Combustion #2 Music Progress 7: The Golden Ratio

The golden ratio, 1.618, or Phi is often associated with aesthetics. Famous visual artists, composers, mathematicians, and writers have used the proportion to help structure works.

So Jordan and I thought it would be fun to try to incorporate Phi into Combustion #2. How? Structurally!

The golden ratio is any ratio where: X + Y / X = X / Y = 1.618. 

So how do you divide musical structure in this way? We decided on one significant event being the divide between parts X and Y for the ratio. That turning point is the climax of the song. Therefore, X represents all of the music before the climax, and Y represents all of the music after the climax. Thinking of the climax as the dividing line for the golden mean has been done countless times before in music (listen to Chopin's Op. 28, no. 4 for just one example).

But creating a song based around a ratio creates a problem. For one, the song isn't complete yet. We don't know how long each part will be, nor do we have a climax written.

What we do have is a significant part of the structure.

We know that A + B is about 90 seconds long that A is 66 seconds, and that B is 24 seconds. Since we already had the entire structure planned out, we started using our imaginations for what the length of remaining parts should be in relationship to the parts we already have.

Here is what we came up with (remember that the overall structure is ABACA, or Rondo Form):

A: 66 seconds

B: 24 seconds

A': ??

C: 40 seconds

A'': 133 seconds

At the time, we left the first return of the A section blank so that we could expand or contract it based on how long the piece needed to be for the golden mean.

But we soon realized there was a pretty big problem. A'' is way too long in relationship to everything else.

When I wrote down the structure, I mean for A'' to be the same length as A. But somehow,  because I had been saying, A'' will be twice as long as A, we started thinking that A'' would literally be twice as long as A.

That isn't what I had been meaning to say though. 

I meant that A'' would have one phrase rather than two phrases (A has 2 phrases), and that the one phrase in A'' would be twice as long as a single A phrase. 

In other words, A and A'' would be close the same length, despite having a different number of phrases.

With that confusion out of the way, we decided to expand A' due to where we think the lyrics will currently fit.

Here's what we came up with the second time around:

A: 66 seconds

B: 24 seconds

A': 60 seconds

C: 40 seconds

A'': 76 seconds

266 seconds total. 266 seconds / 1.618 = ~164.4 seconds.

164.4 seconds is exactly where our climax should be. That puts the climax within the first 10 seconds of C, which is exactly where the climax was designed to be. That is definitely something we can work with!

Interestingly enough, we also have the low rumbling noises in the piece that we can easily adjust the length of. We can use that to our advantage to fine tune the exact location of the climax as well.

-Hayden Davenport