“Recently I tried searching around on the internet to see if anyone else had discovered what I had discovered back then, and while I found some interesting articles (in particular this one by Tim Darling), nobody seems to have happened on the discovery that I made. Darling does a thorough and at times technical analysis of the equipment and delay settings that The Edge uses to get his sound, his conclusion being that his delay is set at roughly 3/16 tempo, or for example on “Where The Streets Have No Name,” his pedal was set at 340-350 ms. But this 345 ms setting is not relevant unless we talk about beats per minute”
“Any guitar player that has fooled around with a delay pedal (and preferably a drum machine or metronome at the same time), knows that that there is a certain point when you are cranking the setting that this “Edge” sound kicks in”
“For example, if The Edge was using delay on “I Will Follow” (which I don’t think he is anywhere on Boy) then it would be set like this, so the delay would coincide exactly with the next note, creating doubled up chords”
“But if you keep cranking it (tighter, so the notes get more bunched together), you get to a point where it just hits a groove. It’s like riding a horse where you are trotting really fast and then suddenly the horse breaks into a gallop. It’s a modulating rhythym that is self-sustaining, self-propagating. There’s a tension there, like it’s offbeat, on the edge of being chaotic, but then it resolves itself with each beat”
“Around the time of Joshua Tree, not only was I fascinated by music, but also mathematics. I was studying both, but opted for degrees in math, and then physics, thinking it was the more practical choice. But also because the more I “studied” music, the more I didn’t want to know what made it tick”
“The natural thing to do when studying this interval, mathematically, was to find this ratio between the two rhythms (the rhythm of the drum and the rhythm of the guitar)”
“When I’d count and take a ratio of (beats per minute)/(delayed notes per minute), I’d always get a number close to 0.36788. This is to say, there was roughly three delayed notes per beat, or as Tim Darling points out, it’s roughly 3/16 tempo (though really I think he meant 6/16 time or 3/8 time, where 3/8 = 0.375, which is a close approximation to 0.36788)”
“But I wasn’t interested in rough approximations. I wanted to know the significance of that number. When you invert the number it is obvious. (1/0.3678794) = 2.7182821 or e, Euler’s number, probably the single most important number in mathematics that is used to explain a lot of natural phenomena such as exponential decay”
“That is, if you divide the (delayed notes per minute)/(beats per minute) you get e! Moreover, the function of the inverse of e, or 1/e, is what is referred to as a natural logarithm, that is used to explain all sorts of natural multiplicative phenomena”
“If we go back to Tim Darling’s analysis, he says the secret setting for “Where The Streets Have No Name” is 340-350 ms. I went back and counted the number of beats per minute in the song, and its actually like 64 beats per minute, so each beat is about 0.9375 seconds. So now if we divide the beat interval of 0.9375 by this setting of 345 ms or 0.345 seconds, we get (0.9375)/(0.345) = 2.7173913, which is pretty damn close to e (2.718281…), which explains why this particular setting works for this particular song”
“So, more precisely, if you have a song that is exactly 60 beats per minutes, or a beat interval of exactly one second, then to get the “Edge” delay, you’d set it to 367.88 ms. For any other beat interval, all you have to do is divide by e to figure out what to set your delay on”
“This is obviously nothing The Edge needs to “know” to play guitar like he does, at least not consciously, just like a sunflower or pine tree doesn’t need to “know” what a Fibonacci number or Golden Ratio is to generate the whorling patterns in it’s flowers and cones (the subject of my math thesis)”
“And the question still remains as to “why e?” In the case of the plants, the golden ratio allows them to optimally space leaves on an axis for maximum sun exposure. There is a physical reason. But why the delay ratio of e sounds most appealing, still remains to be determined. I am not sure I want to know”