…peaks pop up at Golden Ratio intervals, as do smaller peaks within them, reminsicent of the fractal structures in nature.
For more exact visual analysis I examined the wave image in my computer, in which I have a palatte of geometric forms and proportions for quickly identifying an object’s ratios. Sure enough, Golden Ratio relationships were indicated among the different peaks. Am I seeing things? You decide. But the appearance of the Golden Ratio may help explain its popularity.
Here’s my take. Instead of working with the golden ratio φ, we can work with the “golden fraction” 1/φ instead. (It’s equivalent; it just flips our equations upside down.) Because of the nature of the golden ratio, it happens that 1/φ = φ – 1 ≈ 0.618. Now, 5/8 = 0.625, so that’s a good approximation to 1/φ. In particular, if you’re just eyeballing a WAV file, you won’t be able to tell 5/8 from exactly φ.
Now, what’s special about 5/8? In 4/4 time, there are eight beats in two measures. Listen to the Amen and count the beats:
There are big snare hits on two, four, six .. then nothing on eight. The snare you expect on eight is late, so late it’s almost on the ninth beat. So the distance between the fourth beat and the ninth is five beats, or 5/8 of a two-measure loop.
Is there something special about that particular fraction? Maybe, or maybe playing with the listener’s expectations simply sounds funky. My money is on the latter, but it’s an interesting question.