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New Music Concepts 2018

Calculating Dissonance in Chopin's Etude Op. 10 No. 1

Part of the New Music Concepts book series (NMC volume 5)
ISBN: 978-88-6551-278-4

Author(s): Nikita Mamedov, Robert Peck

Abstract: The twenty-seven etudes of Frederic Chopin are exemplary works that display the composer's poetic musical language, combining keyboard techniques, virtuosity, and artistic imagery. Etude Op. 10 No. 1 in C Major presents the pianistic technique of playing arpeggios, where a set of ascending and descending arpeggiated sequences span across multiple octaves. This study mathematically analyzes the dissonance level of this work, using the Interval Dissonance Rate (IDR) - a technique that integrates mathematical and musical analyses and measures the amount of dissonance in a piece of music, using modified interval-class vectors (v) and the frequency of recurrent pitches (pn) to determine the percentage of dissonant (DI) and consonant (CI) intervals. There are three significant theoretical observations that can be deducted, based on the application of IDR. First, the IDR of the composition is 14.14%. Second, the B-section of the work (IDR of 16.16%) is the most dissonant and therefore, most tonally adventurous. Third, the IDR verifies that Chopin emphasizes the d2 interval-class of the modified interval-class vector for dissonance, generating tension in harmonies by using major seconds, minor sevenths, and equivalent intervals.

Keywords: Chopin, dissonance, etude, interval-class