Fractal of Periodic Musical Elements: a re-taxonomy of music for machine learning by Adam Łukawski

The study presents a taxonomy of periodic musical progressions inspired by the properties of Shepard tones, designed for training machine learning models. It is a system, implemented in new computer software, for the synthesis and analysis of music harmony, rhythm, and dynamics in an algorithmic context. In the introduction, motivation is explained for the creation of a new music taxonomy designed for future use with machine learning. In the main part of the text, a new music notation is introduced that enables the representation of any progression of harmony, rhythm, and dynamics in a form of multidimensional arrays. Furthermore, a new taxonomy of Shepard-tone-inspired "Periodic Musical Elements" is introduced and a new method for analysis of musical material is presented together with examples. The paper discusses the benefits of using this method in the perspective of further research connected to algorithmic music composition with machine learning.

Fractal of Periodic Musical Elements

a re-taxonomy of music for machine learning

Adam Łukawski

Conclusions

In the course of this text, I presented a new music notation of harmony, rhythm, and dynamics for machine learning, based on multidimensional data matrices. I introduced a new taxonomy of periodic musical progressions inspired by Shepard tones and provided a proof that any music notated in this notation, can be analysed as a set of modified periodic progressions. The main benefit of the proposed system is the possibility of using it with AI for comparative analysis, re-synthesis and training machine learning models. What is more, the system can be directly used for music composition and analysis.

Some of the presented solutions, like the analysis algorithm, are at the early stage of development. The primary reason to develop them, is to provide a new tool for myself and other musicians in the form of a new computer software. To me as a composer, developing it is at the same time an artistic, and scientific effort, although my main motivation is artistic, not technological. In the near future, a faster algorithm for analysis based on the principles of the taxonomy should be developed, predicting the smallest amount of needed elements for analysis of the music progression. The method should be further tested in artistic practice for creative examples of music composed with Periodic Musical Elements.

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Fig. 17. Fractal of Periodic Musical Elements, first 100 sampling rates

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