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  1. PO
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    <p>To represent an increase from 1.0 to 8.0 and back, you could use a function of this form:</p> <pre><code>f(x) = 1 + 7/2*(1 - cos(2*pi*x/y)) </code></pre> <p>Where <code>y</code> is the number of samples in the resulting track.</p> <p>It will start at 1 for <code>x=0</code>, increase to 8 for <code>x=y/2</code>, then decrease back to 1 for <code>x=y</code>.</p> <p>Here's what it looks like for <code>y=10</code>: <img src="https://i.stack.imgur.com/sZjDj.gif" alt="plot 1 + 7/2*(1 - cos(2*pi*x/10)) from 0 to 10"></p> <p>Now we need to find the value of <code>y</code> depending on <code>z</code>, the original number of samples (20,000 in this case but let's be general). For this we solve <a href="http://www.wolframalpha.com/input/?i=solve+integral+1%2B7%2F2+%281-cos%282+pi+x%2Fy%29%29+dx+from+0+to+y+%3D+z" rel="nofollow noreferrer">integral 1+7/2 (1-cos(2 pi x/y)) dx from 0 to y = z</a>. The solution is <code>y = 2*z/9 = z/4.5</code>, nice and simple :)</p> <p>Therefore, for an input with 20,000 samples, you'll get 4,444 samples in the output.</p> <p>Finally, instead of multiplying the output index by the pitch value, you can access the original samples like this: <code>output[i] = input[g(i)]</code>, where <code>g</code> is the integral of the above function <code>f</code>:</p> <pre><code>g(x) = (9*x)/2-(7*y*sin((2*pi*x)/y))/(4*pi) </code></pre> <p>For <code>y=4444</code>, it looks like this:</p> <p><img src="https://i.stack.imgur.com/vmCTc.gif" alt="plot (9*x)/2-(7*4444*sin((2*pi*x)/4444))/(4*pi) from 0 to 4444"></p>
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    1. POIncreasing the pitch of audio using a varied value
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    1. CONo matter what function you choose to generate, I think Nicolas is right about calculating the new length. Take the integral of the pitch from 0 to the original number of samples, and then divide by the number of samples.
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    2. COThe problem with this solution is that as you step through the array (multiplied by the pitch) you surpass the total amount of samples in the original audio buffer. I'm sure something can be figured out based on this idea, but it is not immediately clear to me.
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    3. CO@Eric - You're right, I've edited.
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