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Published on: October 29, 2018
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Renormalization-group approach to ordered phases in music.
Ryan Buechele1, Jesse Berezovsky2
1Department of Physics, <a href="https://ror.org/00rs6vg23">The Ohio State University</a>, Columbus, Ohio 43210, USA.
Physical Review. E
|August 20, 2024
Summary
This study models music's ordered structure using physics' phase transition principles. Renormalization-group techniques reveal new musical phases and correlations beyond prior models, suggesting novel music generation.
Area of Science:
- Physics
- Music Theory
- Complex Systems
Background:
- Music organization parallels emergent ordering in physical systems during phase transitions.
- A prior mean-field model explored pitch organization in music.
- Understanding music structure can benefit from physical system analogies.
Purpose of the Study:
- To investigate the effects of dimensionality and local correlations on music's ordered structures.
- To extend a previous mean-field model for musical pitch using renormalization-group techniques.
- To uncover new musical phases and correlations not predicted by mean-field approaches.
Main Methods:
- Application of renormalization-group techniques to a model of musical pitch.
- Analysis of lattice dimension effects on the system's phase diagram.
- Computation of nearest-neighbor correlations within the model.
Main Results:
- Convergence of the phase diagram with increasing lattice dimension was observed, corroborating mean-field model results.
- New musical phases, not identified by the mean-field model, were uncovered.
- Nearest-neighbor correlations were computed and compared to both the mean-field model and historical tuning systems.
Conclusions:
- The renormalization-group approach reveals new insights into music's structure beyond mean-field approximations.
- The identified new phases and correlations offer potential for novel music generation.
- The study bridges concepts from statistical physics and music theory to explain emergent order.
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