Noise and orderliness in music: the opinion of physicists

A pair of physicists came up with an experiment in which the true "natural" chaos found use in music. Using indiscriminate (albeit averaged) tap water dripping, the team was able to experimentally demonstrate the evolving idea of ​​how rhythmic figures and sound relate to musical preferences, confirming that most musical genres (starting from classical rock) contain in themselves this measure, a piece of sound disorder. That is noise.

The most restrained rhythm, the most cliché melody, “a song at 3:30, verse through the chorus” - all this was born from the chaos that can still be found in them. This is what music mathematics demonstrates: both melodies and rhythms of composition are subject to power dependencies — relationships that give us the likelihood of a particular pattern depending on a previous event. If I play the “Do” note, how far (and unrelated) the next note can we expect?
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A simple experiment invented by physicists Nitica Sakharwade and Sayak Dasgupta from the Indian Institute of Technology gives an idea of ​​how music can correlate with noise or its various manifestations. The experiment used a dripping faucet - a perfectly suitable and barely perceptible source of chaos.

First, you need to understand that there are different types of noise. White noise first comes to mind. In it, the successive values ​​of some sound (or something else) are not correlated with the previous values. If one value is 5, the chances of having both the number 1002 and the number 4 or 6 are the same (provided that the range of numbers is large enough).

There is also a red noise, which is also known as Brownian noise , and is a much more meaningless accident. While white noise particles can jump from any point to any point within a predetermined range, particles affected by red noise act as if a bunch of other particles pushed them away, and they all push in different directions and with random modules. Thus, instead of jumping everywhere from point to point, the Brownian particle as if oscillates in different directions. This is a very real representation of chance.

If you come from this point of view to the rhythm or the main frequencies in the music (ie, musical patterns), they will be somewhere between the white and red noise. It was previously shown that music of all varieties obeys a power law, but there are different variations of it, corresponding to different types of noise. By adjusting the flow of water in the faucet (in this case, in the tube connecting the two buckets), you can make the frequency with which the drops fall, more or less chaotic.

Here is a power law:


Pretty simple, huh? Its main part is the exponent β. When it is zero, this means that we can expect perfect white noise. As β changes, the fraction quickly rushes to very small values. This is a general definition of a power law: an intense accumulation of probabilities in one narrow range, and these probabilities change very quickly if we go a little beyond its limits.

Graphically:


Indian researchers, who published their findings last week at arXiv, took temporary readings from the drops at the time of their collision with a metal bowl located directly under the "tap". These collisions were recorded in the form of a table containing graph points, with the help of which it was subsequently possible to determine the droplet frequencies.

“At this point, our research turned into a musical study,” wrote Sakharveyd and Dasgupta. “To determine the noise level having a chaotic nature, we drew information about the time of droplets falling into frequencies, taking the difference between the two closest beats of the drops and using the formula f = 1 / (δt), and then scaled them to an audible range. After that, we tuned these frequencies to the notes of the pentaton major C-to-Sharp gamut, which allowed us to relate the frequencies to our intuitive understanding of music. ”

So we got automatic music, created thanks to various types of chaos, drainpipes and GarageBand (as well as MatLab).

“In the next part of the experiment, we listened to the compositions thus obtained and selected three of them, corresponding to the three water flow rates, which, in turn, correspond to completely predictable, random and random noise levels,” explain the physicists. "Then we carried out a spectral analysis of the data obtained in order to obtain the parameter β after carrying out a linear approximation by points of the graph."

The study was conducted if we set aside a clever demonstration of the transformation of chaos into music, to make sure that the power law continues to operate when compared with actual chaos (installation with a tap). “The range of β suggests that the music created by man maintains a balance between predictability (β = 2) and randomness (β = 0),” concludes the article. So, the patterns themselves do not create music, noise is also involved in this process.

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