432 Hz, a new standard pitch?
Over the last 10 years an increasingly widespread discussion on the topic of the concert pitch 432 Hz has given birth to a variety of experiments, research and all sorts of conjectural considerations.
If you search ‘432 Hz’ on the internet nowadays you will find a massive number of links, far more than I was able to find when I first became interested in the topic some 12 years ago. Some of the pages you’ll find provide a well thought and researched presentation, others are inconsistent and approximate.
Many articles and blog posts that oversimplify this topic often include half-baked statements such as “432 Hz is the frequency of life” or “it resonates with the Earth” or “music tuned to 440 Hz is bad for you” and the like.
One of the reasons why this topic is subjected to so much shallow information is that, in the attempt to seek a deep understanding, one is confronted with a research that branches off in many directions, which is obviously time-consuming
I am not presenting a solution here, nor am I attempting a definitive answer to the many questions. My intention is to share my personal experience in combination with the most relevant information among all I have been able to examine so far.
The first time I came across the suggestion that 432 Hz could be a better standard pitch than 440 Hz was while reading the book “The secret music of the soul” by Patrick Bernard sometime in 2004. Somehow this information resonated very deeply with me and one morning I decided to lower the tuning of my classical guitar and try this new pitch. I had an immediate feeling that there was something there, something that I needed to experiment and understand better because somehow it felt significant, almost poignant. At that time I was spending most of my days in the midst of nature, in retreat from the chaos of the big city (Rome) and focusing mainly on deep relaxation and regeneration of my nervous system. Therefore I was very sensitive and open and I believe this is the reason why I was able to appreciate the effect of such a small change in the tuning of my instrument.
Three basic elements
In order for the numbers in this article to make sense you need a basic understanding of three concepts:
1 – The term “Hz” (or Hertz, last name of German physicist Heinrich Rudolph Hertz). Simply put, Hz means nothing more than “times per second” and it is the measuring unit of vibration. The number of Hz indicates how many times in one second the full cycle of a certain vibration occurs: 1 Hz means once per second; 432 Hz means 432 times per second… and so on.
2 – The standard pitch (or reference pitch) for the intonation of musical instruments. In order to make it possible for many musicians to play together, a reference pitch or standard needs to be set. Currently, the international standard pitch (proposed in 1939, 1955 and finally adopted internationally in 1978) is A = 440 Hz, where A or La (the Latin name for the same note) is the sixth note above the middle C (or Do) of a piano. It has been decided that this note has to vibrate 440 times per second. All the other notes of the scale will be then tuned accordingly.
3 – Tonal systems. A tonal system is a framework made of a series of tones arranged in specific ratios. In order to make music, we arrange the notes of the musical scale in a way as to create specific intervals (combinations of two notes) from which we proceed to create chords (combinations of three or more notes) by which we express and experience ‘harmony’. There are several different tonal systems and the one we are more familiar with in the western culture is the 12 tones Equal Temperament, which sets a musical scale of 12 notes. The distance between any one of these notes from the next or the previous is constant.
Bel canto and 432 Hz
On April 9, 1988, in Milan, Italy, the Schiller Institute held a conference on the topic, a pivotal one in the world of Opera singers, of changing the standard pitch from 440 Hz to 432 Hz. The famous soprano Renata Tebaldi and baritone Piero Cappuccilli were present as speakers and big names like Montserrat Caballé, Anneliese Rothenberger, Placido Domingo, Alfredo Kraus and others, unable to attend, sent their messages of support. Luciano Pavarotti was also known to support this cause.
The key point presented at the conference is this: in the traditional Bel Canto technique, passed on through centuries from the Italian masters there is a specific shift in the registers of the voices of the tenors and sopranos. This naturally occurs on the F# when instruments are tuned to A = 432 Hz.
When instruments are tuned to 440 Hz or higher then the shift will occur around the note F, or even lower.
The Schiller Institute maintains that the operas of the great composers of the past were composed on a lower pitch. The changes in registers of the voice were used to accentuate the meaning of the lyrics and therefore these shifts have to occur on the right notes.
The Bel Canto has evolved, been perfected and passed on for centuries by the Italian masters of the voice and it is the result of a close observation of the natural voice and its dynamics. Therefore it is important to adopt the reference pitch the most helps to preserve the natural registers of the voice.
After all the human voice is the basis of human music. Musical instruments came later and their technical issues and specifications should not be allowed to have priority over the natural needs of the singing voice.
A famous letter written in 1884 by the great Italian Maestro Giuseppe Verdi to the Italian government is often quoted in support of the 432 Hz movement. In this letter, Verdi expressed his concern for the raising and fluctuations of the pitch (which at that time had not yet been standardized). He asked for and obtained a regulation of the pitch at 432 Hz. His main arguments were to do with the difficulties of Opera singers and the risks that ancient instruments underwent when tuned to a higher pitch than the one they had been built for.
Actually, in his letter, Verdi asked the Italian government to conform to the French standard of that time, which was 435 Hz. He then added that if the Italian commission believed that for mathematical reasons the reference pitch should be lowered to 432 Hz, he would absolutely agree with that.
It is interesting to notice here that 432 Hz is related to mathematical values. Unfortunately, in Verdi’s letter there is no mention of the reasons why this frequency would be preferred “for mathematical reasons”. It is likely though that 432 would be preferred for ease of calculations of all the other relative frequencies.
Another important aspect is that A = 432 Hz can be understood as the upper limit of the tuning based on C = 256 Hz.
Now, this might seem a bit confusing, but the 432 Hz issue cannot be really separated from the notion of ‘scientific tuning’ which corresponds to middle C on the piano keyboard (the C note just below the A 432 Hz note) tuned at 256 Hz. We will get to this later.
The name of Verdi has recently been taken up as a sort of banner for demanding a new standard pitch of 432 Hz on the basis of his letter mentioned above and the resulting decree by the Italian War Ministry, which, in 1884, institutionalised the A at 432 Hz throughout Italy. Unfortunately, this did not last very long. The following year in a conference held in Vienna and mainly run by the British government, this standard was refused and as a consequence, it was abandoned also in Italy.
Pythagoras and 432 Hz
A very peculiar association I have encountered more than once is that with the name of Pythagoras. I was quite surprised to find the note A = 432 Hz addressed as ‘Pythagorean tuning’.
Pythagoras is beyond the scope of this article and discussing Pythagorean tuning would lead us too far astray. However, I would like to point out that none of the historical sources available on this semi-mythical character make any mention of frequencies of vibration, simply because at that time the assignment of a numerical value representing a periodic frequency had not been yet introduced (as far as we know). Furthermore, all the texts available were written after the lifetime of Pythagoras. We do not possess any written material by Pythagoras himself.
The Pythagorean tuning system is based on a cycle of ‘pure fifths’ (the 3/2 ratio found in the harmonic series). This tuning is not the one commonly in use today and one of the reasons is because a full cycle of 12 fifths should coincide with 7 octaves, but it actually doesn’t. The difference between the note we land on after stacking 12 fifths and the one we land on after 7 octaves is known as ‘Pythagorean comma’ (ratio 531441:524288).
The scientific pitch
Let’s go back to the ‘mathematical reasons’ that Giuseppe Verdi mentioned in his letter for a moment. When I read that line the first time, I suddenly remembered that many years before I had read that for some reason the note C = 256 Hz seems to be considered a ‘scientific tuning’. Normally textbooks on physics, acoustics, sound and music take this frequency as a given, in fact, they do not provide an introductory explanation for this particular choice.
In his article “The Curious Concert Pitch Conflict”, John Stuart Reid reports that the scientific pitch was set to C = 256 Hz in 1713 by French physicist Joseph Sauveur. Sauveur originally proposed this as a standard concert pitch due to the fact that all of its 8 musical octaves would result in whole numbers (32, 64, 128, 256, 512, 1024, 2048, 4096). (1) This was not accepted by the music world but it was instead adopted by the medical community and became known as ‘scientific pitch’.
I return briefly to Pythagorean tuning. The only way I know that relates 432 Hz to Pythagorean tuning is obtaining this note from a cycle of pure fifths starting from C = 256 Hz. Remember that Pythagorean tuning is based on a cycle of perfect fifths and that a perfect musical fifth is defined by the ratio 3/2. Thus: 256 x 3 / 2 = 384 (the note G) 384 x 3 / 2 = 576 (the note D) 576 x 3 / 2 = 864 (the note A one octave higher than A = 432 Hz).
In the Schiller Institute’s book “A manual on the rudiments of tuning and registration” there is a very interesting chapter on the foundations of scientific tuning. The core idea of this publication is that the correct way to approach tuning is to relate it to the physiology of the voice as it has been done throughout history.
Voice registration is the arrangement of the various types of voices according to their range (Soprano, Mezzo-soprano, Tenor, Bass). In this book, it is maintained that the scientific pitch is set in such a way as to allow the trained voices of opera singers to shift registers at very specific frequencies. The exact half of an octave ranging from one C to the next C is F#. When C is tuned at 256 Hz the shift of the soprano voice occurs exactly at F#. According to the authors, this is the reference point of voice registration in the Bel Canto tradition. The classic composers wrote their operas to be performed with this exact registration and in the book, the reader can find an accurate analysis of the lyrics of many operas to support this idea.
A more daring chapter in the same book suggests parallels between voice registration and astronomical ratios in the Solar System: “F# is located as the geometrical mean of C 256 Hz and its octave, C 512 HZ. […] In physical terms, the register shift constitutes a singularity, a non linear phase change comparable to the transformation from ice to water or water to steam. […] Our Solar System also makes a ‘register shift’. It has long been noted that the inner planets (Mercury, Venus, Earth and Mars) all share such common features as relatively small size, solid silico-metallic surface, few moons and no rings. The outer planets (Jupiter, Saturn, Uranus and Neptune) share a second, contrasting set of characteristics: large size, gaseous composition, many moons and rings. The dividing point between these two sharply contrasting ‘registers’ is the asteroid belt, a ring-like system of tens of thousands of fragmentary bodies believed to have arisen from an exploded planet. […] The Solar System register shift falls exactly in the same geometric mean position as the shift of the soprano voice in the proper C 256 Hz tuning.” (2)
The full chapter can be read and downloaded here
In the March-April issue of the magazine “21st Century Science & Technology”, in 1989, an article was introduced with this dramatic statement: “A student of living processes reports on new discoveries in the harmonic “tuning” of the biological domain, with DNA as the tuning fork, precisely 42 octaves above middle C.” (3) The article reports a study in the field of optical biophysics revealing that “living tissues emits and absorbs electromagnetic radiation at a series of specific frequencies or wavelenghts. It turns out that the most important of these frequencies can be arranged in an ordering very similar to the musical scale, but 42 octaves higher. […] the band of absorption of DNA corresponds to wavelenghts between 263 and 269 nanometers (a nanometer is one-billionth of a metre). The centre frequency of this band (corresponding to 265 nm) is 1.1283 x 10 to a power of 15 cycles per second, which is exactly 42 octaves above the frequency 256,54 cycles per second”. (4)
Anthroposophy and Cosmic Tuning
Founded by Rudolf Steiner in the early 20th century, Anthroposophy is a ‘spiritual philosophy’ that promotes the knowledge of the existence of an objective spiritual reality that can be experienced directly through personal inner development. Initially rooted in the Theosophical Society, Steiner’s vision moved away from the Indian-based teaching of the Theosophists to form a more Western-Christian based spiritual science. Rudolf Steiner himself was a very unique character that cannot be easily described in a few words. A philosopher, clairvoyant, esoteric teacher, Steiner was a prolific author on an impressive variety of topics.
There are a few reported instances in which Steiner had given insights that are relevant to the topic of this article. In Maria Renold’s book “Intervals, scales, tones and the concert pitch C=128 Hz” I read that Steiner was once asked which is the correct pitch for our present; his answer was that “C = 128 Hz = Sun” was the correct pitch for modern human minds and spirits. C = 128 Hz is an octave lower than C = 256 Hz. Steiner is also said to have stated that the inner ear of the human being is built on C = 128 Hz. This frequency, according to Steiner, “not only relates to the planet Mars and its metal iron but also to meteoric iron as Sun substance in the cosmos, to Michael [Archangel] as the spirit of the age, to human blood and human freedom”. (5) Now that I have mentioned Maria Renold, a German-American violinist and violist and follower of Steiner’s ideas, it is time to close the circle and connect the two reference frequencies I have been mentioning here: 256 (or its lower octave 128) Hz and 432 Hz. When she first heard of Steiner’s indication of C = 128 Hz, she decided to test it practically. She was also concerned with understanding the problems of tuning and intonation thoroughly. As a classical musician, she was aware that the equally tempered scale is a compromise with significant losses in terms of purity of harmony. She came up with a tuning system that she named the scale of twelve fifths that provided a way of tuning a piano with more acceptable compromises than equal temperament. (6) Using this system it is possible to have both C = 256 Hz and A = 432 Hz in the scale whereas this is not possible with equal temperament.
Maria Renold conducted many experiments, testing the different response of listeners to her tuning system both in 440 Hz standard pitch and 432 Hz. She “found that of 2000 people tested over 20 years, over 90% consistently preferred the lower pitch. The notes were given in different order, on different instruments, with various means to avoid prejudicing the listener. The wide variety of comments all went in the similar direction of calling the higher pitch more “irritating, unpleasant, aggressive, making one stressful and nervous”. The lower one, on the other hand, sounded “right, complete, pleasant, radiant, peaceful, harmonious, heartfelt but leaving one free.” (7)
A special number
It is a matter of fact that the number 432 is a special one. In fact, it can be found encoded in the knowledge of very ancient civilizations. It would be a mistake to believe that in ancient times the choice of numbers would happen randomly. There is evidence that very ancient inhabitants of the Earth possessed often a surprisingly high astronomical knowledge concerning the Earth, the Solar System and even distant stars.
The Hindu cosmology divides the cycles of time into four ‘yuga’ or ‘ages of the world’, The shorter of which (Kali yuga) is 432.000 years. Then we have the Dvāpara yuga of 864.000 years (432.000 x 2); the Tretā yuga of 1.296.000 years (432.000 x 3) and finally the Kṛta yuga of 1.728.000 years (432.000 x 4). The total sum is 4.320.000 years or Mahā yuga. In the Ṛg Veda, one of the sacred books of Hinduism, there are 432.000 syllables. “432.000 was also the number of years in the ancient Babylonian ‘Great year’. For the authors of the Grimnismal, 432.000 was the number of fallen warriors whom the Valkyries carried to Valhalla. For Ptolemy, 432.000 was the least common denominator for his monochord fractions”. (8)
The Borobudur Mahayana Buddhist temple in Indonesia (9th century) has 432 statues of the Buddha on one level and 72 more on an upper level. 432 is a multiple of 72 (6 octaves higher).
The diameter of the Sun is close to 864.000 miles (432.000 x 2); the diameter of the Moon is close to 2.160 miles (432.000 / 200). The Sun and the Moon appear the same size from the Earth, that’s why we can appreciate total solar eclipse. If expressed in metres (or any other measure other than inches, and miles) these numbers would not make much sense. But the inch seems to be a measurement unit that is closely related to astronomic, geophysical and mathematical proportions. Sir Isaac Newton allegedly discovered what is called the Pyramid inch. While he was studying the Great Pyramid of Giza, he realised that the use of this particular unit would turn many of the pyramid’s measurements into whole numbers. If we multiply the height of the Great Pyramid, 481 feet, by 43,200,000, we get 20,779,200,000 feet, very close to the Earth’s polar radius measurement of 20,855,485,564 feet. If we multiply the perimeter of the base of the Great Pyramid, 3,024 feet, by 43,200, we get 130,636,800 feet, very close to the Earth’s equatorial circumference measurement of 131,479,659 feet. Apparently, the English inch was originally the same as the Pyramid inch, but nowadays there is a slight difference, the Pyramid inch being 1,0011 current inches. Probably this happened in recent times with the progressive creation of international standards by the ISO, the same organism that registered the standard concert pitch. The speed of light, if calculated with the slightly longer Pyramid inch is extraordinarily close to the square of 432. 186.291 (official speed of light) x 1,0011 = 186.496 (99,931429 % of 186.624, or 432 squared).
Now back to 432 Hz. When we speak about frequencies we speak about Hertz, which means cycles per seconds. When I first became interested in all of this, a legitimate doubt came into my mind: all these apparently significant frequencies only seem so special because we measure them in seconds, but is a second not an arbitrary unit? If seconds were different from what they are then all the frequency numbers would be different and all this information would have no value. Later on, I found out that a second is defined as 1/86.400 of a solar day. I was pleased to find that the second is after all not such an arbitrary choice, but it has an astronomical basis. A full rotation of the Earth (24 hours) contains 86.400 seconds (43.200 x 2). If we multiply 432 x 60 (the number of second in a minute) we get 25.920, which is the number of years of a complete cycle of the precession of the equinoxes (one complete rotation of the Earth’s axis). If we divide 432 by 60 we get 7,2 (72 / 10). I wonder whether 7,2 could possibly have been the basic frequency of the Schumann resonance of the Earth in ancient times when all these units were created. That would be quite an interesting discovery! It is important to note that all these corresponding numbers are approximate. In articles about 432 Hz, I often find these numbers given as perfect matches. Personally, I do not agree with stating that when something is so close then it is practically the same. However, I do find all this remarkable. The reasons why these numbers don’t match completely could be many. One could be that the ancient peoples, despite their astounding understanding and knowledge, may not have been able to calculate everything exactly. They were obviously trying to point out certain numbers, and they succeeded in that as much as they could. Another reason could be that we are missing something in the way that we interpret their numbers and maybe we are not as accurate as they were. Either way, in my opinion the numbers are close enough for us to understand that there was a specific design to encode information relating to the number 432 as well as other “special” numbers.
Who is this information for?
It is certainly for the musicians who aspire to understand their role and influence in society. It is also for all those who recognise music as an agent of information and transformation.
In olden times, the hermetic motto “as above so below” conveyed the understanding that everything in the universe is interconnected and patterns are repeated endlessly on different scales. By understanding the phenomena we can observe at our level, we can deduce how things work on a higher or lower scale (macrocosm/microcosm).
If we think in terms of resonance, we can picture how the frequencies we emit will resonate with everything they encounter. If the frequencies of the music we create are attuned with their higher and lower octaves in the space around us, then there is a reason to think that we are creating consonant flows of energy.
“The role of the composer is obvious […]: they are the alchemists who help to transmute the earth by making its substance and souls resonate with echoes of heavenly music. […] This is the accomplishment of the Great Work of musical alchemy, which, like alchemy proper, aims towards the redemption of all Nature as well as to the reunion of Man with his Overself.” (9)
As I wrote at the beginning of this article, this is far from being a complete presentation. Each point I have touched on and each source I have quoted would deserve a closer look. I have even left some information out to avoid lengthy digressions.
However, I hope readers have found enough material here to spark their curiosity and maybe the wish to research the topic themselves. The aspiration to create music consciously, if pursued with commitment, can lead to complex inquiries. When I first came to know about other people’s motives for adopting this alternative tuning I enthusiastically joined in. Then, one piece of information after the next, I realised that in order to be truthful and consistent in my Art I needed a deeper understanding of the matter. Now, years afterwards I am still excited to find new pieces of this puzzle and to be able to look at the picture with increasing objectivity.
1 – An octave, in music, is the doubling or halving of a given frequency, so for example 64 Hz is one octave higher than 32 Hz and one octave lower than 128 Hz. The interval of an octave sounds somehow special to the ear. Two notes separated by one octave sound the same and different at the same time. In fact, in music they are given the same name. The octave is a universal phenomenon, found in all tonal systems.
2 – “A manual on the rudiments of tuning and registration” – Schiller institute
3 – “The Musicality of Living Processes” – Warren J. Hamermann
4 – “A manual on the rudiments of tuning and registration” – Schiller institute
5 – “Intervals, scales, tones and the concert pitch C = 128 Hz” – Maria Renold
6 – Equal temperament: the reader will remember the aforementioned Pythagorean comma, that arises when we combine twelve consecutive intervals of a fifth and seven consecutive intervals of an octave (which is what happens on a piano). Equal temperament is one of many solutions that have been found to this problem over centuries and it proved to be a convenient solution to make fixed tuning instruments, like keyboards, easy to build, tune and play. It is the main tonal system in use in the western world for fixed tuning instruments. The loss in this process is the relationships between the notes of the scale (ratios) had to be “tempered” (hence the name “temperament”), that is to say that all the notes had to be adjusted (or altered) in order to fit into a scale made of twelve notes equally distant from each other (hence the name “equal”). The advantage of placing each note at an equal distance form the preceding and following ones is that one can easily transpose music from one key to another or change key within one piece while retaining all the same musical intervals. This means that, in terms of frequency, the distance between a C and C# is the same as the distance between a C# and a D. The distance between D and D# is the same as the distance between D# and E… and so on.
7 – “The spiritual basis of musical harmony” – Graham H. Jackson
8 – “The myth of invariance” – Ernst G. McClain 9 – “Harmonies of Heaven & Earth – Mysticism in music” – Joscelyn Godwin
“A manual on the rudiments of tuning and registration” – Schiller institute
“The myth of invariance” – Ernst G. McClain
“Intervals, scales, tones and the concert pitch C=128 Hz” – Maria Renold
“The Musicality of Living Processes” by Warren J. Hamerman (in 21st century Science & Technology, Vol. 2, No. 2, March-April 1989)
“The Curious Concert Pitch Conflict” – John Stuart Reid “The spiritual basis of musical harmony” – Graham H. Jackson