

U2's Natural Logarhythm: Exponential Decay in the Delay of The Edge's Guitar - atularora
http://5cense.com/Edge_Delay.htm

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anigbrowl
_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.

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simplegeek
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).

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

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simplegeek
Latter i.e. extract the melody via software?

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anigbrowl
OK, then you want to get into the world of Digital Signal Programming, or DSP.
Before you do so, be aware that this is a Hard Problem if you want to achieve
more than the most basic results. The basic tool of DSP is the Fourier
Transform, which allows you to convert a 1-dimensional signal in the time
domain (such as an audio file) to a 2-dimensional signal in the frequency
domain (such as a spectrogram aka graphic equalizer display). Many problems
that look knotty or impossible in the Time domain are soluble with simple math
in the Frequency domain. So you do an FFT, modify or analyze your signal, and
then do another FFT if you want to convert it back to an audio stream.

This is a really excellent starter book that you can also download for free:
<http://www.dspguide.com/> It's far better written than most other books on
the field and will help you to develop an intuitive understanding of the
fundamental math. Many books just say 'here's the math,' without discussing
why it works or why you would want to do it one way rather than another. Many
more cover DSP from the point of view of radio or wireless communication -
although the same principles apply here as for audio, it's somewhat confusing.
This book is very audio-friendly.

The state of the art in pitch extraction from usic recordings is Celemony's
Melodyne: <http://www.celemony.com/cms/> The company was started in the
mid-90s by a German audio geek named Peter Neubäcker with his wife and a
programmer. He says in interviews that he's using a different approach based
on the shape of sounds, but has never published his methods. I've met him a
couple of times at conferences and trade shows, but he knows how to keep a
secret! However, you'd be well advised to try out the demo version of his
software. How he does is it is a mystery, but he's way, way ahead of any
commercial or academic methods.

If you like Matlab, this is the best academic work on the task so far:
<http://isophonics.net/content/reverse-engineering-mix> and you should also
grab a copy of Sonic Visualizer, which is a slow-but-flexible analysis tool:
<http://isophonics.net/SonicVisualiser> Be sure to follow up the links on the
Isophonics site, which will lead you to a rich variety of libraries and tools
for audio programming.

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kree10
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>

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

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wyclif
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.

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luckyland
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>

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strayer
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?

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G_Wen
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>

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turbodog
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.

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

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

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phpnode
it's a play on rhythm....

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gregschlom
Oops, sorry. Thanks for pointing it out

