# Thread: Maths in music. Composer here who needs a little advice.

1. ## Maths in music. Composer here who needs a little advice.

Hello,

I am making a piece of music for a sonic arts class. My idea is that I keep repeating an audio sample hypothetically an infinite amount of times. The sample becomes shorter every time it repeats. I want the sample to become shorter by the same percentage every time so that eventually it reaches a point where it is no longer perceptible and it could be imagined that its repeating infinitely. The sample is currently 5 minutes long, though I can adjust it to any duration. Ideally the piece would last 1 hour, with the sample being 1 second long by the 58th second of the 59th minute so that for the last second of the hour it would supposedly repeat an infinite amount of times. I'd like the process of shortening to be fairly subtle so that it isn't immediately apparent what is happening to the sample.

so to summarise.
How long should the original sample be?
How much should each repetition of the sample decrease so as to reach an infinitely small duration during the span of one hour?

I really lack any knowledge that would help me to figure this out (I'm basically a layman) so figured I'd ask in a forum.

Thanks

2. Sorry, but you'll have to un-layman. For this task, you must understand the Exponential Function. That is how you decrease by the same percentage on each iteration.

3. Originally Posted by Varese
My idea is that I keep repeating an audio sample hypothetically an infinite amount of times. The sample becomes shorter every time it repeats. I want the sample to become shorter by the same percentage every time so that eventually it reaches a point where it is no longer perceptible and it could be imagined that its repeating infinitely. The sample is currently 5 minutes long, though I can adjust it to any duration. Ideally the piece would last 1 hour, with the sample being 1 second long by the 58th second of the 59th minute so that for the last second of the hour it would supposedly repeat an infinite amount of times. I'd like the process of shortening to be fairly subtle so that it isn't immediately apparent what is happening to the sample.
What you are looking for is a geometric series (each term being the time for one repetition) whose sum is 60 minutes. This means you start with some length "a" for the first, and multiply by some number "r" each time. An example is the sum 1 + 0.5 + 0.25 + 0.125 + ... = 2, where a=1 and r=0.5. I recommend you read up on the basics of this topic.

The sum is given by the formula S = a/(1 - r); for my simple example, this is 1/(1 - 0.5) = 2.

So what you want to do is to find a pair of a and r so that S = 60, and r is a little smaller than 1, so that the change is not too noticeable. You might solve the formula for a and make a table showing the starting times required for different values of r to see what seems like a good trade-off between too rapid a speed-up and too short a sample. Or, you could solve for r instead, and see what various values of a (starting with your 5 minutes) require in terms of r. You may find that your a=5 is fine; or you may have to experiment to see what actually works well.

4. Thank you, that's perfect.

I've done something much simpler for now because its due in a couple of days. But for next term, I will read up on exponential functions and geometric series and do it properly!

Thank you so much!

All the best