Complexity measures of music

Abstract

We present a technique to search for the presence of crucial events in music, based on the analysis of the music volume. Earlier work on this issue was based on the assumption that crucial events correspond to the change of music notes, with the interesting result that the complexity index of the crucial events is µ ≈ 2, which is the same inverse power-law index of the dynamics of the brain. The search technique analyzes music volume and confirms the results of the earlier work, thereby contributing to the explaination as to why the brain is sensitive to music, through the phenomenon of complexity matching. Complexity matching has recently been interpreted as the transfer of multifractality from one complex network to another. For this reason we also examine the mulifractality of music, with the observation that the multifractal spectrum of a computer performance is significantly narrower than the multifractal spectrum of a human performance of the same musical score. We conjecture that although crucial events are demonstrably important for information transmission, they alone are not sufficient to define musicality, which is more adequately measured by the multifractality spectrum.

Self‐Organized Temporal Criticality: Bottom‐Up Resilience versus Top‐Down Vulnerability

“…In that case, at criticality the mean field fluctuates around the vanishing value and the crucial events correspond to the occurrence of this vanishing value [15,23]. We follow [36] and evaluate the fluctuations around the proper nonvanishing mean value of = 1.5. To explain this choice notice that in the conventional case of criticality, generated by the choice of a proper control parameter , with = 100, = 1.5 is the value at which the onset of phase transition occurs.…”

Damage Evolution Analysis in a “Spaghetti” Bridge Model Using the Acoustic Emission Technique

“…Its calculation is schematically described in Figure 4. This type of fluctuation is widely observed in many different scientific fields, such as geology [27], finances [28], bioengineering [29], and even music [30,31], as observed in [32] and many other works. Moreover, the distributions described in Equation ( 4) is also observed to hold for frequencies ranging from fractions of hertz (in seismology) to gigahertz (microelectronics), which clearly illustrates the fractal character of this distribution and the phenomena to which it applies [32].…”

Biophotons: low signal/noise ratio reveals crucial events

“…In fact, according to Refs. [44,45] the crucial events hosted by the music of Mozart match the crucial events of the human brain. Note that the spectrum S(f ) in case when anomalous diffusion is generated by crucial events has the 1/f noise form…”

“…The recent work of Refs. [44,45] shows that the music of Mozart hosts crucial events with µ = 2. It is important to stress that according to the principle of complexity matching [46], two complex systems communicate mainly through their crucial events.…”