FAREY SEQUENCES MAP PLAYABLE NODES ON A STRING. (January 2020) - Nicholson, Thomas; Sabat, Marc
Abstract: Natural harmonics, i.e. partials and their harmonic series, may be isolated on a vibrating string by lightly touching specific points along its length. In addition to the two endpoints, stationary nodes for a given partial n present themselves at n − 1 locations along the string, dividing it into n parts of equal length. It is not the case, however, that touching any one of these nodes will necessarily isolate the n th partial and its integer multiples. The subset of nodes that will activate the n th partial (termed playable nodes by the authors) may be derived by following a mathematically predictable pattern described by so-called Farey sequences . The authors derive properties of these sequences and connect them to physical phenomena. This article describes various musical applications: locating single natural harmonics, forming melodies of neighbouring harmonics, sounding multiphonic aggregates, as well as predicting the relative tuneability of just intervals.