U2's Natural Logarhythm: Exponential Decay in the Delay of The Edge's Guitar

by atularora • 16 years ago

74 20 16 years ago

anigbrowl4• 16 years ago

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).

No, I think he meant 3/16, especially since he explains the derivation of that value. It's a fixture in reggae music and dub because it provides instant syncopation, and later found its way into a lot of electronic dance music for the same reason. Get started with Dub at http://en.wikipedia.org/wiki/Dub_music and then study the early studio history of Lee Perry, who pioneered a great many audio production tricks by necessity. This 1978 track is a seminal work: http://www.youtube.com/watch?v=hs9Z2TEqSZo All the sound effects going on are done with a mixer and 2 delays, using tricks like splitting the output of a channel back into 2 inputs and inverting the polarity on one.

The 'number of delayed notes per beat' comes in around 3 because the delay unit is feeding back on itself, and a 4th repeat (being equal to 12/16ths) is likely to fall exactly on a beat: 1/16, 5/15 and 12/16 are the strongest beats in rock and dance music. If you hit the 9/16 beat it's straight rock or dance, if you delay it by half a beat you get the basic rhythm of hip hop. You can of course turn the feedback up higher but above a certain level it tends to run away and make a horrible noise, independently of the delay time.

Edited to add: I hope that explanation didn't sound blithely dismissive of the mathematical investigations. The 1/e hypothesis is compelling, but has the air of being 'so beautiful, it must be true' - be careful of this! I have several notebooks' worth of similar explorations of geometry, golden ratio and so forth as applied to music. It's wonderfully inspiring, but it's easy to find yourself trying to square the circle or retrieve the Lost Chord.

stratospark• 16 years ago

Fascinating, can you recommend any good resources that you stumbled across in your explorations of music theory and math?

anigbrowl4• 16 years ago

Offhand not really; discussions about math and music from the math end tend to either be very dry and technical or quickly tilt into pseudoscience, and good musicians (of which I am not one) tend to look at the math as an interesting curiosity, but only for as long as it takes to get a handle on some new compositional technique.

http://electro-music.com/forum/index.php is the best place I know for serious-minded discussion of the interface between math and music, though it's (surprise) heavily geared towards users/designers of synths and sequencers.

simplegeek2• 16 years ago

Per your comment I think you've got a good handle on Music and Math. I'm totally naive but, briefly, what background should one have if he intends to start working on extracting a melody from a song? I will appreciate your reply (didn't find your email in your profile so posting it here, thanks).

anigbrowl4• 16 years ago

Can you be more specific - do you mean so you can learn to play the tune yourself, or extract it via software?

turbodog• 16 years ago

He lost me at sentence 3: "Even before he started using a delay pedal, like on Boy".

Um, practically every U2 song ever makes heavy use of guitar delay.

mcobrien• 16 years ago

Boy was U2's first album, so the sentence suggests Edge was using delay before he started recording U2 songs.

frampton• 16 years ago

U2's Pre-Boy recordings (1978/79) have a very different sound because they mostly don't use delay:

http://www.youtube.com/view_play_list?p=1616B39A07992AF0

luckyland• 16 years ago

This technique, and some instruments outfitted with specific DSP components to achieve it, was developed by Michael Brook.

http://en.wikipedia.org/wiki/Michael_Brook

wyclif• 16 years ago

This was The Edge's "secret weapon" before they moved to all-digital equipment: http://www.ehx.com/products/deluxe-memory-man

Still one of the best analog stomp boxes on the market.

strayer• 16 years ago

Since e is a number, not a function (the function is exp = lambda x: e^x) then 1/e is not log but one divided by e.

I once was told that using, say, 1/cos for acos is specific to English-speaking countries. Does anyone know about that?

lkozma• 16 years ago

If I recall correctly from high school, we used to call 1/cos "secant", or sec(A).

G_Wen• 16 years ago

I think you're thinking of the inverse cosine function arccosine. The reciprocal of the cosine function is known as the secant. I do not know if this is specific to English speaking countries. However the Chinese version of wikipedia suggests it is: http://zh.wikipedia.org/zh/反三角函数

gregschlom2• 16 years ago

Not to be pedantic, but logarithm is actually spelled with an i

phpnode• 16 years ago

it's a play on rhythm....

gregschlom2• 16 years ago

Oops, sorry. Thanks for pointing it out

kree10• 16 years ago

Reminds me of a use of math in rock that was actually calculated: the beat in Queen's "We Will Rock You".

"I mixed all the tracks [...] with different delays, related to each other in length with prime numbers, so there would not be any discernible 'echo'." -- http://www.brianmay.com/brian/brianssb/brianssbsep07.html

jcl• 16 years ago

...which is expected from Brian May -- an astrophysicist rock star. :) http://en.wikipedia.org/wiki/Brian_May

U2's Natural Logarhythm: Exponential Decay in the Delay of The Edge's Guitar

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