On the Usage of Musical Keys: A Descriptive Statistical Perspective
Ethan Paik Marzban, Caren Marzban · 2014
A great deal has been written about the affinity between composers and musical keys. For instance, it is well-known that Mozart composed the majority of his works in the key of C major, and that some of Beethoven's most popular works are in the key of C minor. But little is written about composers’ least used keys, or more generally about their usage of all keys. Here, a methodology is proposed which allows one to 1) concisely describe a composer’s usage of keys, and 2) compare different composers in terms of their key usage. The main tool underlying the former is the key histogram, and the latter is displayed in terms of the scatter plot of keys and further quantified by the correlation coefficient. The comparison itself is performed in two ways: 2a) pairwise, between all composers, and 2b) by comparing each composer's key histogram with a “gold standard” key histogram (e.g., key histogram across all composers). The former allows for a focused comparison of key usage between two composers, while the latter is useful for ranking of the composers in terms of their key usage. The method is demonstrated on a list of ten composers. For example, it was found that Mozart composed primarily in the keys of C, D, E, F, G, and E-flat; and with very few to no works in any other key. By contrast, Rachmaninoff’s works appear in every key, with near-equal frequency (as assessed by the chi-squared statistic). The pairwise Home Submit Archive Contact comparisons show that some expected similarities between composers (e.g., Haydn and Mozart), as well as some expected dissimilarities (e.g., Haydn and Rachmaninoff), can be placed on a firm, quantitative setting. The comparison of the individual composers' key usage with the key usage across all ten composers, suggests that Rachmaninoff and Schubert occupy the extremes, respectively least similar and most similar to the key usage across all ten composers.