Nowadays, the deep learning technics used in the algorithms of computer music generation are rapidly developing. One of the common problems of the deep learning-based methods is the successful reproduction of music score sequences within the short time intervals as well as on long ones. To solve it, one may use so-called hierarchical models, which typically lead to a computational load. Earlier systems based on evolutionary computation methods, especially genetic algorithms, had already proven their ability to model variations of musical sequences within the long time scales. The purpose of the presented study is to demonstrate how to incorporate deep learning models, evolutionary computations, and rule-based computer music generation technics to approach the most e ective features of each one technic correspondingly. The paper presents the combined method of music sequence generation based on a distributed genetic algorithm with the Variational Autoencoder(VAE) genotype-to-phenotype mapping. The research includes experimental investigation of the latent space vectors evolutionary driven dynamics, to gure out the ways of how one can achieve the state of a controllable evolution process. The paper also presents the set of rule-based approaches to modify system-generated music sequences to meet predictable high perceptual di erences at the low computational costs. The outcomes of the genetic algorithm runs at the various numbers of agents and di erent mutations are given, together with several examples of music scores, generated within the research.
Algorithmic music generation, also known as algorithmic music, has a long history of development, originated in the days of Mozart to undergo the rapid Copyright c 2019 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0). progress due to co-evolution with the informational and communicational technologies. Comparing to the days of Illiac Suite by ILLIAC I (Illinois Automatic Computer) mainframe coded by Lejaren Hiller in 1957, the state-of-art software allows user to have his/her own pocket mobile `Illiac' running on iOS/Android. Meanwhile, the computational advantage still not able to reach the singularity frontier for the computer music systems, mostly because of the simplicitycomplexity dualism of human-generated music. Human music can be simple to its extreme, but at some particular moment, one little pause, or unexpected modulation can turn several measures into the masterpiece. The authors' present study continues their previous research in the eld of distributed computer music generation systems, aimed to set of competing agents, for imitation of humanfeatured process of selection between several creative thoughts. 2
Computer music generation remains one of the problems of machine creativity.
Since 1960s, applied technics has been evolved from simple rule models and
Markov chains [
Nevertheless, while technics based on deep learning models appear to be most
advanced, there some known limitations of the usage of them:
{ deep learning methods do not actually compose a new piece of music, but
rather produce a sequence of notes, which is statistically equal with the given
dataset; thus the new genre could not appear in such generation model;
{ complex hierarchical models are to be applied to achieve good results for
generation pieces in long time ranges [
On the other hand, evolutionary computation-based methods are proven to
provide a way to model music melody variations on long time scales [
In [
It has been shown that VAEs and GANs can be used to perform the
genotypeto-phenotype mapping, performing the interactive evolutionary computation for
image generation[
We propose the following technique for in nity personalized music generation, based on the genetic evolution of latent vectors (see gure 1): { the distributed genetic algorithm is used as an attractor for the music generation; each agent in the system is associated with the one user; all agents together form the population for the genetic algorithm; { VAE is used for the genotype-to-phenotype mapping; { each agent has a target state, the distance to that is used as the tness function; { the agent target states are set by users, mapped to the natural language descriptions; { at each system run loop step, agents obtain the states of others to perform the next iteration of the genetic algorithm.
The current version of the system model is available online3. MusicVAE
autoencoder[
In the experiments, the following genetic algorithm realization was implemented: { agent get current states of all other agents in the system; { the Hamming distance closest to the current target state agent is determined; { single point crossover runs at current and closest agents providing two new children candidates; { system speci ed number of random mutations runs; { closest to the target state candidate replaces current agents state. The model system has the following variable parameters: { N - number of agents; { lch - chromosome length; { pm - number of mutations after crossover; { l - gen's alphabet length. where c1 and c2 are some constants de ned by system con gutaion.
Figure 4 and 5 show the in uences of mutation probability, and the number of agents on the median distance of current agents states to the target ones for di erent chromosome lengths. With the growth of chromosome length number of agents required to achieve relatively close stable distance to the target increases.
Figure 6 shows the decay of the distance to the target state with the agents' population size. For a given chromosome length stable distance to target state may be approximated with an inhibitory dose-response curve, Dst: Dst
lch 1 + ( cN2 )c1 ; Dst lch(1 e c1l ); (2) (3) where c1 and c2 are constants de ned by system con gutaion.
Figure 7 shows the growth of the stable distance to the target state with the alphabet length. For a given population size stable distance to target state Dst: where c1 is a constant de ned by system con gutaion.
Provided analysis of the distributed genetic algorithm behavior on system variable parameters is to be used to keep the correct run. As the genetic algorithm is used not for optimization but generation, it should always be close enough to the extremum but never stack on it. Random mutations may be used to prevent continuous repeats of every solution. If there are not enough agents to be close enough to the target system may generate virtual ones. 4
Figure 8 gives an example of a generated sequence of the 16 bar length. Note that implemented VAE was trained to produce the 2 bar length sequences. One can notice that the presented sequence is in the key of B- at minor. The melody generally remains within the selected tonality. We must admit that with the described approach on the long timescales (32 to 64 bars) system 'losses' memory of the initial sequence and its attributes.
To get better scale stability, one may apply some algorithmic constraints
to the generated sequences. In [
After the original scale is determined, the sequence may be quantized to the
desirable one by replacing out of scale notes with the closest one from the scale.
There are also more complex algorithmic technics to determine the original
sequence's key [
Another constraint application is a rhythmic modi cation. In spite of original VAE was trained to decode latent space vectors to a sequence in four-four time signature, the generated sequence can also be easily quantized to three-four time, see gure 10, or six-eight time, see gure 11.
Rhythmic transformations may also be performed according to statistically
motivated rules. Depending on the music genre, di erent rhythmic sequences
rudiments - are more or less common [
Therefore, one of the approaches to improve nowadays' most advanced deep learning-based music sequences generation techniques is to combine them with the well- known algorithmic solutions such as genetic algorithm and rule-based constraints. This approach leads to consistent results with a low computation load. 5
The approach that has been discussed in the paper leads us to further study of the proposed distributed genetic algorithm with VAE genotype-to-phenotype mapping music generation model. The combining technics of algorithmic music proved to play a key role in the e ective composition. Di erent approaches possess their peculiar strong and weak sides, thus suitably combining them will produce a compositionally attractive outcome. Generally speaking, an agentbased approach with competing 'ideas' can be treated as a model of world music evolution, i.e. starting from the basic simple sequences, it evolved into very complex, polytonal, and even atonal structures. There are already some popular applications and online services existing. We can assume that their e ectiveness both in the sense of speed and music 'ideas' is also due to a proper combined approach. The application area of such services allows us to estimate the future of such systems. Various recreational zones, both private and public, with ability to be adjusted, i.e. to the weather conditions, daytime, team progress, wearable device data etc. In addition, as a set of assistive technologies for the human composers, virtual reality randomization e ects etc. One of the greatest features of such systems is their ability to be individualized according to the client data.