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Page 00000001 GENERATING MUSICAL PATTERNS USING MUTUALLY INHIBITED ARTIFICIAL NEURONS Pauli Laine University of Helsinki, Department of Musicology Vironkatu 1, 00170 Helsinki. Abstract New method for generating musical patterns is presented. Method is based on mutually inhibited neuronal circuits found in biological organisms. Using this MINN-method pulsative and cyclic musical processes can be generated. The method can be used in modelling rhythmical imagining and in investigating the connections between music and movement. 1 Introduction The starting point for this research project has been cognitive oriented interest about the imaging and representation of musical material in human mind. When considered only as cultural phenomenon the music is learned and constrained by complicated cultural and social norms and rules. Very often artificial neural networks are used to model learning or to structure learned material. It has to be emphasised that method presented in this research report is not at all a learning method. The purpose for the current system is to model the musical processes in human mind which occurs when he or she is making, listening or imagining music. This is done using modelled biological pattern generators to produce test material. Further aim is to investigate the contextualization problematics of the material thus created. In further research it is of course possible to try make a model which would connect the nonlearning functions presented here and learning neural networks. When investigating music principally as an generative act by a human individual we can propose a hypothesis about representation of musical time and rhythm as a subcognitive motor oriented imagery. If this is the case then in the rhythmic and pulsative music the most important thing is to investigate the use of the mechanisms that are also used when we biologically are producing movements and rhythms. Especially interesting from the musical movement point of view is the neuronal networks which act as so called locomotive central pattern generators (CPG). Control mechanisms for CPG's have been investigated for example by Matsuoka [Matsuoka, 1987]. 2 Music, Imagining Moving and According to Jeannerod the imagining of movement activates the same neural populations as the real movement. [Jeannerod 1994]. states further that representation of movement or imaging of moving object can really be investigated using careful introspection. Our hypothesis is that mental representations of moving object is also used when imagining music. Music perception research has proposed some models which uses similar neural methods [Ohya, 1994]. In this case the listening to dance music for example would activate the same neural populations as the dance itself. 3 MINN-system Natural neural systems are capable of producing large variety of cyclical and even chaotic patterns without external impulse. [Glass 1988]. The basis of these pattern generators is usually mutually inhibited neuron populations, which in either words decrease the activation level of connected neurons. Properties of these systems have been investigated in connection with sustained locomotive motor actions like heartbeat, walking and swimming. Mathematical
Page 00000002 properties of mutually inhibited neuronal populations have been investigated among others by L. Glass and K. Matsuoka. Models for neurons can be based on so called postinhibitory rebound phenomenon. [Wang 1992] or on the utilisation of different kinds of neurons [LoFaro 1994]. Glass has noted also that biological CPGs produce complicated rhythmical patterns, which can behave chaotically. can be adjusted using aftermath parameter. Each neuron is inhibited by the neurons connected to it. For example the connected neuron pair A and B produces activation time series having locomotive behaviour. If the connection is more complicated can these activations and firings produce very complicated cyclical and even chaotic patterns. Program generates discrete time series, which can be represented graphically or saved as a list of instances of timepointcl class. Figure 2 shows graphically the result of typical test run. An instance of timepointcl has variables for activation level, firing and other time varying information. List of instances can be mapped using contextualisation function to produce MIDI-file. -O 0O Figure 1: Connections between neurons are inhibitory. Similar excitatory input for both neurons comes from outside. It is possible to change and restructure the connection presented in figure 1. It is also possible to construct a network consisting of several neurons. In biological networks different kind of networks are used for different movement tasks. Usually in our tests we have used six neurons. The larger the neuron network is the longer also comes the cycles of processes it makes. 4 Implementation Implementation of MINN-systems is quite straightforward. The program is implemented in an object oriented way where each neuronal population is represented as a neuron as an instance of neuroncl class. Together they form a network that is presented as a list. Connections between neurons are implemented by adding a reference for neuron to be connected (A) to current neuron. (B). Connection strength can be adjusted. Each neuron is connected to impulse source, which can vary from neuron to neuron or it can also be similar monotonic input to all neurons. Impulse causes the neuron activation and after enough activation the neuron fires. After firing the neuronal activation level is decreased to resting level. The decrease time 5 Contextualisation Contextualisation function means here the mapping function or the group of mapping functions that is used to convert the activation time series of MINN-system to musical output. We can say that contextualisation function defines sparse cultural context, like very narrow musical style which is coupled with network activity. When MINN-output is mapped one dimensionally, like array, we can investigate time-related objects only. This means that only the rhythm is present in the mapping. The mapping function can then insert a drumbeat or a note onset to places where there is a neuron firing. To investigate the possibilities of multidimensional MINN-networks, also the pitch (and dynamics) is used in the mapping. We have to choose a way to interpret the MINN-list of timepointcl instances using the linear continuum like pitch. One interpretation could be, that neuronal activation levels represent the motor movements of an instrumentalist, who is playing rhythmically. The activation levels could be the neuronal control signals controlling the motoric movements of fingers (or the imagination of rhythmic finger movements). In this case there is an analogy from the activation level to the actual pitch. We have to remember though that going over certain physical boundaries in actual music
Page 00000003 -......-- -... -.. --.. -..--.-.- ~-. \.-.....~. Neuron 1 activation I I I I I I I I I I I I I I I I I I I I I I I Figure 2: Example of typical MINN test run - amplOd. Small circles indicate neuron firing. Larger circles indicate that mapping to note is done for this neuron firing. playing, like over an octave is not reached linearly. It is not usually done only by adding activation the neurons controlling the muscle stretching, but nonlinearly by making a hand movement, which means using other group of controlling neurons.. In practice the mapping function is constructed by combining the activation level and the hierarchical position of each individual neuron. Using the mapping function musical process is generated which reflects the network activity and also the activity in each of the individual model neurons. The mapping function also transfers the values to some given musical scale. It is also possible to take harmonisation in to account, but this has not been done yet. 6 Results Using described MINN-system it has been possible to generate large variety of rhythmical figures and both cyclic and repeating processes. During the tests several different network architectures have been tried also using different parameters. Also the effect of different has been tested. The results have been compared against systematic passages in baroque music. In Figure 3 there is shown notation transcribed and contextualised from the test visualised in Figure 2. We can remark that generated passage resembles some passages in real music like sequences in J. S. Bach's music or accompaniment figures in Beethoven's piano sonatas. Contextualisation used here is very simple and sparse when compared to complicate harmonisation and voice leading schemes in real music.
Page 00000004 j j -iF ~ MIDIl --j a a 4 jJJ]ZJ] -i EjFT2 7 10 Figure 3: MINN test ampolOd contextualised to notation. Functioning of the process can be seen in neuronal firings and dynamics. Because the process was very active the rhythm is continuous and there are no pauses or even longer notes. 7 Concluding remarks and further research The method presented in this research report is aimed to be a start a series of cognitively motivated algorithmic music generation functions. Using these simulation tools we try to understand the possible mechanisms which have been used to make some piece of music or some part of it. MINN-system is forming a basis for different test algorithms and mapping functions. Possible directions for the future research includes feedback from controlled motor systems, contextualisation with more stylistic features, architectural improvements, and learning using the MINN-coded musical patterns. Of these directions, learning is maybe the most interesting because it can help us to understand the mental mechanisms which able us to remember and use long musical processes. References [Glass 1988] Glass L & Mackey M. C., From Clocks to Chaos - The Rhythms of Life. Princeton University Press 1988. [Jeannerod 1994] Jeannerod M., The Representing Brain - Neural Correlates of Motor Intention and Imagery. Behaviour and Brain Sciences. Vol. 17, no: 2. March 1994. [LoFaro 1994] LoFaro T., Kopell N., Marder E., Hooper S., Subharmonic Coordination in Networks of Neurons with Slow Conductances. Neural Computation Vol. 6 No:1 Janary 1994. [Matsuoka, 1987] Matsuoka K., Mechanisms of Frequency and Pattern Control in the Neural Rhythm Generators. Biological Cybernetics 56, pp. 345 -366 (1987). [Ohya, 1994] Ohya K., A Rhythm Perception Model by Neural Rhythm Generators. Paper for ICMC94. Proc. pp. 129-130. [Wang 1992] Wang X-J.& Rinzel J., Alternating and Synchronous Rhythms in Reciprocally Inhibitory Model Neurons. Neural Computation 4, pp. 84 - 97 (1992).