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On the emergence of Zipf's law in music
##manager.scheduler.building##: Edificio Santa Maria
##manager.scheduler.room##: Auditorio San Agustin
Date: 2019-07-08 11:45 AM – 03:30 PM
Last modified: 2019-06-22
Abstract
Zipf's law is one of the most robust statistical properties found in written texts.
This law establishes that when the words in written texts
are ordered according to their frequency of apparition, the rank-frequency distribution follows a power law with an exponent close to one. Interestingly, this law is also
observed in many natural and human systems such as, the frequency
of opening in chess databases, the intensities of solar flares, and the wealth
distribution of the richest people (Pareto law), just to mention few examples.
In particular, Zipf's law seems to be manifested in music which
is usually considered as another form of human language.
Power laws emerges in music when several metrics are used to analyze music records, for instance, pitch, duration, notes, melodic intervals, and harmonic consonance. However, it is still under debate what the natural Zipfian units are.
Finding the proper Zipfian units in music is a difficult task because at variance with
texts music lacks of a functional semantic, therefore it is no easy to identify
an analogous of the concept of words in music.
This open the question of which are the proper Zipfian units in music, and also
in other natural systems. This is an important question, since even in the case
of written texts several alternatives have been proposed---besides the canonical
use of words---seeking to extend the range of validity of Zipf's law.
In this work we introduce a comparative statistical analysis of musical scores
and literary texts, with the idea of introducing a general frame to validate a
natural election of Zipfian units in music.
We found that Zipf's law emerges in music when chords and notes are chosen
as Zipfian units, since both Heaps' and Zipf's law hold.
Our results are supported by a consistent analysis of the statistical
properties of music and texts, supporting the general validity of Zipf's law in human languages.
Moreover, our framework can adapted to the study of the emergence of Zipf's law
in other natural phenomena.
This law establishes that when the words in written texts
are ordered according to their frequency of apparition, the rank-frequency distribution follows a power law with an exponent close to one. Interestingly, this law is also
observed in many natural and human systems such as, the frequency
of opening in chess databases, the intensities of solar flares, and the wealth
distribution of the richest people (Pareto law), just to mention few examples.
In particular, Zipf's law seems to be manifested in music which
is usually considered as another form of human language.
Power laws emerges in music when several metrics are used to analyze music records, for instance, pitch, duration, notes, melodic intervals, and harmonic consonance. However, it is still under debate what the natural Zipfian units are.
Finding the proper Zipfian units in music is a difficult task because at variance with
texts music lacks of a functional semantic, therefore it is no easy to identify
an analogous of the concept of words in music.
This open the question of which are the proper Zipfian units in music, and also
in other natural systems. This is an important question, since even in the case
of written texts several alternatives have been proposed---besides the canonical
use of words---seeking to extend the range of validity of Zipf's law.
In this work we introduce a comparative statistical analysis of musical scores
and literary texts, with the idea of introducing a general frame to validate a
natural election of Zipfian units in music.
We found that Zipf's law emerges in music when chords and notes are chosen
as Zipfian units, since both Heaps' and Zipf's law hold.
Our results are supported by a consistent analysis of the statistical
properties of music and texts, supporting the general validity of Zipf's law in human languages.
Moreover, our framework can adapted to the study of the emergence of Zipf's law
in other natural phenomena.