Noise from Integer Sequences

Headphones are strongly recommended for listening to the sounds 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 audio events at times corresponding to the terms of the sequence.

If the sequence is {a1, a2, ...}, then we can create sound events at times {r a1, r a 2, ...} for some suitable scaling factor, r.

Depending on the value of r and the nature of the sound events 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 r is 1/44,100 of a second, corresponding to 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 sounds from a sequence, and from the complement of that sequence, sound identical, since one is the inverted waveform of the other. Harmonic components can appear due to the presence, or non-presence, of certain multiples.

When a sequence is not too "regular", and doesn't thin out too quickly (as, e.g., the squares sequence below illustrates), we may get something interesting.


Winter 2017 WXML creations

Autumn 2016 WXML creations

Spring 2016 WXML creations

Matthew M. Conroy