The golden ratio defines the harmony of most objects and thus is the most perfect expression of beauty.
How to compose a song with the golden ratio and the Fibonacci sequence /
The section aurea or the golden ratio is the essence of many artistic works. We can easily find it in architecture, painting and sculpture when the pattern is used to achieve an ideal symmetry. If this is reached then these pieces establish a direct liaison with nature: from the leaves that grow on a tree, to the spirals in pinecones and the geometric formations of snowflakes, to the dynamic of black holes and galactic dimensions. In every scale, the universe follows the enigmatic algorithm; it defines the harmony of most objects and thus, beauty in its most perfect expression. When it comes to observing the golden ratio, music is the art that we struggle the most with, and nonetheless, it is easy to achieve.
We can observe how the golden ratio has maintained a constant relationship with music since remote times, the discipline of Pythagoras, for example, allows us to infer that the reason that led him to discover the resonance of a taught string and all of its notes was, in fact, the golden ratio (which at the time was not known as such); an equation that was also related to the distances between stars. These ideas would later be adopted by Plato for his sphere theory, where he poetically named each of the musical notes after a planet in our solar system. If we jump ahead, to the twentieth century, György Ligeti, dared to compose songs like “Apparitions” where the longitudes of each section is ruled by a time proportional to the golden ratio.
Before we can begin to create music with the algorithm, we must first be able to tell that this measurement is a basic principle of mathematics, a formula, which resulted in the second term that will introduce the theory: the Fibonacci Sequence, where each number is the result of adding the two previous ones: 1, 1, 2, 3, 5, 8, 13, 21, etc…
The golden number (also known as Phi, represented by the Greek letter Φ) is a concrete point that we can find between the proportions of two segments on a straight line, we’ll let the diagram explain:
A F B
Where F is the Φ equivalent to «1,6180339885…». This is the golden number, an endless and irrational figure that does not represent a periodic repetition.
Thereupon this basic scheme, we can define how we want to begin composing. If your song lasts from A to B, then we would be dealing with the F element as the modifier of the rhythm of the track in the following manner: we divide our work into two parts, which will be defined by 61.8% and 38.2%, in accordance with the golden ratio. Afterwards, these will be multiplied by «x», where x represents the length of the work.
Putting it into practice makes it even easier: if your song lasts 4 minutes (240 seconds), then:
240s*0.618Φ = 148.32s or, at 2 minutes with 48 seconds we must intercept the work with a change, a bridge, an arrangement with a different instrument or a new melodic composition.
Now, using the Fibonacci sequence, we can also create embellishments and changes in the rhythm of our song to make it all the more attractive, where the sequence 1, 1, 2, 3, 5, 8, 13, 21… will correspond to the minutes or seconds when we’ll make changes in the tone that implies emphasizing the note that is played at that moment.
Great composers like Beethoven, Mozart and Wagner intentionally changed the rhythm of their sequence. These compositions were actually really complex, since the numbers they used where not prime, but large ones like 2178309 or 53316291173.
The simple fact of analyzing the score for a piano piece takes us back to the golden ratio again, which follows the Fibonacci sequence: in a scale we find 8 white keys and 5 black ones, equivalent to musical notes that will be ordered in groups of 2 and 3. This sequence is organized as 2, 3, 5 and 8.
The golden ratio can produce several geometric shapes, from a simple star-shaped pentagon to infinite hexagonal networks, and they both share the property Φ. Musical notes progress in the same manner: the high and low pitches have the same infinite spiral. We don’t have to be a mathematician to understand this. It has frequently been believed that the golden ratio is merely a coincidence, but after understanding its sublime examples in music, we can seriously consider redefining it and trying to consider it a logical and supreme result, in Plato’s words: it is impossible to combine two things without a third, there must be a relationship between them that joins them, the best liaison for this relationship is everything. This algorithm, created by the cosmos, is nothing more than a mathematical explanation of the beauty that we all seek in the sky, taking into account that it is also found within us and our planet.
Tagged: composers, Golden Ratio, fibonacci, Fibonacci sequence, music