# 1/f “Pink Noise” for the Math-Disabled

I have very little skill when it comes to math beyond all the elementary level operations (addition, subtraction, multiplication, division, mean, mode, etc) and a vague grasp of statistics, what a graph is, and algebra.

I'm a writer at heart, and noticed a few discussions online about 1/f wave patterns or "pink noise." As much as I tried to comprehend the maths, the subject is over my head

What I want to do is structure the beats of my text to produce a more pleasant experience that helps hold reader attention using natural mathematical rhythms as a guidelines.

Would someone write up a set of steps, or pseudo-code explaining how the relations of intervals between points on a number line produce 1/f "pink noise"?

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Can you post links to some of these online discussions? –  wj32 Oct 18 '12 at 20:33

Pink noise has contributing amplitudes inversely proportional to each corresponding frequency. It appears more sinusoidal than white noise (constant power spectrum) because the low frequency components have large amplitudes. The high frequency components do not contribute that much to the overall noise amplitude:

The following pseudocode gives an idea of how to generate pink noise in a programming language such as MATLAB:

1.) Generate a square wave (ones(n) will create a square wave of width n in MATLAB).

2.) Take the Fourier Transform of the signal (fft(x) in MATLAB). This will give you the sinc function. The DC component will be 1.

3.) In a for loop, add noise to the amplitude of each frequency of the FFT sinc function. The range of values of the noise will be dependent on 1/f.

4.) Take the inverse Fourier Transform of the noisy FFT. Then subtract 1 to yield a pink noise vector of length n centered around 0.

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Sound is "pink" if the volume decreases by roughly 10 dB every time the frequency is multiplied by 10. So if the volume at 131 Hz (low C) is 40 dB, the volume should be 30 dB at 1310 Hz (E above high C, two octaves above middle C).

You can break this into smaller pieces, if convenient. For example, if you increase the frequency by 50% the volume should decrease by 1.76 dB.

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Apologies for bumping the old thread, but...

I think what you're looking for is related to Zipf's Law (http://en.wikipedia.org/wiki/Zipf%27s_law). A special case of this is Benford's Law, which is what forensic accountants use to analyse record books for irregularities. The idea is that the most common numbers will appear in a 1/f frequency, i.e. Pink Noise.

1: .30 2: .18 3: .12 4: .10 5: .08 6: .07 7: .06 8: .05 9: .04

So for your purposes I would suggest writing a piece, like a chapter, and then analyzing your beats for pacing/length. The shortest segments (fast action) should account for about 30% of the whole, and the longest segments (deep dialog) about 4%...

Naturally if you want more or less granularity, you'll have to run the math on it to get the appropriate values, but this should give you a start.

Another thing to keep in mind, is that this is fractal. So your beats should follow this pattern, your word lengths, paragraph lengths, chapter lengths... The more scales you apply it to, the more you should see your work start to flow.

Hope this helps!

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