"Warta (*pronounced 'varta'*) is a large lowland river, whose drainage
basin, covering the area of 54 529 km^{2}, 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
).

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.

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