What I first noticed in the wave picture are the distinct peaks representing the beat. I considered the biggest peaks near each end as the limits of a whole.
Having looked at the geometry of the Golden Ratio a great deal, and its expressions in worldwide art, I have a decent sense of its place along a line. The Amen Break had that feel. For a quick check I used homemade Golden Ratio calipers to examine the peaks. Indeed, 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.
To appreciate this relationship between the Golden Ratio and sound, it's worthwhile to consider some of the ideal, eternal, unchanging principles of Golden relationships which can only be approximated in nature, and byartists, architects and musicians. I'm not going to re-teach here everything there is to know about this wonderful ratio since some great websites already tell you everything you want to know, such as this and this. Most pertinently, information about the appearance of the Golden Ratio in worldwide music, such as in the work of the classical composers Mozart, Beethoven, Bartok, Debussy and Satie can be found here.
For our interests, the main principle to appreciate about the Golden Ratio is this: A whole line may be divided in such a way that the length of the whole relates to its large part in the same way that the large part relates to the small part. In other words, the same relationship appears on different scales, comprehending a mathematically balanced whole.
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