Elektronika 2009-11.pdf - Instytut Systemów Elektronicznych

Generated harmonic sequence in the metrum of 3/8 Wygenerowana sekwencja harmoniczna w metrum 3/8
After thorough analysis in accordance to the theory of
tonal harmony it turned out that alleged matching errors are
non-existent or minimal.
As a matter of fact, it turned out that, in some cases, for
certain combinations of harmonic progressions and for some
tones (see tabl. 5) there was no obvious solution proposed by
the network, e.g. the network proposed two possible harmonic
functions. After performing the data analysis, it also turned out
that in some combinations of the input data, there were also
two tones proposed by the network. This means that it was
possible to choose among different tones or harmonic functions
to fullfil tonal harmony rules.
Comparing observed behavior to the real composing
process, human composers are facing the same dilemma [8].
It’s their genius, their mind, that, depending on the emotions
that are being poured down into a piece of art, makes a decision
on the tonal content, the chord, and the harmonic dependencies.
Tabl. 5. Results generated by neural network - border case
Tab. 5. Wyniki wygenerowane przez sieć - przypadek skrajny
Sounds Meaning
Network results
-0.0000
-0.0000
D 0.5000
-0.0000
E 0.5000
0.0000
0.0000
0.0000
0.0000
-0.0000
-0.0000
0.0000
0.0000
Tonic 0.5000
0.0000
Dominant 0.5000
A neural network is emotionless. It can be taught about
some dependencies and rules, e.g. that a particular tune is
sad while another is cheerful and bright. It has to be remembered,
though, that this is a subjective feeling.
How to resolve this problem?
It can be done in two ways. One of them would be to
prepare another decision degree, implemented in the neural
network, that would reflect the knowledge about emotions.
The second solution, which is considered better at this
stage, is to implement some random mechanisms, that will
automatically make the decision based on the received data.
This second solution has been chosen. In the example
presented, a harmonic sequence with the random choice of
the solution in case of a conflict is shown.
To complement the presentation of the results obtained
from designed neural network and applied procedures of input
and output data processing, a musical effect is shown in the
form of scores with the assumption of using different rhythmical
values.
As it can be observed, the effect is not perfect, because of
the visible parallelism, but this aspect of harmonic rules was
not implemented in the described issue, however it has no impact
on the conclusions made on the whole process.
Summary
It has been shown that computer with implemented neural network
methods is a useful tool to create and generate music.
Of course, these are only basics, only fundamental creation,
but with further research it will lead to the handling of more
complicated and wider musical aspects.
Because of the fundamentals of octave notation, the resolution
obtained is automatically transposable up and down the
scale, and requires only minor modifications in case of an
extension of the tone domain on more than one octave. In the
future, further work in the field of using neural networks for Computer
Generated Music is planned, as well as an attempt to implement
other parameters of musical opus, such as rhythm,
rhythmical values, or tempo. Also, attempts will be made to determine
and write emotions in a way that would allow their
acquirement by a neural network - even in a limited form.
This research will certainly contribute to the development
in the area of Computer Generated Music, both in Poland and
abroad, in the aspect of using the methods of computer
science in musicology. One can see also some possible commercial
uses of this research results in musical instruments, in
composing tools and maybe even in rehabilitation praxis.
References
[1] Baggi L. D.: Computer-Generated Music. IEEE Computer, 1991.
[2] Lerdahl F., Jakedoff R.: A Generative Theory of Tonal Music. MIT
Press, 1983.
[3] Sikorski K.: Harmonia cz. I. Polskie Wydawnictwo Muzyczne,
1991.
[4] Wesołowski Fr.: Zasady muzyki. Polskie Wydawnictwo Muzyczne,
Kraków 2004.
[5] Demuth H., Beale M.: Neural Network Toolbox: User’s guide version
4. The MathWorks, Inc., 2000.
[6] Tadeusiewicz R.: Sieci neuronowe. BG AGH, Kraków, 2000.
[7] Rutkowski L.: Metody i techniki sztucznej inteligencji. PWN, Warszawa,
2006.
[8] Gang D., Lehamnn D.: Melody Harmonization with Neural Nets.
International Computer Music Conference, Banff, 1995.
24 ELEKTRONIKA 11/2009