The Interval Dissonance Rate: An Analytical Look into Chromaticism of Chopin’s Op. 10 No. 2 and Scriabin's Op. 11 No. 2

Nikita Mamedov and Robert Peck
Proceedings of Bridges 2017: Mathematics, Art, Music, Architecture, Education, Culture
Pages 475–478 Short Papers


The concept of dissonance and consonance in music is established from two or more simultaneous notes. There are multiple approaches into dissecting this concept; some of these are acoustical, psychological, and mathematical. An Interval Dissonance Rate (IDR) is an innovative tool that integrates musical and mathematical analyses in non-monophonic Western music, using interval vectors and the frequency of recurrent pitches in the vectors to determine the percentage of dissonant and consonant intervals. Two tonal pieces with musical chromaticism by Frédéric Chopin and Alexander Scriabin are used for IDR analysis. According to results, the IDR of Chopin’s Étude Op. 10 No. 2 is equal to 17.65%, while the IDR of Scriabin’s Prelude Op. 11 No. 2 is equal to 29.37%. The IDR also allows one to look for intervallic patterns of various composers and in music of specific genres.