It would take too long to describe in detail the origin of the note 'A' (notified La in french); a convention in our francophone culture which corresponds to the Anglo-Saxon 'A'. I develop on this topic in my book "Le Son de Vibrations" (The Sound of Vibrations), to be published by Quebecor in 2014.
I explain in detail where this 'A' comes from, the names of the notes currently used in francophone culture and why. The standardization of the current 'A', 60 years ago, was imposed as the unique 'A', referenced to 440 Hz, as we know it today. Although this 440 Hz frequency was in effect for tuning instruments long before the 20th Century, its standardization is a clearly a recent invention.
In 1859, the French musicologist Adrien de la Fage published a book entitled "De l'unité tonique et de la fixation d'un diapason universel" (About the tonic unity and setting a universal musical tuning). At that time, a 'A' of reference became necessary to facilitate the trade of musical instruments and the musical practice of orchestral musicians who traveled from one country to another.
Franz Liszt and Richard Wagner has been used some instruments tuned in 440 Hz. This pitch was often used in Austria durig 19th Century.
If the French Baroque tuning varied around 392-415 Hz, the English Baroque tuning of the second half of the 17th Century was near. By cons, in Italy, if the pitch is low in the South, it rises depending on the latitude. We find it at 393 Hz in Rome while it is around 460 Hz in Venice. From 1511 to 1953, the pitch of the 'A' rose from 377 Hz (in 1511) to 440 Hz (in 1955). The work of Bruce Haynes deserve to be mentioned. He studied the tone of approximately 1'200 instruments from the Baroque period. He added more than 300, overlapping the Renaissance period until the Romantic era.
Therefore, the 'A' has largely fluctuated and musicological research shows that the increase is not constant. In fact there was none. It was proven that the 440 existed during the Baroque period and the La was even played on higher frequency. The pitch could vary in the same city and inside the same temple. The 'A' pitched at 440 Hz was first adopted in Germany in 1834.
The renowned musicologist Bruces Haynes has proved that the A 440 Hz pitch was already used during baroque area (18th european Century).
Between the years 1830 and 1840, Franz Liszt and Richard Wagner have favored the 'A' on a higher pitch than the usual one, 440 Hz and above. Even then, the pitch was very variable and some very different 'A' were found in various European theaters. Otherwise, the Nazis advocated the adoption of the 440 Hz reference frequency; but to say that the 440 Hz is a Nazi frequency is misleading. This frequency existed long before this regime adopted it and wanted to make it an absolute reference. This frequency may have been used by the Nazis but nothing more.
The same remark can be made about the swastika, which is not originally a Nazi symbol, it was only used by the Nazis. It is now recognized that the swastika, regardless of its direction of rotation, belongs to the Vedic tradition and is found throughout the East on temples and statues representing Buddha.
After this too long but necessary introduction, there is another additional aspect I wish to clarify: the 432 Hz tuning that has become some kind of myth. This tuning is called the Verdi pitch.
Handel had his: 423 Hz and also Mozart: 422 Hz.
At a time when the turning fork was vibrating to the 435 Hz frequency in Paris by ministerial decision; and to 439 Hz in London by royal decree, the renowned Italian composer Giuseppe Verdi adopted himself the 432 Hz frequency.
From this point, some authors have written about the 'A' at 432 Hz, challenging the current La with this different frequency. Using reasoning, they try to make the public believe that one is better than the other, based on fragile demonstrations.
As I briefly summarized the 'A' tuning fork is a recent invention and its standardization was made half a century ago. It should be noted that the 'A' tuned to 430 Hz at a temperature of 15°C may go up or down between 427 and 434 Hz, depending on the temperature change; as the temperature and humidity affect the height of sounds.
Some historical instruments have kept their own pitch. On a horn, a clarinet or a trumpet, the C may vibrate to 392 Hz (Bb), 370 Hz (A) or 294 Hz (F).
These are remnants of a time when the pitch was not fixed and where a C could sound like a La, an F or Bb.
Félix Savart, mentioned earlier in relation to its cymatic experiments on violins - see the book Le Son de Vie (The Sound of Life) - has paid close attention the violins manufactured by the renowned Italian maker Antonio Stradivari. His research undertaken with the famous stringed-instrument maker Jean-Baptiste Vuillaume allowed him to find a resonance frequency of the sounding of Stradivarius violins, measured at 512 Hz.
What remains unknown is whether Antonio Stradivari used the Pythagorean ratios to define the other notes range, which seems likely. In such case, the 'A' tuning to 432 Hz on Stradivari’s violins is plausible.
However, one question comes to mind: Did Savart experiences have been redone using modern scientific tools? We wonder, knowing that the standard tuning fork of Paris, set to 435 Hz, designed and manufactured by Lissajous Secretan in 1858, actually vibrates to 435.4 Hz. Therefore, was the measured resonance done by Savart really 512 Hz? No temperature is specified, so we place a caveat on this assertion, at least until other scientific measurements are completed.
Stradivarius violins, from the name of their creator, are the object of an unreasonable speculation, while blind tests have shown that modern instruments sounded better. This does not diminish the high quality of the violins made by Stradaviri which can be explained by the use of a secret geometry, based on the Golden Ratio, applied to acoustics. Stradivari was reportedly initiated by Alessandro Capra, architect and mathematician from Cremona, stepfather of his first wife Francesca Ferraboschi.
If the tuning frequency of Stradivari violins correspond to the note C at 512 Hz, the La pitch would be 432 Hz in the Pythagoras scale. 512 Hz would correspond to a 'A' at 430.55 Hz in Verdi’s time conventional scale and to 430.33 Hz in other systems. Giuseppe Verdi was interested in Félix Savart experiences and decided to adopt the 432 Hz frequency to tune his 'A'. But all this remains very unclear.
For us it is just a curiosity. There is nevertheless a militant movement that seeks to awkwardly demonstrate that the 432 would be better than the 440.
I also witnessed a scene, by way of archive, where a performer sings the same opera aria, accompanied by two pianos tuned successively with an 8 Hz difference, one at 432 and the second at 440.
The signer begins with the 440, sings his aria, then moves, followed by his accompanist, and signs the same aria tuned on the second piano, 8 Hz lower. After the performance, the public is in turmoil and many use this excerpt to prove that one reference frequency is better than another.
But please make no mistake. All this is very subjective.
This is a subterfuge, able to fool many people, somehow an illusion, a magic trick. The famous baritone Piero Cappuccilli did this demonstration. He was already convinced and had an obvious preference: the 432 Hz frequency. He wanted to demonstrate that one frequency is better than another. His emotion, his facial expressions and unconscious behaviors had the ability to influence the tone of his voice and give a better interpretation of one tone rather than the other. So we are not talking here about a scientific experiment but about an emotional demonstration.
The argument that the pianos do not support the high tension of the 440 Hz tuning is also refutable. Conductor Herbert von Karajan tuned his pianos to 445 Hz, for example. The manufacturers design their instruments capable of supporting various tensions due to humidity or orchestral changes.
Far from leaving it at that, some authors develop questionable theories about this tuning. From various argumentation, they come to the dubious conclusion that 432 Hz resonates with the universe, the Precession of the equinoxes, the Pyramid of Khufu, the Maya temples, the frequency of the human heart and that of water, without any solid scientific evidence.
This seems purely fanciful and inappropriate. A musical frequency as that of the universe cannot be fixed and varies constantly. The sounds change of height depending on the temperature and the quality of the humidity of the air found on the Earth, its main distribution medium.
In our method "Toucher par les Sons®" (Touch by Sounds), we use two different 'A' from our scale of therapeutic tuning forks: the 'A' at 432 Hz, corresponding to the ratio 27/16 in the Pythagorean scale, from a C at 256 Hz; and the 'A' at 426.6 Hz in the scale of Zarlino which is more accurate than the previous one. It corresponds to the ratio 5/3 and is part of the scale called "just intonation". We simply say that the C at 256 Hz - from which many different 'A' origin, according to the scale and the selected interval system - is an octave of the 8 Hz, known to be in agreement with the Schumann Resonance frequency discovered by Nikola Tesla and the interface between the alpha and theta brain waves.
I also use different flutes during my concerts. Some are tuned at 440, others at 415. Electronic flutes can be tuned on request and are easily giving the desired frequency, adjusted thanks to a small potentiometer. When the author himself plays the shakuhachi, tuned to 440 Hz, it is easy for him to vary the pitch by the position of the lips and breath pressure.
Incidentally, the difference of 8 Hz between the two frequencies 440 and 432 Hz is very small, almost one-sixth of a tone and it would be misleading to say that one is right and not the other, because the difference is barely audible. In addition, 440 Hz is the higher octave from 220 Hz, which is itself a healing frequency, according to the research done by Dr. Royal Rife.
Asserting that singers irritate their voice when they sign at 440 Hz versus 432 is eccentric, considering the difference of one-sixth of a tone between the two tunings. The signers saying this cannot be taken seriously. A sixth of a tone is smaller than a quarter tone. It's exaggerated, to say the less!
Asserting that no ethnic or ancient music was tuned at 440 is incorrect: for ancient ethnic music, we do not know. For older music, the tuning was set at 440 in Europe until 1670 on cones and other wind instruments.
As a reminder, the tuning at 440 Hz was found in Italy between 1730 and 1800 or on organs in Holland, Italy, France and England, in the period from 1770 to 1800, in 1834 in Stuttgart; and the tuning at 442 Hz was found in Paris earlier. Instruments were tuned differently depending on whether they were played in temples or in the royal courts.
For older music, we do not know. In 1543, the La was tuned to 481 Hz in Hamburg; and in 1640, to 458 Hz in Vienna. Before that, during the Middle Ages, there was no specific reference in use in any monastic order. There were only tones based on human voice (bass, middle and low) and all this varied constantly according to the seasons and monasteries.
432 Hz and the heart rate
The 432 Hz frequency is said to be the 360th harmonic of a heartbeat at 72 beats per minute; i.e. 1.2 Hz and not 72 Hz as it could be said by mistake.
The calculation no longer applies if the heart beats at 71 beats per minute (or 1.18 Hz) which would give 424.8 Hz in the same dynamic. The 432 Hz frequency would then be the 360th harmonic of a heartbeat at 72.20 beats per minute.
These considerations are fantasy because the heartbeat is constantly changing depending on the type of activity. Moreover the heart rate also varies with age:
¤ New born: 140 +/- 50
¤ 1–2 years old: 110 +/- 40
¤ 3–5 years old: 105 +/- 35
¤ 6–12 years old: 95 +/- 30
¤ Teenage or adult: 70 +/- 10
¤ Old age: 65 +/- 5
Consequently the 432 Hz pitch of 'A' has no direct link with the heartbeat.r.
432 Hz, the frequency of water?
Stating that 432 Hz is the frequency of the water seems wacky. What is the frequency of the water? It is often said that microwave ovens operate on the water molecule. So the frequency of the water should be close to 2'450 MHz, the magnetron frequency.
This vibration corresponds to the note D in the current system. The microwave oven used in kitchens consist of a wave generator called a magnetron and an antenna housed in the upper part of the appliance. The frequency used does not correspond exactly to the resonance of the H2O water molecule. It is a compromise that allows efficient agitation of water molecules under the action of the frequency.
What is the vibrational frequency of the water?
Water, despite its apparent simplicity is still a mystery to science. Water is liquid because the molecular bond between two molecules (called bridge or hydrogen bond) breaks every billionths of a thousandth of a second. At this level, it is called Terahertz vibration, a frequency close to that of the infrared. Water is like a liquid crystal in continuous vibration and when the temperature drops, it freezes. This undulation ceases and water crystallizes to form ice. One thousand billion Hertz: 1 THz. This frequency, transcoded to the 31st lower octave, gives a D3 sharp to 310.44 Hz. This is far from 432.
The ratio of Kheops Great Pyramid have nothing to see with A 432 Hz.
432 and the Great Pyramid
Additional mistaken conceptions are disclosed about 432 Hz, illustrating the confusion often made between frequency, measured in Hertz, and a wavelength, measured in meters. The 432 Hz frequency at 20°C corresponds to a wavelength of 79.63 cm. Even if a building having a square-based, as this is the case with the Egyptian or Mayan pyramids, containing a measure of 432 STU (Standard Teotihuacan Unit), this absolutely cannot related to the 432 Hz frequency; because in the first case we have a measure of length (wavelength) and in the second, a frequency measurement. And as everyone knows, they are reverse to each other, which is to say that the measuring of a frequency is inversely proportional to its wavelength. For example, if a temple or monument has a major structure measuring 432 m, the corresponding frequency is: 0.7962962 Hz, rounded to 0.8 Hz. It is difficult to give a tuning a precision greater than one tenth of Hz.
We can fix history at will and pick measures by matching theories. We know that the Egyptians used as a basis for measuring the "Small Cubit", equal to about 45 cm (24 fingers); inherited from the "Nippur Cubit", which found use in Sumer about 6,000 years ago. The conventional value of this 24 fingers cubit is approximately 45 centimeters. The Egyptians of the Old Kingdom used the 28 fingers from the Sumerian division to determine their Royal Master Cubit (or Sacred Cubit) of 52.5 cm. Later, during the 26th dynasty, it was extended to 52.9 cm. The base of the pyramid is 440 Royal Master Cubits, approximately 230.5 meters. There is no 432 anymore, but 440 Cubits! But 440 or 432 should be no concern because Cubits are not Hertz, as discussed in the previous paragraph.
Other errors, inaccuracies or subjective views
Is there any link between the 432 Hz frequency and the Precession of the equinoxes? Some authors made calculations by stating that the Precession of the equinoxes is 25'920 years old. In fact I think they propose this figure to make it once again match a numerical relation according to their theories. In regards of the exact duration of the Platonic Year (this is the name also given to the Precession of the equinoxes) the figures vary: 25'770, 25'290, 26'000, 25'800, 25'812 years. Which is correct? We do not know and doubt on anyone who pretend to know beyond any doubt. Here is what a quick astronomical Google search reveals. These figures are approximate and as the universe, they also vary. So we believe it is misleading to claim that 432 Hz is in exclusive relationship with the Precession of the equinoxes because 440 or 426 would do the same.
“When we divide 25,920 by 360, we get the number 72. The equinoxes move from 1 degree every 72 years, which corresponds to a harmonic of the note D to 288 Hz/4 = 72 Hz when the 'A' or A is tuned to 432 Hz.”
For us this statement found on the Internet is not quite right, because everything depends on the type of scale that is used. In just intonation, the La based on a scale with a C to 256 Hz, is at 426.6 Hz and also gives a D at 288 Hz; moreover since measurements are approximate. The displacement is about 1° every 72 years. The tuning fork is not stable, for example it varies according to temperature. Everything moves in the Universe. It would be fanciful to suggest otherwise. Only one thing is permanent: the impermanence.
Through convoluted calculations in so-called quantum physics (that is fashionable and they do not specify exactly which), other researchers linked 432 Hz to chlorophyll, the speed of light (which is not constant, according to the latest advanced studies published in physics) or the vibration of oxygen.
According to us, these are once again fantasies that are not based on any study or serious scientific publication and they are all very subjective.
Numerology proves nothing either, it is anecdotal. 430, 432, 435, 439 or 440 correspond to vibrations per second and an arbitrary repository encoding (a measure in Hz) and no scientific study worthy of the name proves beyond any doubt that the 432 Hz frequency would be better than 440. For example, many parameters interfere with the use of frequencies and music to improve the seed germination or plant growth.
Photo of 432 Hz vs. 440 Hz frequency. Wich picture is the more beautifull? Tha is very subjective.That picture is in any case scientific proof of superiority of one.
Since 2007, a Dutch author, Robert Boerman, publishes beautiful pictures of vibrant water.
In 2010, he published two photos of the 440 and 432 Hz frequency. This publication raised passions and several persons see this as a scientific demonstration of the energy difference between these two frequencies. I personally find the two images beautiful and that none is superior to the other. Seeing one more beautiful than the other would demonstrate a subjective interpretation and my close interest is in the scientific approach that has helped produce such images. Outside a strict protocol and parameters control, these experiences are anecdotal and have no value other than artistic.
I developed on the subject of cymatics in Le Son de Vie (The Sound of Life) and explained how some plates filled with all kinds of powders or liquids on their surface could highlight their resonant structures: the images produced are always related to the dimensions and the resonant frequency of the support. Therefore if the plate is tuned with a 432 Hz proportional frequency, it will vibrate differently when a 8 Hz sharper frequency will be applied; in this case, 440 Hz. The slight variation in tuning shows less clear forms than with the frequency tuned to 432 Hz.
The intention carried by a music is more influential than the pitch to which it is tuned. The choice of scales - and therefore the resulting intervals - are also fundamental in my understanding. There are several. There are 15,000 scales in Indian music. We use different available La, depending on the case, with selected instruments or therapeutic tools. I lead students to sing their own heart and let it be. So I have some La tuned to 440 Hz, to 415 Hz (baroque flute), or else. It is also easy to vary the frequency with an electronic instrument, such as the Ewi flute I play for more than 20 years, as well as a lyre or zither. Our scales of tuning forks use different La: 426.6 Hz with the Zarlinian scale and 432 Hz with the Pythagorean scale (with a C to 256 Hz). In this case, the La to 432 Hz is obtained on the 27th harmonic of the harmonic scale having for fundamental the 16 Hz frequency. The Pythagorean ratio of 27/16 applied to a scale having a C to 256 Hz, is 432 Hz. Meanwhile the Zarlinian ratio of 5/3, used to just intonation, always from the C to 256 Hz, gives a 426.6 Hz frequency. When two identical lyres are tuned using on one the Pythagorean scale and on the other the Zarlinian scale, the difference is minuscule. Both scales have their own color and one is not superior to the other; even if the Zarlinian scale is more accurate as the Pythagorean third harmonic are false. We use one or the other, or both, depending on the inspiration of the moment.
If you decide that a music tuned to a specific frequency sounds better than another, it will do. The important thing is the intention for which the frequency will be the medium.
Stating that 432 Hz corresponds to the proportions of the Cheops pyramid, Maya temples, the speed of light, the frequency of the water, the frequency of the human heart or the Precession of the equinoxes is therefore pure fantasy and I classify these statements as fragile and partisan.
A scale with a 'A' tuned to 432 Hz is beautiful. At 440, it is also beautiful. The most significant for us is the proper architecture of the scale whether the just intonation, the Pythagorean scale or the equal temperament.
I have sought to write this study in a scientific manner. Some aspects certainly remains to be clarified. My conclusion is that 432 Hz is a frequency as another, which does not necessarily have the miraculous properties attributed to it. Its use in the history of music is very minor and its alleged generalization is not, to date, musically or historically demonstrated. Finally I see no striking superiority over the use of the reference to 440 Hz established at 1/6th of tone higher. Replacing it by the 432 Hz would simply be an attempt to replace a convention by another. To each one his pitch. Vary your songs, vary your colors!
Please be careful about reductionist attempts imposing a single system of thought, including the normalization of whatever tuning as an example. Like I often say during my classes or lectures, the important aspect is not the reference pitch of the note you sing but the pitch of your heart and the frequency of love it reveals, whichever note carrying it.
The precession of the equinoxe. Any astronomer would be able to quantify exact time of the cosmic year. Any scientist are able to give the exact duration of the great cosmic cycle of the Earth that takes about 25 000 years.
Additional notes
The ratios of the Pythagorean scale are:
1 - 9/8 - 81/64 - 4/3 - 3/2 - 27/16 - 243/128 - 2
Therefore the ratio for the note La is 27/16. The Zarlino scale - more accurate than the Pythagorean - would give a 'A' at 426.6 Hz with the same starting note.
Gioseffo Zarlino (1517-1590) was an Italian composer who sought to improve the Pythagorean scale in which the third harmonic are false. His scale named "just intonation", meets the following ratios:
1 - 9/8 - 5/4 - 4/3 - 3/2 - 5/3 - 15/8 - 2.
The 2,450 MHz frequency gives a D, 23 octave lower: 292.06 Hz. The D4 in a temperate scale with tuned on 'A' at 440, has a 293.66 Hz frequency.
Resonance phenomena also occur on nearby frequencies.
In the current temperate scale the D2 sharp tuned on 'A'4 at 440, has a 311.13 Hz frequency.
0.8 Hz corresponds to a wavelength of 430 m and therefore 0.79 Hz is 435 m in length; for a sound velocity of 344 m/s, measured at sea level at a temperature of 20°C.
The Precession of the equinoxes is the time on the great cosmic cycle of the Earth where the sun rises in the same zodiac sign, the day of the vernal equinox. It was highlighted by Hipparchus of Nicaea, Greek astronomer, 190-120 before the Common Era.
He did the synthesis of earlier measures (Sumer and Egypt) known in his time and established that the precession was worth at least 1° per century. Today, we know it is about 1° every 72 years. Hipparchus "From changing solstice and spring equinoxes", a book from which several extracts were transmitted by Ptolemy.
This change of direction is caused by the torque exerted by the tidal forces of the Moon and Sun on the equatorial bulge of the Earth. These forces tend to cause the actual excess mass at the equator to the ecliptic plane. Earth is rotating, therefore these forces cannot change the angle between the equator and the ecliptic but they cause a shift in the axis of rotation of the Earth in a direction perpendicular to this axis and torque.
Apart from the small disturbances acting on this displacement (e.g. nutation), the axis of the Earth describes the surface of a cone or "funnel" in the manner of a spinning-top. This movement leads to move the direction of the North Pole from the stars, so that over the centuries we need to change our polar star. This movement of the Earth's polar axis carries with it the plane of the equator.
Therefore, the vernal equinox, or the equinoctial point, precedes each year its previous position on the ecliptic relative to the direction of the Earth orbit around the sun. Hence the term of Precession of the equinoxes given to this movement. The equinoctial point also completes one complete revolution of the ecliptic backwards, in roughly 25,800 years. The Earth's axis describes a complete cone during the same period. As the orbit of the Moon is inclined relative to the ecliptic plane, the action of the moon is slightly disturbing the precession by adding small oscillations in a period of 18.6 years.
This effect is called nutation. Because of the Precession of the equinoxes, the cycle of seasons (tropical year) is about 20 minutes shorter than the time the Earth takes to be at the same position with the stars (sidereal year). This difference is important for calendars and their rules about leap years. The current value of displacement is 50.290966" per year, or about 1° every 72 years (Source Wikipedia).
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