Noise from Integer Sequences

Headphones are strongly recommended for listening to the mp3s on this page.

For a given integer sequence (by which I mean an increasing sequence of positive integers), we can make an audio file by creating an audio event at time an if the number n appears in the sequence.

Depending on the value of a and the nature of the sound event created, many results are possible.

Here, I have taken this to an extreme. The sound events are one sample in length, of maximal amplitude, and a is 1/44,100 of a second, corresponding with the standard CD sound sampling rate.

Thus, the audio file created has samples that are merely "on" or "off". The n-th sample is on only if n appears in the sequence.

The result is "noise", in most cases, with characteristics which depend on the nature of the sequence.

A curious feature of this method is that the resulting sound from a sequence, or from the complement of that sequence, sound identical, since one is the inverted waveform of the other. As a result, harmonic component can appear due to the presence, or non-presence of certain multiples.

I'll certainly be thinking of other sequences from which to make noise. Ideally, the sequence is not too "regular", and doesn't thin out too quickly (as, e.g., the squares sequence below illustrates).

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