say with certainty, however, is that the arguments about numerical or mystical properties of the number 432 are utter nonsense. It is important to understand that 432 Hz refers to the number of vibrations per second, and “one second” is a rather arbitrarily chosen unit.

Originally (from ancient times through the Middle Ages), the hour was divided into 2, 3, 4, or 12 equal parts, but never into 60 (so there wasn’t even a minute). Fractions of a minute were not used at all (there were no devices at the time that could measure such short periods of time). Had we stuck with dividing everything into 12 parts, the “second” could have become 1/12 of a minute or perhaps 1/1728 of an hour (1728 = 12 $×$ 12 $×$ 12), which would give a completely different numerical value for the same frequency. The current definition is just a coincidence.

The practice of dividing a minute into 60 smaller segments did not appear until the 16th century, and even then different clocks ticked at slightly different rates. In order to standardize time measurement, people defined units of time as a fraction of the mean solar day, which is the average time (over one year) the Earth needs to rotate around its axis relative to the Sun, and the first clocks that could accurately keep track of seconds over long periods were constructed only in the 18th century.

However, in the 1940s, scientists discovered that the speed of rotation of the Earth is not constant (due to various tidal effects), and the second was eventually redefined as “the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom”.

So, yeah. The 432 Hz tuning, the divine tuning of nature itself, is ultimately defined as one vibration per 21279240.2083 periods of radiation of an uncommon chemical element. Very spiritual, indeed.

Why do we use A = 440 Hz? (spoiler: no Nazis)

In Bach’s era, there was no standardized way to tune instruments. The same piece could sound much higher or lower depending on where and when it was performed, and even organs in different churches in the same city could be tuned in completely incompatible ways.

The pitches musical instruments produce change over time due to heat and mechanical wear and tear, so until the tuning fork was invented in 1711, there was no simple way to make tunings consistent among different regions and even performances in one region. However, even after the invention of the tuning fork, there was no single standardized tuning. Ensembles in different regions used tuning forks resonating at different frequencies.

And then, in the 19th century, the era of pitch inflation started. You see, it is the relationship between the thickness of a string and its tension (i.e. “how many times you turn the tuning peg”) that tells you how high the string sounds; the higher the tension, the higher the sound, and the thicker the string, the lower the sound. That’s why the double bass has huge thick strings, whereas the violin has thin strings.

It turns out that strings sound better (up to a certain point) when their tension is higher. The way instrumentalists increase tension now is that they simply buy a thicker set of strings, which, when tuned to the same pitch as thinner strings, produce higher tension. Unfortunately, obtaining thicker strings was not that easy in the 19th century. Manufacturing of strings was a complicated procedure, so rather than changing the manufacturing process, it was much easier to tune the same strings to a higher pitch to increase tension and thus improve the sound.

Orchestras, competing with one another over better sound, started to tune their instruments higher and higher. This eventually led to problems for singers, who complained about having to perform pieces in higher registers than they were originally meant to be performed in. At the urging of singers, the French government made the tuning A = 435 Hz officially standard in France in 1859, and many orchestras and Opera houses in Europe adopted this standard. In Britain, however, the French standard was interpreted in an erroneous way (it was understood as being relative to a certain temperature), due to which British orchestras commonly tuned to A = 439 Hz.

In 1939, there was an international conference held in London that resulted in a recommendation to use A = 440 Hz, as a compromise between the various tuning systems used at the time, some of which reached beyond 450 Hz. This recommendation was further supported by the fact that the BBC required their orchestras to tune to 440 Hz instead of 439 Hz because 439 is a prime number, and the corresponding frequency was hard to generate electronically with standard electronic clocks. Eventually, in 1955, the standard A = 440 Hz was adopted by the International Organization for Standardization (ISO).

Virtually all commercially produced contemporary music is tuned to A = 440 Hz. Nevertheless, most symphony orchestras ignore the standard and tune to 441, 442 or 443 Hz instead, while orchestras specializing in older music may sometimes use a tuning close to the one for which the piece was originally written, which may range from 415 Hz to 470 Hz.