Power Laws in Opera

A recent addition to the Concert Datasets page is Operabase, a database of over 500,000 opera performances worldwide since 2004. I plan to look at this data more closely in a future article, but for now, I thought it would be interesting to see if opera performances follow a power law.1

Operabase’s “statistics” page gives details (among other things) of the total number of performances, both for individual operas, and for composers. Using this data, I produced the following chart showing that both of these are approximate power laws for most of the range of the data, with an exponent of about 1.7 (shown by the slope of the dotted line).

In total there were 5,328 different operas performed over the period from the 2004-5 season to the 2019-20 season. 573 of these were performed just once, but at the other extreme, La Traviata was performed 9,877 times, followed by The Magic Flute, Carmen, La Bohème, Tosca (7,149), and plenty of other big names.

2,303 composers were represented, with Verdi at the top with 41,952 performances, followed by Mozart, Puccini, Rossini and Wagner (12,010). 201 composers had just a single opera performance.

The exponent of 1.7 is, as predicted by the Law of Evenly Distributed Log-Success, not far from 2.2 The fact that it is slightly lower than two tells us that the big names (whether operas or composers) are over-represented in the split of total activity, compared to the less familiar ones. This is limited at the very top end (both curves fall more steeply on the right of the graph), probably to avoid excessive exposure of the very familiar names. It is also limited at the bottom end, suggesting some special efforts to get new and unfamiliar works performed.

Cite this article as: Gustar, A.J. 'Power Laws in Opera' in Statistics in Historical Musicology, 13th November 2020, https://musichistorystats.com/power-laws-in-opera/.

  1. See my recent papers on the subject – links are here.
  2. See the articles mentioned in footnote 1.

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