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From Microcosm to Cosmos: Quantum Harmonies and the Great Symphony of the Universe
New Perspectives on the Relationship between Music Theory and Mathematics
In the vastness of the universe and in the depths of subatomic physics a hidden melody resonates, a language made of waves, proportions and harmonies. But what is the connection point between quantum mathematics, the musical interval of the perfect fifth and Johannes Kepler's idea of celestial harmony?

Let's start from the beginning. The Pure Harmony of the Perfect Fifth

The perfect fifth is one of the most harmonious musical intervals. In technical terms, the frequency of the upper note is the 150% of the lower one. For example, starting from a C at 261.63 Hz, the G which forms the perfect fifth vibrates at 392.44 Hz. This relationship of proportionality is not only pleasant to the human ear but is also emblematic of the intrinsic order that regulates the our universe.

Waves and Proportions in Quantum Mechanics

In the seemingly chaotic world of quantum mechanics, wave functions and energy levels play a crucial role in determining the behavior of particles. Here too, proportions and harmonies emerge in forms surprisingly similar to those of the musical world, suggesting a common fabric that binds together cosmic and subatomic phenomena.

Kepler's Celestial Harmony

Johannes Kepler, influenced by a deep sense of harmony and proportionality, formulated his laws of planetary motion. His Third Law describes a precise relationship between a planet's orbital period and its distance from the Sun, an interpretation which he considered a manifestation of “heavenly harmony“. Kepler himself saw the solar system not just as a mechanical model, but as a divine score, orchestrated with mathematical precision.

The Unexpected Connection: Universe, Particles and Harmonies

Music, quantum physics and astronomy come together in a universal language of waves and proportions. The quintessence of this intertwining is the perfect fifth, a harmonious fusion between notes that finds echo in the quantum descriptions of particles and in Kepler's celestial laws. Our understanding of the universe is enriched as we discover how it favors certain proportions and relationships, which manifest themselves both in the microcosm of subatomic particles and in the vast spaces between celestial bodies.

The melody of the Universe

The universe is an ever-developing symphony, an infinite composition written in the universal language of mathematics and interpreted by nature under the direction of the laws of physics. With each new scientific discovery, we refine our ability to “listen” and actively participate in this great cosmic orchestra.

So, the next time you hear a perfect fifth or read about new research that explores the farthest corners of the universe, remember that you're participating in something extraordinary. You are not simply a passive listener, but an active member of the great cosmic orchestra. In this universal symphony, every note, every particle, every star has an essential role in creating the harmony that animates life.

Ultimately, maybe we're not just "learning to listen” but we are also “playing” in the great cosmic concert, contributing our notes to this infinite and wonderful composition which is, in effect, the music of the universe.

There is more

Pythagoras and Harmony: an Unexpected Bond

According to Iambicus (philosopher of the 4th century AD) Pythagoras made a discovery that would become fundamental to the entire history of science. Passing near a blacksmith shop, he realized that the hammers, beating on the anvil, produced a harmonic variety of sounds based on their weights. He noticed that the hammers that produced harmonious sounds had weights that related to simple fractions (such as 1/2, 2/3, 3/4). Conversely, the absence of these fractional relationships resulted in disharmonious sounds.

This simple observation was enough for Pythagoras to discover that the pitch of a note is proportional to the length of the string that produces it. This inspired the great astronomer Kepler (1571 - 1630) to discover the laws of motion of the planets.

Other information

Let's understand better

In music, a “perfect fifth” is a type of interval between two notes. Let's take the C major scale as an example, which is: C, D, E, F, G, A, B. If you start from C and count up to the fifth note, you arrive at G. This interval between C and G is called a “perfect fifth“.

Why is it called "perfect“? Well, it's a technical term in music theory.

The denomination "fifth” comes from the position of the interval within a diatonic scale. Starting from a note (for example, C), the fifth note of the major or minor diatonic scale (in this case, G), is separated from the starting note by five scale degrees (C, D, E, F, G) . The word "perfect” is added to distinguish this interval from its altered (diminished or augmented) versions, which do not have the same consonant stability.

Acoustic and mathematical characteristics:

The perfect fifth is particularly appreciated for its acoustic purity. This interval has a frequency ratio of 3:2, meaning that the frequency of the highest note is one and a half times that of the lowest note. This relationship creates a particularly pleasant resonance to the human ear, since the sound waves overlap very regularly and without creating beats, which are perceptions of pulsation caused by close but not identical frequencies.

There is also discussion about how some find the name “perfect fifth” may have roots more in mathematics or geometric patterns, rather than in the practical use of intervals in music. Some believe it is called “Perfect” because it has a simple and beautiful frequency ratio, while others think that the naming has more to do with its position in the circle of fifths.

So, "perfect fifth” is a technical term in music theory that describes a specific type of harmonic interval between two notes, and is called “perfect” for a variety of historical and theoretical reasons that we leave to classical music scholars.

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Author: Uber Bertiè

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