A quantitative approach to evolution of music and philosophy

Abstract

We propose a methodology to study music development by applying multivariate statistics on composers characteristics. Seven representative composers were considered in terms of eight main musical features. Grades were assigned to each characteristic and their correlations were analyzed. A bootstrap method was applied to simulate hundreds of artificial composers influenced by the seven representatives chosen. Afterwards we quantify non-numeric relations like dialectics, opposition and innovation. Composers differences on style and technique were represented as geometrical distances in the feature space, making it possible to quantify, for example, how much Bach and Stockhausen differ from other composers or how much Beethoven influenced Brahms. In addition, we compared the results with a prior investigation on philosophy 1 . Opposition, strong on philosophy, was not remarkable on music. Supporting an observation already considered by music theorists, strong influences were identified between composers by the quantification of dialectics, implying inheritance and suggesting a stronger master-disciple evolution when compared to the philosophy analysis.

A quantitative approach to painting styles

“…Skewness index is presented with oscillating but increasing values during all the time-series, suggesting a constant innovation through art movements. These results present an interesting counterpart with previous results in philosophy -where opposition is strong in almost entire timeseries -and in music -where the dialectics is remarkable [1].…”

“…This could reflect a strong influence role of a movement in its members together with an increasing desire to innovate, present in each artist, stronger in modernists. Both opposition, skewness and dialectics measurements can be compared with results already obtained for music and philosophy [1]. Music composers seems to be guided by strong dialectics due to the recognized master-apprentice role.…”

“…The set of all prototypes following a chronological order defines a time-series where the main purpose of this study is performed: the quantitative analysis of the historical evolution of art movements. Extending a method already applied to music and philosophy [1], opposition, skewness and dialectics measurements are taken. These concepts are central in philosophy -e.g.…”

Nano-Molar Deltamethrin Sensor Based on Electrical Impedance of PAH/PAZO Layer-by-Layer Sensing Films

“…This system revealed to be able of recognizing the taste below the biological limits and was used in the evaluation of the quality of several types of beverages in classes in accordance with taste, allowing intensity quantification as well as detection of non-electrolytic substances [12–14]. In this case the capacitive part of electrical impedance at, the frequency of 1 kHz [13], was used to describe the sensor response with quantification and classification carried out through the component principal analysis (PCA), neural networks or complex networks theories [15,16]. The production of thin layers of active molecules to be used as sensing sensor part can be achieved by the layer-by-layer (LBL) technique [17–19], which consists of the alternate adsorption from solution of positive and negative polyelectrolyte molecules.…”

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“…por apresentar alta dialética entre os músicos estudados). A Filosofia apresenta valores altos de oposição entre os representantes escolhidos (1), sugerindo que sua evolução apresenta constante oposição de ideias. Já na Pintura nota-se um outro padrão: aumento constante da inovação, baixa oposição entre membros do mesmo período artístico e picos de oposição no momento de transição entre estes períodos.…”