Information content of note transitions in the music of J. S. Bach
Music has a complex structure that expresses emotion and conveys information. Humans process that information through imperfect cognitive instruments that produce a gestalt, smeared version of reality. How can we quantify the information contained in a piece of music? Further, what is the informatio...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2024-02-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.6.013136 |
| _version_ | 1797210275431055360 |
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| author | Suman Kulkarni Sophia U. David Christopher W. Lynn Dani S. Bassett |
| author_facet | Suman Kulkarni Sophia U. David Christopher W. Lynn Dani S. Bassett |
| author_sort | Suman Kulkarni |
| collection | DOAJ |
| description | Music has a complex structure that expresses emotion and conveys information. Humans process that information through imperfect cognitive instruments that produce a gestalt, smeared version of reality. How can we quantify the information contained in a piece of music? Further, what is the information inferred by a human, and how does that relate to (and differ from) the true structure of a piece? To tackle these questions quantitatively, we present a framework to study the information conveyed in a musical piece by constructing and analyzing networks formed by notes (nodes) and their transitions (edges). Using this framework, we analyze music composed by J. S. Bach through the lens of network science, information theory, and statistical physics. Regarded as one of the greatest composers in the Western music tradition, Bach's work is highly mathematically structured and spans a wide range of compositional forms, such as fugues and choral pieces. Conceptualizing each composition as a network of note transitions, we quantify the information contained in each piece and find that different kinds of compositions can be grouped together according to their information content and network structure. Moreover, using a model for how humans infer networks of information, we find that the music networks communicate large amounts of information while maintaining small deviations of the inferred network from the true network, suggesting that they are structured for efficient communication of information. We probe the network structures that enable this rapid and efficient communication of information—namely, high heterogeneity and strong clustering. Taken together, our findings shed light on the information and network properties of Bach's compositions. More generally, our simple framework serves as a stepping stone for exploring further musical complexities, creativity, and questions therein. |
| first_indexed | 2024-04-24T10:08:00Z |
| format | Article |
| id | doaj.art-f19002ed69cf49d09858438124f5dac9 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:08:00Z |
| publishDate | 2024-02-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-f19002ed69cf49d09858438124f5dac92024-04-12T17:38:53ZengAmerican Physical SocietyPhysical Review Research2643-15642024-02-016101313610.1103/PhysRevResearch.6.013136Information content of note transitions in the music of J. S. BachSuman KulkarniSophia U. DavidChristopher W. LynnDani S. BassettMusic has a complex structure that expresses emotion and conveys information. Humans process that information through imperfect cognitive instruments that produce a gestalt, smeared version of reality. How can we quantify the information contained in a piece of music? Further, what is the information inferred by a human, and how does that relate to (and differ from) the true structure of a piece? To tackle these questions quantitatively, we present a framework to study the information conveyed in a musical piece by constructing and analyzing networks formed by notes (nodes) and their transitions (edges). Using this framework, we analyze music composed by J. S. Bach through the lens of network science, information theory, and statistical physics. Regarded as one of the greatest composers in the Western music tradition, Bach's work is highly mathematically structured and spans a wide range of compositional forms, such as fugues and choral pieces. Conceptualizing each composition as a network of note transitions, we quantify the information contained in each piece and find that different kinds of compositions can be grouped together according to their information content and network structure. Moreover, using a model for how humans infer networks of information, we find that the music networks communicate large amounts of information while maintaining small deviations of the inferred network from the true network, suggesting that they are structured for efficient communication of information. We probe the network structures that enable this rapid and efficient communication of information—namely, high heterogeneity and strong clustering. Taken together, our findings shed light on the information and network properties of Bach's compositions. More generally, our simple framework serves as a stepping stone for exploring further musical complexities, creativity, and questions therein.http://doi.org/10.1103/PhysRevResearch.6.013136 |
| spellingShingle | Suman Kulkarni Sophia U. David Christopher W. Lynn Dani S. Bassett Information content of note transitions in the music of J. S. Bach Physical Review Research |
| title | Information content of note transitions in the music of J. S. Bach |
| title_full | Information content of note transitions in the music of J. S. Bach |
| title_fullStr | Information content of note transitions in the music of J. S. Bach |
| title_full_unstemmed | Information content of note transitions in the music of J. S. Bach |
| title_short | Information content of note transitions in the music of J. S. Bach |
| title_sort | information content of note transitions in the music of j s bach |
| url | http://doi.org/10.1103/PhysRevResearch.6.013136 |
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