The music of the river Warta

The concept

"Warta (pronounced 'varta') is a large lowland river, whose drainage basin, covering the area of 54 529 km2, lies entirely within the boundaries of Poland." (from 'Fractal analysis of flow of the river Warta' by Z.W.Kundzewicz and M.Radziejewski , where what follows was described shortly).

This page is devoted to a simple idea that I've got a few years ago: Take a series of values of monthly mean flows of a river and play them as a tune, using the values as pitches of subsequent notes.

For this to work and be bearable to a human ear (trained to hear specific intervals) we have to round each pitch at least to the nearest half-tone. The nearest tone in the pentatonic scale is a much better choice, however, as it adds more harmony to the tune. Initially the notes will be of equal lengths, but because of the rounding, some successive notes may turn out to have equal pitches and sound as a single, longer strike.

Of course instead of the river flow values, one can take any sequence of numbers describing the evolution of a natural phenomenon in time. The ones I took were the series that have naturally emerged from a project in which I was involved. They were all transformed versions of natural series - 'transformed' means that they were rescaled, sometimes replaced by series of monthly means and in some cases the values described the flow speed relative to the typical flow speed in the same season (i.e. the series was deseasonalised).

You can listen to the effect by choosing one of these links:

Important: please click here to read the disclaimer first! Proceeding further means that you have accepted and agreed to the disclaimer .

Please click here to download a tiny program that I have written (compiled for the PC). The Pascal source code and necessary data files are included.

If you are using another platform, you may wish to download the source code and data files alone.

This is a version of my favourite Warta tune in the MIDI format.

My favourite is a piece obtained from the Warta flows by rescaling, deseasonalising and taking monthly means. You can hear it, if you invoke the program by entering musicbox 7 .

One more detail still has to be sorted out: the way in which the flow values are converted to pitches. The program above lets you have the values shifted by one parameter and multiplied by another. The result is interpreted as the logarithm of the note's frequency (in Hz), which is close to the normal understanding of pitch. The two parameters are necessary to put the melody into the domain of human perception. We couldn't appreciate it, if it consisted of ultrasounds only or if it were almost constant. Special care has to be taken to chose proper values of the parameters, as the aesthetic value of the tune depends on them highly (see credits ).

The background

Mathematical analysis of music has revealed, that spectral properties of musical scores often show remarkable similarities to those of the so called 1/f noise (see for example Random fractal forgeries by R.F.Voss, in Fundamental algorithms for computer graphics ed. by R.A.Earnshow).

The term  1/f  noise   was actually coined to describe spectral characteristics observed in many natural processes. Various methods have been developed to investigate such properties and to mimic them in artificially generated data. That has naturally lead to the idea of artificial generation of music, as described in the above mentioned article (for instance). But given that, what could be more natural than just taking a natural process and interpreting it as music? I am surprised that nobody mentions this more direct way. Surprising as it is, it's probably not true. I'm sure people have thought about it before, I just haven't found it anywhere.

I have tried several approaches to mathematical generation of music, but the results I have got were much less pleasing than those obtained for natural series. I have also tried to use an artificial series with spectral properties identical to those of Warta, following the same procedure as for Warta, but it didn't sound nice at all. There must be something more to it than spectral densities and the intervals of pentatonic scale. That would serve to show, that the musicality of the Warta score (if you find it has any) is not an artefact of transformations, aggregation and rounding, but a result of the omni-present harmony of nature.


I would like to thank Professor Zbigniew W. Kundzewicz for supporting the idea. Special thanks to Mrs. Malgorzata Chalupka for invaluable help in finding the best parameters for the Warta tune.

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To send me an e-mail, it should be enough to click on my name: Maciej Radziejewski.