Is there a connection between a music piece’s form and its impact on the listener? Why do some music works seem more beautiful than others? The ancient architects knew the answer to this question long ago.
The Great Pyramid of Cheops. Photographer: Berthold Werner. Source: Wikipedia
One of the Seven Wonders of the World – the Pyramid of Khufu (popularly known as the Pyramid of Cheops) – has been admired for its grandeur and perfect proportions by millions of tourists for years. A lot of its mysteries still remain undisclosed. Up to now, the scientists can’t explain the exact way this giant construction had been erected. But there is one indisputable fact about the pyramid: back in 2500 years B.C., the architects knew the “formula of harmony” – a special correlation between the sides’ length known as the “golden proportion”. This correlation is also the base of numerous architectural masterpieces, like the Parthenon and Notre-Dame de Paris.
Leonardo Da Vinci, one of the most outstanding thinkers and artists of the Renaissance has also left a lot of mysteries for his descendants. His famous “Gioconda” is still one the most discussed paintings. According to one of the hypotheses, Leonardo endowed the woman depicted in his creation with his own features, which means that the painting could be Da Vinci’s self-portrait as a woman. Gioconda’s ephemeral smile carries some secret meaning that the experts still cannot interpret. In order to create that special impression for the viewer, the painter used many techniques, including the rule of the “golden proportion”.
It becomes obvious that there is a certain correlation between the parts of a work that helps us to experience positive emotions. The “golden ratio” phenomenon is observed when the ratio of the whole and the bigger part is the same as the ratio of the bigger part and the smaller part. Besides being used by the ancient architects, this correlation was mathematically proved in the Middle Ages by another great “Leonardo” – Fibonacci. He was talking about a special sequence of numbers that got the name of “the Fibonacci numbers”. Every number in that sequence is the sum of the two preceding numbers: 1, 2, 3, 5, 8, 13, 21, 34 and so on. Moreover, starting with the 5 - 3 ratio, every number is in the golden proportion with the preceding one. Mathematically, this ratio equals 1.6.
How did the ancient architects manage to discover the formula of the “golden proportion”? In fact, nature gives us hints whenever we are observant enough! One of the bright examples is a sunflower. The number of seeds in every row starting from the center corresponds to the Fibonacci numbers. Another hint is a nautilus conch. The lengths of the conch’s spirals are in the 1.6:1 proportion. This allows the conch to grow proportionally during the mollusk’s entire lifetime.
The “golden proportion” had been used in the music of many great composers, too. Let’s take the renowned music piece by one the world’s most famed composers – “Moonlight Sonata” for piano by Ludwig van Beethoven, and particularly, its mystical first part. (By the way, at MusicaNeo you can download for free the sheet music for the Moonlight Sonata as well as other high-quality popular works). After making some simple calculations we can state that the composer used the rule of the golden proportion in the first part of his piece.
The reprise is an important part of a sonata: it is often accompanied by a special feeling that can be compared to a catharsis. Taking into consideration this fact, let’s divide the first part of the sonata into two unequal segments: a bigger one – before the reprise (consisting of 42 bars), and a smaller one – starting from the reprise and till the end of the first part of the sonata (consisting of 27 bars). The proportion between the general number of bars and the number of bars in the bigger part is thus 69:42. Now let’s divide the number of bars in the bigger segment by the number of bars in the smaller one: 42:27. In both cases the result equals 1.6, which IS the golden ratio. This fact only proves the hypothesis that the rule of the golden proportion had been accurately used by the great composer.
But why does this correlation between the parts bring the magic feeling of harmony and beauty when we are listening to music, enjoying the paintings or looking at the sunflowers? The answer to this question still remains one of the biggest puzzles of the human consciousness.