Surveyor 2Triangulation is a research technique that involves looking at the same thing from two different perspectives. In surveying, it enables positions and distances to be calculated by measuring angles from two locations. In the social sciences, it can increase the reliability of conclusions if they are found by two (or more) different methods. And in statistical historical musicology, looking for the same works or composers in two or more datasets can tell us a lot about the characteristics of the datasets, and about the works’ patterns of survival or dissemination.

Once you have a sample of data from one source, the process of triangulation simply involves looking up each entry in another source. Sources used for triangulation therefore need to be searchable, which is often the case even if they are not easily samplable (‘black-box’ datasets such as AllMusic or iTunes are easily searchable, but difficult or impossible to sample from, for example).

There are three main reasons to triangulate an existing sample. One is simply to get additional details – a sample of composer names, for example, might need to be triangulated against a different source to find birth dates and nationalities. The second reason is to check the existence or otherwise of the works or composers in other sources. A sample of works and composers from Pazdirek,1 for example, was triangulated against a range of modern sources including library and record catalogues and online encyclopedias, revealing that only about 50% of the composers and 25% of works were found in any of the modern sources. The third reason is to compare information across sources, such as looking at how different editions of the Penguin Record Guide assess the same composer, work, or recording.

Triangulation is a useful technique for finding out both about the dynamics of the population of works or composers, and about the sources we use. The Pazdirek example above, for example, reveals something about the rate at which composers and works fall into obscurity – in this case between the first decade of the twentieth century (when Pazdirek compiled his handbook) and the beginning of the twenty-first. Triangulating a sample of works from the first half of the nineteenth century against modern sources reveals that the surviving works from that period are twice as likely to be available as recordings as to have been recently performed in concert, and twice as likely to have been recently performed as to be currently in print. There are lots of other examples where triangulation can provide insights into how music survives over time, moves across borders, or materialises in different forms.

Triangulation also gives us a way of comparing sources against each other, showing, for example, how the various large nineteenth-century biographical dictionaries by Gerber, Fétis, Grove, Mendel and Eitner appear to have drawn on similar sources, and on each other, to varying extents; or that the ‘Chronology of Composers’ by Detheridge shows the same pattern of biases as Grove, which was almost certainly used as the main source.2

All datasets are biased in some way, and it is almost impossible to assess the extent of any absolute bias. Triangulation, however, is a way of measuring relative bias which, if done across several sources, can provide a useful indication of absolute bias. So a larger proportion of British composers in Grove compared with Gerber, Fétis, Mendel, Eitner and other sources is suggestive of an absolute bias (perhaps not surprisingly) by George Grove in favour of his fellow countrymen.

One of the hazards of triangulation is that sources may name composers or works differently. Sometimes the variations are easy to spot – Fétis, for example, ‘frenchifies’ all names and places (e.g. ‘Louis de Beethoven’) – but often the differences can be very difficult to track down. It was only in the last century or so that the numberings of Haydn’s and Mozart’s symphonies were standardised, for example, so the numbers given in the titles of early publications are not necessarily those of the works you would expect. The maiden names, married names, titles or pseudonyms of women composers, in particular, may appear differently between sources, and these are impossible to match up without a list of possible variants. Oxford Music Online is useful for this, listing variant names at the top of each biographical entry.3 Among composers born before 1800, and speaking French, German, Italian, Russian or any of the Scandinavian or East European languages, over 40% have more than one variant surname, with around 175 surnames per 100 individuals. The incidence of variant names is lower for later composers and other languages. For lesser-known composers not appearing in sources such as Oxford Music Online, variant names can be a significant problem.

Whilst some progress can be made using semi-automatic techniques to search for works and composers, and to deduplicate them across different sources, triangulation often turns out to be a time-consuming, largely manual process. But, as is the case in most statistical research, time and effort spent in collecting the right data in the right form is always worthwhile.

Cite this article as: Gustar, A.J. 'Triangulation' in Statistics in Historical Musicology, 24th January 2018,
  1. Further details can be found on the Printed Music Datasets page.
  2. Details of these sources are on the Composer Datasets page.
  3. One of the longer examples is: “Cavalli [Caletti, Caletto, Bruni, Caletti-Bruni, Caletto Bruni], (Pietro) [Pier] Francesco.”

Leave a Reply

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.