LATERAL's "La": between music, mind, science and humanity
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LATERAL's "La": between music, mind, science and humanity

By Fernando De Lucchi, Researcher, educator and musician LATERAL
March 2023

This article is dedicated to the importance of "La" as a phenomenon that demonstrates the capacity of the human being to imagine and relate the world of the visible and measurable with the world of the invisible and ungraspable. ("La" is the way to call the musical note "A" in Latin languages)

Before we begin, let's awaken your curiosity a little: Do you have "absolute hearing" and don't know it? There are thousands of people who have it and don't know it. Find out what is your case while you follow the thread of "La" in this article.

The LATERAL icon

I am very excited that Lateral has adopted as an icon something that has accompanied me all my life and that, besides being like a compass for thousands of professional musicians around the world, is also very important for non-musicians: the note "A" in Latin languages.

Perhaps many of us know that "A" is the sixth note of the diatonic musical scale of "C" "Major" (C, D, E, F, G, A, B), but perhaps fewer of us know that musical "A" is connected to disciplines as diverse as physics, medicine, neurosciences, telephony, sound engineering, industry, lutherie, chemistry and even numerology along with other branches of religions and mysticism. This transversality has managed to disturb minds as brilliant as those of Confucius, Pythagoras, Plato, Galileo, Newton, Tesla or Einstein.

Why is the note "A" so important for musicians?

The note "LA" of 440 Hz is something like the "kilo", "liter" or "meter" in the world of weights and measures. An international standard perfectly measurable and reproducible even visually anywhere in the world.

In the world of Latin music theory and notation, "La" is the name of the "pitch" that is used as a reference for tuning most musical instruments around the world. We call "pitch" the auditory sensation or perception that we commonly think of as the "height of sound" (e.g. "high" versus "low" or "treble" versus "bass").

There are ancient books on acoustics that relate that the great Galileo Galilei experimented with tone generation through such ingenious devices as rubbing the blade of a knife on the grooved edge of a coin at different speeds to demonstrate the relationship between frequency and the perceived "pitch" of tones. This is something you can also experiment with by scratching a coin with your fingernail....

Galileo explained in his book Dialogues on Two New Sciences published in 1636, how the vibratory frequency of a string is related to its "pitch", and in the same year, the French philosopher, mathematician and religious Marin Mersenne published his Harmonie Universelle, an 800-page book on music theory in which he relates the number of vibrations per second to the "pitch", presents the illustration of a monochord in which the number of vibrations per second of the note "A" and all the other notes of the diatonic scale are observed.

If you have ever attended a symphony concert, you will have noticed that before it begins, all the instruments are tuned to the same "pitch". That "pitch" is what we musicians call nothing less than "A". When all the instruments in an orchestra are perfectly in tune, the music sounds beautiful. If they are not perfectly in tune, even if the musicians play each instrument very well, the music will sound discordant.

Establishing the vibratory frequency of "A" at 440 Hz has been a great contribution of the West which, together with the division of the octave into 12 logarithmically equal parts, has allowed standardizing the manufacture of millions of musical instruments, not only symphonic, but also of other types, such as guitars, accordions, keyboards of different types, synthesizers, etc.

Before the 440 Hz "A" was established, many other frequencies were used, being the 432 one that many long for or claim due to its numerological value and the supposed coincidences with other types of frequencies present in nature. The monochord presented by Mersenne in his famous book considers the "A" of 432.

<p>The tuning fork on the left side predates the 1939 conference and the one on the right is a 440 Hz tuning fork. In the center is a violin tuner which, when blown through the tube with the letter "A" on it, produces the 440 Hz "A".</p>

The tuning fork on the left side predates the 1939 conference and the one on the right is a 440 Hz tuning fork. In the center is a violin tuner which, when blown through the tube with the letter "A" on it, produces the 440 Hz "A".

What is "440 Hz"?

In simple terms, "440 Hz" means that something happens repeatedly and regularly 440 times every second: it can be the oscillation of the string of a musical instrument ("vibration"), the back and forth of the piston of a combustion engine, the changes of polarity in an alternating current, or even any household appliance that rotates at a frequency of 440 times per second.

The frequency with which our heart beats ("pulse") or the frequency with which we inhale and exhale when we breathe, is much slower, we count it in minutes and the sounds they produce are so far apart that they could never be perceived as "tones".

The human ear perceives as "tones" only those regular or stable vibrations that occur not less than 16 to 20 times every second and up to a maximum of approximately 20,000 times per second. Tones between approximately 5,000 Hz and 20,000 Hz are not used as fundamental sounds in music because they are extremely high-pitched and in some cases even annoying, yet we perceive them in different ways.

"Hz" stands for "Hertz" or "Hertz" which is the unit of measurement of the frequency at which something occurs within one second and is part of the International System of Units. Previously the terms "Cycles Per Second" or "CPS" were used, something that was perhaps easier to understand, but the IEC (International Electrotechnical Commission) established the term "Hertz" in 1930 as a tribute to the German physicist Heinrich Hertz and, about a decade after being adopted by the CGPM (General Conference on Weights and Measures, 1960), the term "Cycles Per Second" was abandoned and replaced entirely by "Hertz".

The use of the unit of measurement "Hertz" in the world of music and sound engineering is restricted to the average human hearing ability however in the field of electromagnetism and physics in general it is so broad that the International System of Units considers a range from the sub-multiple 10⁻³⁰ Hz ("qHZ" or quectohertz) to the multiple 10³⁰ Hz ("QHz" or quettahertz).

These data might seem irrelevant or merely anecdotal to many, but not to the curious minds that LATERAL promotes, inquiring minds, such as yours who have read this far and who probably resemble others who throughout history asked questions that gave rise to the greatest discoveries in the history of mankind.

<p>Each of the rods of this tuning fork vibrates 440 times per second from the moment it is struck until the sound is extinguished.</p>

Each of the rods of this tuning fork vibrates 440 times per second from the moment it is struck until the sound is extinguished.

How to measure and visualize pitch "A"?

Especially during the 19th century many devices were invented, such as the Cagniard de Latour siren, the Savart cogwheel, the Duhamel Vibroscope, various chronograph recorders, the phonoautograph, the stroboscope, etc, which allowed audio-visual experiments with different tones, recording vibrations graphically or mechanically until Edison invented the famous phonograph in 1877, which not only recorded the oscillations but could reproduce them sonically. Today we have an infinite number of oscilloscopes and computers with digital analog converters that allow us to visualize, count and even redraw the vibrations of a tone... But... how did Pythagoras calculate the number of oscillations of the strings if none of the aforementioned devices existed...?

Pythagoras, one of the greatest geniuses of the pre-Christian era, managed to study and calculate various relationships and proportions between the vibratory frequencies that a string had and the lengths of its segments subjected to oscillation or tensions: he built a monochord (a single-stringed instrument, simpler than Mersenne's obviously but built several centuries before Christ) that allowed him to experiment physically and sensorially with different string lengths that produced sounds of different pitches. Pythagoras and in general the Greeks of the time were trying to discover the secret formulas of the divine creation such as the distances between the stars, orbits and other phenomena that demonstrate that there is a lot of order in the universe. It is believed that Pythagoras not only studied in Mesopotamian schools but continued his education in Egyptian temples. While it is true that he apparently did not focus on determining the actual amount of oscillations of the strings, he did study extensively the relationships between the different tones (which we musicians call "intervals") and set valuable precedents for the development of the scales we call "diatonic" and "chromatic" which are the basis of most music around the world to this day.

Today, although there are mobile applications for producing or capturing tones, the traditional metal tuning forks (see photo) are still used because they produce almost pure tones that help the ear to capture the tone accurately. There are also tuning forks for blowing and electronic devices ("Tunners") specially made to fulfill similar functions to those of traditional tuning forks. "Tuning fork" or "sonic" (high-end) clocks were a variety of clocks whose operation was based on the same principle of regular oscillation or "isochronism" of a tuning fork but controlled electronically. It was an intermediate technology between mechanical and quartz watches that appeared in the 1970s.

<p>Duhamel's vibroscope is a pioneering invention in the history of human attempts to make sound vibrations visible</p>

Duhamel's vibroscope is a pioneering invention in the history of human attempts to make sound vibrations visible

Does "La" 440 Hz harmonize like heaven and earth?

The history preceding the official choice of the 440 Hz frequency as the universal standard for the "A" spans several centuries and countless proposals. According to one of the world's largest (29 volumes) and most respected music dictionaries, the New Grove Dictionary, it was "at the meeting of the International Organization for Standardization (ISO) held in London in May 1939 and confirmed in 1953" that this standard was agreed upon. "International meetings had already been held in 1834, 1858, 1862 and 1885, and in Italy laws setting the pace were passed in 1887, 1936 and 1888." These meetings and agreements responded for the most part to practical needs in the musical as well as technological and especially industrial fields, however human interest in finding "the most perfect pitch possible" and establishing its use dates back to ancient China....

In the 1st volume of the "General History of Music" by Robertson and Stevens it is narrated that "the starting point of Chinese (musical) theory was the existence of a "base" tone (huang chung, literally "yellow bell"), which was conceived simultaneously as a sacred and eternal principle, origin of the omnipotence of the State, and a musical note of defined pitch. Lü Pu-Wei attributes it to the mythical emperor Huang Ti (third millennium B.C.), who sent Ling Lun (the "mystic, musical ruler") to the western borders of the kingdom. In a mountain valley, Milan cut a bamboo reed at one of the knots, so that it would give a basic tone or sound: that of a man's voice when he speaks without passion. He considered it important to find out what exact pitch of the "tone" was needed in each dynasty, for from this, political disorder could result."

Just as the Bible relates that God created the world with his voice "And God said, let there be light; and there was light" or that "In the beginning was the word...", other books from non-Jewish traditions agree in linking the creation of the world and even the universe with the power of sound. According to Robertson and Stevenson, the great Kung Fu-Tse known as Confucius "edited the oldest books in China," one of them "the Record of Rites (Li Chi), which contains an important chapter known as "Memorial of Music" (Yüeh Chi), and the metaphysical Book of Mutations (I Chin), where the first sketches of music are said to have been based on the cosmic elements." "This is how the frequencies of vibration in the Chinese system are based on powers of the numbers 2 and 3. "Music expresses the harmony of heaven and earth," says the Memorial of Music, and, according to the Record of Rites, "since 3 is the number of heaven, and 2 that of earth, sounds in the ratio 3:2 harmonize like heaven and earth.""

<p>Fludd's mundane monochord is part of the graphics of his publications on the relationship between music, physics, metaphysics, microcosm and macrocosm among other things.</p>

Fludd's mundane monochord is part of the graphics of his publications on the relationship between music, physics, metaphysics, microcosm and macrocosm among other things.

Can you identify the 440 Hz "A" without help?

As I wrote at the beginning, there are thousands of people in the world who, without knowing it, have "absolute pitch" and in some cases even have an innate ability similar to that of some musical geniuses. To have "absolute pitch" means to have the ability to remember one or more tones heard at some time without the aid of any musical instrument, tuning fork or reference tone. For example, if someone makes you listen to the 440 Hz "A" one day, the tone will be so engraved in your memory that the next day or several days later you will be able to recognize it without any doubt as well as perceive the difference between it and other tones you hear. Some people with "absolute hearing" perceive additional non-auditory sensations as if they were seeing colors, smelling aromas, etc. These added sensations are called "synesthesias" (syn, set and aisthesis, perception). The term "absolute hearing" actually refers not so much to hearing itself but to perception involving both the ear and the brain.

If you want to know if you have "absolute hearing" you can experience it with the help of LATERAL by following the simple instructions below:

  1. Click here and listen to the 440 Hz A tone once or as many times as you like so that it will remain in your memory;
  2. After a few hours, the next day or several days after having done the previous step, (not at this moment, nor immediately after having done step 1, for the experiment to be valid), click here (without listening to the previous link) and try to recognize which of the tones that sound is the one you heard and tried to memorize.
  3. Once you have listened to the audio, you can click on the following link to find out which is the correct answer.

If you guessed right, you almost certainly have "ABSOLUTE HEARING".