# Listen! The golden ratio in music: too easy?

## Attention ! This column is more to listen to than to read!

It is a number whose decimal writing is infinite: 1,618,033,988, etc. This number would govern everything around us: from the number of petals in a daisy to the architecture of the Parthenon, from the spiral of sunflower seeds to the shape of an entire galaxy, it is hidden in the famous Fibonacci sequence. I want to talk to you today about the golden ratio.

It is a number whose decimal writing is infinite: 1,618,033,988, etc. This number would govern everything around us: from the number of petals in a daisy to the architecture of the Parthenon, from the spiral of sunflower seeds to the shape of an entire galaxy, it is hidden in the famous Fibonacci sequence. I want to talk to you today about the golden ratio.

It is a number whose decimal writing is infinite: 1,618,033,988, etc. This number would govern everything around us: from the number of petals in a daisy to the architecture of the Parthenon, from the spiral of sunflower seeds to the shape of an entire galaxy, it is hidden in the famous Fibonacci sequence. I want to talk to you today about the golden ratio.

We say “golden section”, but it’s actually a proportion: You find this proportion by dividing a line in two, so that the longer part divided by the shorter part gives the same result as dividing the whole line by the longest part. If it helps: imagine a rectangle. Fill the left part with a square. Well, the ratio of the long part of the rectangle to the length of one side of the square is the golden ratio.

In equation form this gives: a (the long part of the line) / b (the short part of the line) = (a + b) / a = 1.61803398887498948420 etc. Infinite decimal number also called PHI. Phi can be rejected in the form of a spiral, such as. allows the flower to arrange its petals in such a way that it regains the maximum exposure to the sun.

And in the music, Christophe, we also spot this golden number. Yes, and it’s one of the great myths that begs to be challenged on a regular basis, because there’s a kind of eerie ease in repeating this number in music history.

In what area of ​​music can we place this share? It can be placed at the level of a range. You know that the gaps between each note are somewhat unresolved, “problematic,” if you will. And it is true that by saying that the golden ratio is absolutely everywhere, which is definitely not the case, some believe, for example, that the ideal cut would match the golden ratio. There have been attempts at this, especially by an engineer specializing in microwaves: Heinz Bohlen, but without real success, with intervals that are a little complicated for the ear, intervals like these

But there is another way to place this proportion, this golden ratio, in music. Yes, and there it is much more tangible, with a slightly disturbing systematic side. It is in the proportions of a room. If we place a piece on a straight line, then there will be an event, a climax, an apotheosis, a climax! by … about 3/4 of the room … And it happens quite often. Take this piece by Frédéric Chopin: his first prelude. The piece is 33 bars long. I’m letting you figure it out, Gabrielle? 33? Well, it’s a first section that’s 20 and a half, and a shorter second section that’s a 12 and a half. So. Something was going to happen in the 21st bar. Listen.

Excerpt 1 – 1st Prelude by Chopin

You see, apotheosis to the golden section and then conclusion. This is quite often the case with Bartok. In his Music for strings, percussion and celesta. The first movement is 88 bars long. So Gabrielle? There should be something about bar 55 or 56. We’ll see, hear.

Excerpt 2 – 1st movement of Music for strings, percussion and celesta

Is it voluntary? That’s where it’s going to be interesting, and that’s my little conclusion

In general, there is little evidence of voluntary action, except in Debussy, for example, when he wrote to his publisher Durand that he was trying to get the number of bars to correspond to the “magic number” as he puts it. Gardens under the rain .

And so … the golden ratio: ubiquitous in music? Not really, but we like to think so. It’s just that we’re not going to put a climax in the middle of a piece, otherwise we would be bored in the second half, and that it’s better to put it, not at the END, but between the middle and the end, and it falls more or less on the golden section. But above all: we are talking about the number of measures, and not the duration … or by ear: if the golden ratio needs a climax, we are going to talk more in terms of duration than in number of measures. Yes, we can have 40 very fast beats and 3 very slow beats and that will completely distort the share.