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Analyzing 20th-Century Guitar Harmonies with Discrete Fourier Transform

Editor

A new music-theoretical article, coauthored by SbS editorial board member Oliver Chandler with Isabella Thorneycroft, was recently published online and open access in the peer-reviewed journal Music Analysis. It features discussion of pieces by Leo Brouwer, Frank Martin, and Heitor Villa-Lobos, utilizing a new analytical tool, It can be read here: https://onlinelibrary.wiley.com/doi/10.1111/musa.12223

The abstract reads as follows:

One of the six-string classical guitar's most distinctive features is its unbalanced timbre. That is to say, only four pitches of the chromatic aggregate are overtonally supported by the resonances of the guitar's three bass strings. A common pitch- and structure-generating strategy, exploited by twentieth-century composers who wrote for the guitar, is bound up with this affordance. Local and global harmonic contrasts are often built around an antagonism between open-string sets and fretted harmonies that largely avoid duplicating notes associated with the open strings. Open-string/fretted binaries derive their sonic antagonism not just from timbral distinction, however, but from the fact that their pitch materials often lie at diametrically opposed positions on the circle of fifths. In many instances, this colouristic conflict replaces harmonic-functional tension as a structure-generating agent; the latter is reduced to a surface-level topic. Representative works by Frank Martin and Leo Brouwer are taken as exemplifications of this trend.

In demonstrating the subtle interactions between instrumental affordance and abstract pitch relationships and hierarchies, an invaluable theoretical approach developed by Ian Quinn and finessed by Jason Yust entails the study of harmonic quality through the discrete Fourier transform. This mathematical formula has been processed into an easy-to-use but powerful web application by Jennifer Harding – the Pitch Class DFT Vector Calculator – making its explanatory power available to music analysts without mathematical expertise. Part of the raison d’être of this article is to show how this application might be used and, more important, how the information that it yields might be interpreted.



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