by John E. Johnson, Jr. Editor-in-Chief
When you attend an orchestra symphonic concert, before the conductor goes onto the stage, the first violinist stands up and plays the note A, above middle C. The rest of the orchestra then tunes their instruments to that note.
I have several recordings of Vivaldi’s The Four Seasons, composed circa 1721. When listening to two different recordings, I noticed that they were played in two different keys. I didn’t understand why this was the case, since the music was composed in a specific key.
Wikipedia says that “Prior to the standardization on 440 Hz [for the note A above middle C], many countries and organizations followed the Austrian government’s 1885 recommendation of 435 Hz, which had also been the French standard since the 1860s. The American music industry reached an informal standard of 440 Hz in 1926, 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. This standard was taken up by the International Organization for Standardization in 1955 (reaffirmed by them in 1975) as ISO 16. Although not universally accepted, since then it has served as the audio frequency reference for the calibration of acoustic equipment and the tuning of pianos, violins, and other musical instruments.
It is designated A4 in scientific pitch notation because it occurs in the octave that starts with the fourth C key on a standard 88-key piano keyboard. On MIDI, it is note 69.
A440 is widely used as concert pitch in the United Kingdom and the United States. In continental Europe, the frequency of A commonly varies between 440 Hz and 444 Hz. In the period instrument movement, a consensus has arisen around a modern baroque pitch of 415 Hz (A♯ = 440 Hz), baroque for some special church music (Chorton pitch) at 466 Hz (A♭ = 440 Hz), and classical pitch at 430 Hz.”
While scanning the October-November issue of Nexus – New Times, a British publication, I noticed an article written by Simone Vitale, a philosophical musician and composer, and the subject matter was about concert pitch. I asked him to write an article for Secrets, about the standardization of the note A above middle C at 432 Hz as the concert pitch for playing and recording musical compositions that we at Secrets, and our readers, listen to on our audio systems at home. I think you will find this article very interesting.
For the sake of interest, click here to download a 10 second wav file for 440 Hz that you can play and then click here to download the wav file for 432 Hz. I recorded them at – 5 dB, which is close to the maximum level, so turn your audio player volume down before downloading them, and then when playing them, turn the volume up so you can hear them at a comfortable level.
Here is an audio spectrum of the two frequencies. The red peak is at 432 Hz, and the yellow peak is at 440 Hz.
There is not a lot of difference, but as Simone Vitale will explain, there is a significant and logical reason for standardizing the concert pitch as 432 Hz.
John E. Johnson, Jr.
432 Hz, An Argument for Standardization of the Concert Pitch for the Note A, above Middle C
Author: Simone Vitale
Frequency. Vibration. Resonance. We all know how these words (as well as a few others) once belonging to the fields of physics and acoustics, are now commonly used outside of their original context. If we enjoy someone’s company, it’s because they have a “good vibe” and we “resonate” with them. If there is a good understanding between two people, it is because they’re on the same “wavelength”.
Possibly, the reason why these words work so well in these examples is because they hint to an underlying order of things that, although not cognitively aware of, we perceive and recognise at some level.
After all, quantum physics, as well as ancient spiritual traditions, teaches us that “everything is vibration” and everything is interconnected.
Another word that has recently overflowed from the pot of its original context is Hertz (abbreviated as “Hz”), named in honour of a 19th century German physicist, Dr. Heinrich Rudolf 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, 200 Hz means 200 times per second, and so on.
In the last couple of decades, an increasing number of people has become familiar with this term. This word has become the symbol of a quest (often a craze) for the “perfect frequency” or a set of God-given “perfect frequencies” that is supposed to have all sorts of esoteric properties.
One such frequency is 432 Hz, about which a lot has been said and written. Over the last twenty-five years, a growing movement has risen to promote 432 Hz as a standard concert pitch as opposed to the current standard of 440 Hz.
Well, it turns out that, if one has the patience to do some proper research on the topic, there seem to be several good points to this proposal.
What is exactly the standard concert pitch?
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 and 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 middle C or do on a piano. It has been decided that this note has to vibrate 440 times per second. All the other notes of the scale will then be tuned accordingly.
Before this standard, the intonation of musical instruments used to vary significantly from country to country and even from region to region. However, some trends would emerge from time to time, like the European “mean pitch” at the time of Mozart, ranging between 421 and 425 Hz. (1)
But how was it possible to measure frequencies so precisely before the advent of electronic instruments?
The turning point in the measurement of frequency can be identified with the invention of the tuning fork in 1711, attributed to John Shore. “Measuring the frequency of a tuning fork was typically achieved by attaching a small brush to one of its prongs. The brush was arranged to lightly touch a revolving cylinder, or other method of mechanically moving a drawing surface, which was coated with candle soot. The vibrant fork would draw a sine curve on the drawing surface and the distance between the peaks of the curves was used to calculate the frequency of the fork’s sound, factoring in the speed of the moving surface, as measured with a watch. The fork could be raised in pitch, if needed, by filing its two prongs a little shorter, then rechecking it on the apparatus.” (2)
Bel Canto and 432 Hz
On 9 April 1988 in Milan, Italy, The Schiller Institute held a conference on the topic 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, Plácido 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 the centuries from the Italian masters, there is a specific shift in the register of the voices of tenors and sopranos.
This naturally occurs on the F-sharp (F#) when instruments are tuned to A = 432 Hz. When instruments are tuned to 440 Hz or higher, the shift occurs around the note F or lower.
The Schiller Institute maintains that the operas of the great composers of the past were composed in a lower pitch. Voice registration is the arrangement of the various types of voices according to their range (e.g., soprano, mezzosoprano, tenor, bass). The changes in voice registers were used to accentuate the meaning of the lyrics and, therefore, these shifts need to occur on the right notes.
Bel canto has evolved, been perfected and passed on for centuries by the Italian masters and is the result of a close observation of the natural voice and its dynamics. Therefore, it is important to adopt the reference pitch that 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.
Giuseppe Verdi’s 432 Hz Pitch
In 1884, in a letter to the Italian government, the great Maestro Giuseppe Verdi expressed his concern about the raising and fluctuations of pitch (which at that time had not yet been standardised). 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.
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 aforementioned letter 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, at a conference held in Vienna and mainly run by the British government, this standard was refused and, as a result, was also abandoned in Italy.
The Scientific Pitch
It is not unusual for textbooks on physics, acoustics, sound and music to mention the frequency of 256 Hz as the “scientific pitch”, without providing an introductory explanation for this particular choice.
In his article “The Curious Concert Pitch Conflict”(3), John Stuart Reid reported that the scientific pitch was set at C = 256 Hz in 1713 by French mathematician and physicist Joseph Sauveur. Sauveur originally proposed this as a standard concert pitch due to the fact that all of its eight musical octaves result in whole numbers: 32, 64, 128, 256, 512, 1024, 2048, and 4096. (3)
This was not accepted by the music world but instead was adopted by the medical community and became known as scientific pitch.
432 Hz tuning is often referred to as “Pythagoran tuning”, and I have found that often this happens not without a certain amount of confusion.
Pythagoran tuning is not the one commonly in use today, and one of the reasons why is because a full cycle of 12 fifths should coincide with seven octaves, but it actually does not. The difference between the note we land on after stacking 12 fifths, and the one we land on after seven octaves, is known as the Pythagorean comma (the ratio of 531441:524288).
The Pythagorean tuning system is based on a cycle of pure fifths (the 3:2 ratio found in the harmonic series).
If we apply Pythagorean tuning to C = 256 Hz we will end up with A = 432 Hz:
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 this case, it is possible to relate Pythagoras to 432 Hz, but it’s important to notice that Pythagorean tuning can be applied to any given starting frequency, so it can also be completely unrelated to 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’s been done throughout history.
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 to 256 Hz, the shift of the soprano voice occurs at exactly F#. According to the authors, this is the reference point of voice registration in the bel canto tradition. The classical 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 registers 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 nonlinear 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.” (4)
An article in the March – April 1989 issue of 21st Century Science & Technology 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.” (5)
According to The Schiller Institute’s book, this article reported a study in the field of optical biophysics, revealing the following:
“Living tissue emits and absorbs electromagnetic radiation at a series of specific frequencies or wavelengths. 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 . . . This [DNA absorption] band corresponds to wavelengths between 263 and 269 nanometers (a nanometer is one billionth of a meter). The center frequency of this band (corresponding to 265 nm) is 1.1283 x 1015 cycles per second, which is exactly 42 octaves above the frequency 256.54 cycles per second.” (6)
The Anthroposophic Standpoint
Founded by Rudolf Steiner in the early 20th century, Anthroposophy is a spiritual philosophy that promotes 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 teachings of the Theosophists to form a more Western, Christianity-based, spiritual science. There are a few reported instances in which Steiner gave insights that are relevant for 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 about what is the correct pitch for our present time; he answered that “C = 128 Hz = Sun” is 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 [Archangel] Michael as the spirit of the age, to human blood and human freedom.” (7)
Maria Renold, a German–American violinist and violist who followed Steiner’s ideas, was concerned with understanding thoroughly the problems of tuning and intonation. As a classical musician, she was aware that the equally tempered scale is a compromise with significant losses in terms of purity of harmony. Renold came up with a tuning system that she named the scale of twelve fifths, which provides a way of tuning a piano with more acceptable compromises than those of equal temperament. (8)
Using this system, it is possible to have C = 256 Hz and A = 432 Hz in the scale, whereas this is not possible with equal temperament.
Renold conducted many experiments, testing the different responses of listeners to her tuning system both in 440 Hz standard pitch and 432 Hz pitch.
“Maria Renold found that of 2,000 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’.” (9)
A Special Number
It is a matter of fact that the number 432 is a special one, and it can be found encoded in the knowledge of very ancient civilisations.
For example, Hindu cosmology divides the cycles of time into four Yugas or “world ages”, the shortest of which, the current Kali Yuga, is 432,000 years. Then we have the Dvapara Yuga of 864,000 (432,000 x 2) years; the Treta Yuga of 1,296,000 (432,000 x 3) years; and, finally, the Krita Yuga of 1,728,000 (432,000 x 4) years. The total sum is 4,320,000 years, comprising the Maha Yuga. In the Rig Veda, one of the sacred books of Hinduism, there are 432,000 syllables.
“[The number] 432,000 was also the number of years in the ancient Babylonian ‘Great Year’. For the authors of the Grímnismál, 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.” (10)
The ninth-century Borobudur Mahayana Buddhist temple in Indonesia has 432 statues of the Buddha on one level and 72 more on a upper level; 432 is a multiple of 72 (six octaves higher).
The diameter of the Sun is close to 864,000 (432,000 x 2) miles; the diameter of the Moon is close to 2,160 (432,000 / 200) miles.
If expressed in meters, or any measure other than inches and miles, these numbers would not make much sense, but the inch seems to be a unit of measure that is closely related to astronomical, geophysical and mathematical proportions.
Sir Isaac Newton allegedly discovered what is called the pyramid inch. (11)
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 measuring approximately 1.0011 current inches. This has probably happened in recent times with the progressive creation of standards by the International Organization for Standardization (ISO), the same organisation that registered the standard concert pitch.
The speed of light, if calculated with the slightly longer pyramid inch, is extraordinarily close to 432 squared. The official speed of light, 186,291 miles per second, multiplied by 1.0011 equals 186,496 (99.931429 per cent of 186,624, or 432 squared).
Now, back to 432 Hz. When we speak about frequencies we speak about hertz, cycles per second. When I first became interested in this subject, 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 1/86,400th of a solar day. I was pleased to find that the second is not such an arbitrary choice after all, but has an astronomical basis. A full rotation of the Earth (24 hours) contains 86,400 (43,200 x 2) seconds.
If we multiply 432 by 60 (the number of seconds 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. I wonder whether 7.2 could possibly have been the basic frequency of the Schumann resonance of the Earth in ancient times when these units were created. That would be quite an interesting discovery!
It is important to note that all these corresponding numbers, although remarkable, are approximate and as such they should not be taken as perfect matches. However, in my opinion they 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.
In olden times, the hermetic motto “As above, so below” conveyed the understanding that everything in the universe is interconnected and that patterns are repeated endlessly on different scales. By understanding the phenomena that we can observe at our level, we can deduce how things work on a higher to a lower scale, from macrocosm to 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 to their higher and lower octaves in the space around us, then there is reason to think that we are creating consonant flows of energy.
Digital Pitch Conversion
Because of all the reasons above or others not mentioned in this article, there is a wide-spread trend on the internet that encourages people to convert their music the “healing” tuning of 432 Hz. The software Audacity, being free, is generally recommended to accomplish this task. Someone recently mentioned an iPhone app to me which converts any musical file directly while listening, simply by slowing it down enough to change the pitch from 440 to 432 Hz.
The first method is a very complex one. Modern software can work quite well on a monophonic input signal. Let’s say a song needs to be transposed in another key and the voice has already been recorded and cannot be re-made. In this case, pitch shifting the voice track alone can work quite well if one is happy with some very minute artifacts as a result. The same goes for any monophonic input such as a guitar solo, a violin or a bass, as long as the interval of the pitch shift is not too large.
But changing the pitch of a whole stereo mix (e.g., a song) is another story. The resulting file will be full of artifacts like a sort of tremolo and something that sounds like phase shifting. If one is used to only listening to lowest quality mp3 files, they may not notice the difference because the original file is already intensely compromised. But if one aspires to a better listening experience, then the effect of the pitch shift is not tolerable (I am assuming a basic understanding that anything below uncompressed audio files is really not advisable, or, if compression is necessary, at the VERY least 320 kbps mp3 files).
The slowing down option usually works a little better in terms of the quality of the sound, but it slows down the song! Yes, it’s true, it does so by a very small measure. Still, I personally don’t find this a viable option.
As we have seen, there may be good reasons to prefer music that is tuned at 432 Hz and it is not outrageous to think that to a certain extent it may be beneficial. My advice, if you believe so, is to keep enjoying your classics as they are and to find new music that has been originally recorded at 432 Hz. The specific frequency of tuning is only one of the factors that contribute to the magic of music and even to its healing qualities.
This article is not meant to be a complete presentation of this complex topic. Each point I’ve touched on and each source I’ve quoted would deserve a closer look. However, I hope readers have found enough material here to spark their curiosity and maybe the wish to research the topic themselves.
About the Author:
Simone Vitale is a visionary musician, composer, and sound healer. His work is dedicated to promoting an ecology of sound and music where kindness and mindfulness are the keys to a deeper connection with ourselves and each other.
In his project The Sound of Golden Light, Simone is following the call for a more ethical approach to Art. His deep understanding of the effects of sound and music on the human body, mind and soul is offered for the higher purpose of contributing to a reconnection with Nature in a time when this is urgently needed. Bridging the worlds of Art and Medicine, The Sound of Golden Light presents a transformational, uplifting and heart-opening musical experience grounded in a well-researched and competent use of frequencies and harmony.
Simone’s musical creation is multifaceted and includes: healing music, music for pregnancy and birth, music of the plants, live music for yoga and movement, inspirational songs and more. Simone is also a certified vocal yoga teacher and tuning fork therapy practitioner.
Originally from Rome, Italy, Vitale is currently based in Auckland, New Zealand, after spending four years in Berlin, Germany. He has been sharing his work since 2012 in India (Kerala, Tamil Nadu), Germany, Estonia, Finland and New Zealand.
Simone Vitale can be contacted by email. For more information, visit his website http://www.soundofgoldenlight.com.
- Reid, John Stuart, “The Curious Concert Pitch Conflict”, CymaScope.com, 2014, http://tinyurl.com/hqnkz83
- An octave, in music, is the doubling or halving of a given frequency. 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 Schiller Institute, A Manual on the Rudiments of Tuning and Registration, Washington, DC, 1992, pp. 9-10
- Hamerman, Warren J., “The Musicality of Living Processes”, 21st Century Science & Technology, vol. 2, no. 2, March–April 1989
- The Schiller Institute, op. Cit., p. 15
- Renold, Maria, Intervals, Scales, Tones and the Concert Pitch C = 128 Hz, Temple Lodge Publishing, UK, 2004, p. 82
- The reader will remember the aforementioned Pythagorean comma that arises when we combine 12 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 the 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 that the relationships between the notes of the scale (ratios) had to be “tempered” (hence the name “temperament”); that is to say, all the notes had to be adjusted (or altered) in order to fit into a scale made of 12 notes equally distant from each other (hence the name “equal”).
The advantage of this system 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 the interval (or distance) between a C and a C# is the same as the interval between a C# and a D; the interval between a D and a D# is the same as the interval between a D# and an E; and so on.
- Jackson, Graham H. Spiritual Basis of Musical Harmony, Battered Silicon Dispatch Box Press, Shelburne, Ontario, Canada, 2006, p. 177
- McClain, Ernest G., The Myth of Invariance: The Origin of the Gods, Mathematics and Music from the Rig Veda to Plato, Nicolas-Hays, Inc., USA, 1976, pp. 73-75
- Retune the Planet, “Egyptian Pyramid Inch”, http://tinyurl.com/zww492z