Why is it that a Mozart aria sounds tuneful and pleasant, while the works of modernists like Schoenberg and Webern are dissonant and unsettling? The key lies in the arrangement of the chords that make up the harmonies of the pieces, and now Dmitri Tymoczko at Princeton University in the US has developed a mathematical model to help understand musical structure. He has been building computer models that represent chords as points in geomteric space, so it is possible to analyse the relationships between the chords. He found that chords that from pleasing harmonies tend to gather together in geometric space, whereas chords that sound dissonant are found in different regions. This research can help us to understand why certain compositions are easy or difficult to listen to, and may help composers to understand more about harmonies as they write new pieces.
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