Statistical Analysis and Graphic Representation of the Correlation of Bach and Chopin Preludes

摘要

This study uses statistical techniques to compare the Roman numeral analysis of the first phrase in each of the 24 preludes composed by Johann Sebastian Bach and 24 preludes of corresponding key composed by Frederic Chopin. Bach composed a book of 24 preludes, The Well Tempered Clavier, consisting of a prelude in each major and minor key. Chopin also composed 24 preludes in each key throughout his career. Initially, this study will use Roman numeral analysis and other music theory techniques to analyze the first phrase of these works. Statistical methods will then be used to describe and compare, by key, elements of each Chopin and Bach prelude. The music analysis will be done by hand for the first phrase of each of the 48 pieces. The statistical analysis will focus on certain musical features, specifically chord frequency, chord progression, and non-chord tone frequency and use hypothesis tests and confidence intervals to quantify their differences. The results will include a graphical summary of each separate piece, composer, and comparisons of each. The results will also include p-values that illustrate the closeness of the musical elements being studied. This study will show how the relationship of these specific components of the compositions can be portrayed, and will determine how much statistical similarity there is between the components being studied. It will generally demonstrate how elements of musical compositions can be observed and measured statistically.