An algorithm to compute fingering for string instruments

Introduction To the aims of investigating the automatic music performance, that is in computing gestures and controls and in transmitting them to sound synthesis equipment [Roads, 1985], we pursue an approach that is cognition-based, and relies on a physical model in order to define a strict relationship between the score in input and the sound produced. The music performance process involves several representational levels [Moore, 1990], such as physical, perceptual, operational, symbolic, structural. Consequently, a performance environment should be concerned at least in: i) getting a score in input (symbolic level), ii) analysing it, like a human performer would do (structural), iii) modelling the constraints posed by body-instrument interaction (operational), iv) manipulating sound parameters (physical). It should be pointed out that passing from the symbolic level to the physical level requires filling a gap: while the first one specifies some notes to play, the latter one provides the actual gestures that an executor would perform. While there exist some satisfactory solutions at level iv) (e.g. in the case of the guitar, the physical model described in [Cuzzucoli & Lombardo, 1999]), levels ii) and iii) are still open problems. In general terms, operating at the boundary between operational and physical levels enables to simulate gestures and controls of human performer, by investigating the interaction between the performer and the instrument, and manipulating sound parameters accordingly. In particular, in the present work we focus our attention on a problem present in both structural and operational levels, and very relevant for string instruments, namely the problem of fingering. Fingering is the process that, given a sequence of notes or chords (set of notes to be played simultaneously), yields to assigning to each note one position on the fingerboard and one finger of the left hand. Although it is often non-included in music scores, fingering is recognized to significantly affect the technical and expressive qualities of a musical performance [Sloboda, 1985], to such an extent that “a significant part of music instruction and pedagogy is concerned with assisting the learner to choose fingerings that will best achieve an intended performance” [Parncutt et al., 1997]. This topic has been addressed both by psychologists and computer scientists: Parncutt et al. [1997] propose an ergonomic model for short fragments of keyboard music, that features a two-step control strategy: generation of all the possible fingerings and ranking of fingerings through the application of preference rules on ergonomic difficulty. On the other side, an algorithmic approach in [Sayegh, 1989] proposes a computationally efficient solution, based on a shortest path algorithm, to the fingering process in string instruments.