GUITAR FINGERING FOR MUSIC PERFORMANCE
Daniele Radicioni
Centro di Scienza Cognitiva
Universita' e Politecnico di Torino
Via Po, 14 - 10123 Torino, Italy
ABSTRACT
This paper presents a computational model of fingering
for string instruments, based on a graph search approach.
The implemented fingering model, which accounts for the
bio-mechanical constraints of the performer's hand, is interfaced with a physical model of the classical guitar, which
exploits the fingering to compute some sound synthesis
parameters. The output of the system is validated against
the performance of a human expert.
1. INTRODUCTION
Fingering is a cognitive process that maps each note on
a music score to a fingered position on some instrument.
Fingering involves several competences: i) musical analysis (including both structural and aesthetical issues), for
the interpretation of the notes in input, ii) physical constraints, posed by the instrument where the notes have to
be played, iii) bio-mechanical constraints, which characterize the possible figures of the hand. However, despite
the salience of fingering in music performance, scores often lack of fingering indications, considered unnecessary
(being common knowledge within a certain musical practice) or an execution choice. In the present paper we propose a general model for providing pieces with fingering, and we focus on physical and bio-mechanical constraints, leaving the contribution of musical analysis to a
later work.
The fingering problem consists in determining for each
note in the score, a position <string, fret> on the fingerboard and a finger of the left hand that presses it. The
notion of position provides a unique identifier for the correspondence between the note and the fingerboard. Afingered position is the triple <st ring, f ret, f inger>, combining a position with one of the four available fingers.
Provided that guitarists do use four fingers of the left hand
(from the index to the little finger), rt notes generate up to
4Th different fingerings. Since the same note can be found
on up to 4 positions (Figure 1), this number might grow
up to 16Th.
Works from several scientific areas approached fingering for its contributions to music performance [9]. Heijink & Meulenbroek [3] have carried out ergonomic and
motor behavioral studies based on the complexity factors
Vincenzo Lombardo
CIRMA,
Centro di Scienza Cognitiva,
Dipartimento di Informatica
Universita' di Torino
Corso Svizzera, 185 - 10149 Torino, Italy
frets 0 1 11 111 IV V i vil V illVIX X XI XiI
n 2 -6 -1 74 75
6 41
Figure 1. Outline of the notes (indicated as MIDI numbers) on a guitar fingerboard, showing that the same tone
can be found on up to 4 different positions, i.e., the case of
E treble (MIDI number 64), that lies at <1, 0>, <2,r5>,
<3, 9>, <4,r14 > (the figure displays only the first XII
frets). The fret 0 indicates notes produced by plucking the
string without pressing any fret.
that are implied in left hand movements of guitarists. In
the modeling area, Parncutt et al. [5] (lately updated by
Jacobs [4]), on piano playing, and Sayegh [8] on the guitar, have implemented the principle of penalizing difficulties. Cabral et al. model [1] also includes frequency in the
repertoire.
In previous papers we have addressed two separate cases of translating the notes in the score into the actual executor's gestures, namely the case of melodies of individual notes [6], and the case of isolated chords [7]. In this
paper we improve the fingering model in accounting for
both cases, so that it assigns fingerings to melodies that
also include chords and polyphonic passages (e.g., when
a note is held, and new notes are to be played). The overall methodology transports Parncutt ergonomic approach
[5] from keyboard to guitar, and shares the graph search
framework with [8]. The novelties of our approach lie
in the facts that we tackle melodies formed by individual
notes and chords, by applying the same physical and biomechanical sources of difficulty to both succession and
simultaneity of positions, and that we provide an experimental validation of the approach.
2. FINGERING AS GRAPH SEARCH PROBLEM
Given a music score, we build a graph that represents all
the possible fingered positions sequences. For each note
from left to right in the score we generate all the possible fingered positions for that note (Figure 2). This con
