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On the emergence of Zipf ’s law in music
ظهور قانون Zipf در موسیقی-2020 Zipf’s law is found when the vocabulary of long written texts is ranked according to the
frequency of word occurrences, establishing a power-law decay for the frequency vs rank
relation. This law is a robust statistical property observed even in ancient untranslated
languages. Interestingly, this law seems to be also manifested in music records when
several metrics – functioning as words in written texts – are used. Even though music
can be regarded as a language, finding an accurate equivalent of the concept of words
in music is difficult because it lacks a functional semantic. This raises the question of
which is the appropriate choice of Zipfian units in music, which is extensive to other
contexts where this law can emerge. In particular, this is still an open question in
written texts, where several alternatives have been proposed as Zipfian units besides
the canonical use of words. Seeking to validate a natural election of Zipfian units in
music, in this work we find that Zipf’s law emerges when a combination of chords and
notes are chosen as Zipfian units. Our results are grounded on a consistent analysis of the
statistical properties of music and texts, complemented with theoretical considerations
that combine different reference models, including a simple model inspired in the
Lempel–Ziv compression algorithm that we have devised to explain the emergence
of Zipf’s law as the consequence of languages evolving into more efficient forms of
communication. Keywords: Zipf Pareto Heaps information music |
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