Volume 10, May 2019
Intonation in the Performance of the Double Bass: The Role of Vision and Tact in Undershoot and Overshoot Patterns

by Fausto Borém and Guilherme Menezes Lage

2. Review of the Literature

Traditionally, music teachers and performers of non-tempered instruments have long believed that proprioceptive and auditory information are the main feedback sources in movement control. Auditory information is an anticipative sense (Bender, Resch, Weisbrod, & Oelkers-Ax, 2004) but, when left-hand fingers lose contact with the fingerboard, it does not produce relevant information to adjust the ongoing movement and acts solely as feedback during the fine adjustments after the note has started (Borém et al, 2006). So, musicians are left only with proprioceptive information during the movement.

Motor learning is a complex process of movement control changes over a span of time that focuses on the acquisition of skills due to practice. During the process of teaching and learning to play a musical instrument, no matter the pedagogical approach, both teacher and student usually face problems in the execution of movements essential to performance. Although Morrison and Fyk (2002, p.194) call attention to the fact that in the musician's real world ". . . intonation appears to be more negotiation than conformity. . .", they also agree that pitch control is a goal that musicians should strive for. The basic knowledge consolidated in the area of motor control can shed some light into several questions still not investigated in the field of music. This article focuses on the evaluation of pitch control skills as result of movement in a controlled environment, hence the experimental nature of this study. It is our hope to offer some insights that may partly apply to real music making double bassists face on stage.

Non-tempered orchestral stringed instruments (violin, viola, cello and double bass) have no frets on their fingerboards (as opposed to, e.g., guitar and electric bass) to indicate where the fingers must land for each note. This enormous challenge requires a high level of accuracy because slightest variations in pointing the left hand's fingers deteriorate intonation (Sloboda, 1996). The analysis of accuracy of the upper left limb movement towards a musical note in the fingerboard shows that when the finger does not reach the target, it lands either too short (undershoot) or too long (overshoot). These two types of errors, observed in movement amplitude during music performance may generate consistent undershoot or overshoot patterns caused by several factors inherent to manual movement control. Moreover, they usually reflect the participation of error correction mechanisms.

Constraint of sensorial sources in the preparation and execution (including corrections) of the movement during the gesture plays an important role in undershoot and overshoot patterns. The restriction of vision, for example, and that includes the bassist not looking at the fingerboard to play, leads performers predominantly to an undershoot pattern (Elliott et al., 2014; Proteau & Isabelle, 2002). One of the explanations is that in the programming of movements directed to a target, two phases take place. Initially, a subcomponent of the movement is generated, which tends to undershoot the target. Subsequently, as the limb approximates the target, final corrections need to be made to reach the objective precisely. However, these final corrections are performed with higher accuracy when the performer resorts to visual information (Khan & Franks, 2003; Lage et al., 2014).

In experimental music research, leading studies have been conducted mainly on auditory feedback (Gabrielsson, 2003), ignoring visual and tactile aspects of performance. Not surprisingly, in the context of music performance pedagogy, the great majority of consolidated teaching methods of orchestral non-tempered strings (violin, viola, cello and double bass) do not include vision or tact as important sensorial sources to improve intonation, relying only on audition and proprioception¹ in the generation of essential information for movement production and control (Lage et al., 2007). Only a few leading pedagogues such as Paul Rolland (Rolland & Mutschler, 1986) and Shinichi Suzuki (Starr & Suzuki, 1976) intuitively mention the role of vision for the novice in locating markers on the instrument fingerboard, but only as a temporary sensorial source, subsidiary to the audition/proprioception combination. As far as tact goes, also intuitively, Galamian (1962, p.21-22) talks about the left hand "double contact" to secure intonation, but he limits his approach to very few and imprecise tactile references of the instrument (in his own words, "side of the neck", "body of the violin", "various parts of the instrument" and "right side rim") or the violinist's non-specific body areas ("side of the first finger" and "lower part of hand"). His non-scientific approach has major contributions to violin playing technique and pedagogy, but it is far from providing precise anchors for intonation control. Galamian is also against the triple physical contact of the left hand as if it would prevent expressiveness, such as in the use of vibrato.

But the triple contact of the left hand on the instrument does not prevent expressiveness if the player uses it punctually and briefly, dismounting the fingers fixed positions right after locating the target note. Moreover, the use of a triple contact anchor provided by the thumb being the vortex of a triangle formed with two other left-hand fingers, combined with three specific reference points of the double bass (1- the nut, the saddle, 2- the meeting point between neck and 3- the top of the bass, respectively) may provide precise tactile anchors (Figure 1) for the double bassist to nail down target notes (Borém, 2011).

Figures 1a, 1b, 1c — Examples of intonation control on the double bass by means of triangular left-hand shapes ("triple contact") combining the BT5 vortex and its angles (Borém, 2011, p.91-92).

Some other factors influence undershoot and overshoot patterns in manual movements. The movement execution is affected by both initial position of the limb and interpolated movements that may be characterized by random direction (Carlton & Carlton, 1984; Imanaka, 1989). Thus, in the performance of non-tempered musical instruments such as the double bass, a constant change in the initial position of the upper left limb (a permanent demand in music performance since melody is constructed from continuous shifts of notes) may cause difficulties in the adjustments for the fingers to reach the required positions in the fingerboard. Moreover, during the performance, proximal-to-distal movements and distal-to-proximal movements on non-tempered strings are naturally and continuously interpolated, generating a greater probability of producing undershoot or overshoot patterns. It should be observed that, in both double bass and cello, ascending pairs of pitches occur in descending proximal-to-distal movements, while in the violin and viola, ascending pairs of pitches occur in horizontal distal-to-proximal movements.

Another influence factor is movement direction, which is constrained by biomechanical variables. Movements on the double bass can be performed in opposition (ascending) or in congruence (descending) with the gravitational force creating different levels of energy costs to the system. Precision and movement control of limbs may be differently influenced by gravity (Lackner & DiZio, 2000). Target undershooting is more pronounced under conditions in which relative temporal costs of a target overshoot become greater than undershooting (Elliott et al., 2014; Elliott, Hansen, Mendoza, & Tremblay, 2004). In a descending distal-to-proximal movement, a target overshoot requires lower energetic and temporal costs to make corrections than in an ascending proximal-to-distal fashion due to gravitational effects on antagonist muscles activation (Lyons, Hansen, Hurding, & Elliott, 2006; Roberts, Elliott, Lyons, Hayes, & Bennett, 2016). It is important to point out that these experimental findings were only observed in proximal-to-distal movements.

Not many of the most recognized methods of orchestral strings teaching cover the relation between intonation control and left upper limb movement in ascending and descending pairs of pitches. However, there seems to be an agreement within this vast non-theoretical literature that intonation control is more difficult in descending pair of pitches (from a higher to a lower fundamental pitch frequency; fundamental pitch frequency is simply referred in this paper from here on as frequency or F0) in both more horizontal movements, such as in both violin and viola (Havas, 1979, 1995) and more vertical movements, such as in both cello and double bass (Kenneson, 1974). Only a few and not conclusive experimental studies have been done on intonation regarding the musician's tendencies of sounding out-of-tune above or below the target note. Madsen (1966) found that overall pitch deviation was closer to equally tempered target notes in descending scales than in ascending ones. Kantorski (1986) and Sogin (1989) showed that advanced string players performed descending whole-tone tetrachords (a tonally instable scale fragment) sharper than in the opposed ascending fashion. On the contrary, Yarbrough and Ballard (1990), also studying advanced string players, stated that their performance was sharper in ascending pairs of pitches.

In spite of these contradictory results, which illustrate the challenge in reaching every next target note in non-tempered string playing, there may be a perception among musicians that it is less uncomfortable and embarrassing to be out-of-tune within the same melodic direction (that is, the need to complete the movement to reach the target note) than having to slow down, stop and initiate the movement in contrary direction to reach back the desired target note, which he or she just slid through. Although there are no studies with humans relating preference for melodic contour, McKenna, Weinberger and Diamond (1989) found different levels of auditory perception for the same note within different melodic contours in cats. In other words, instrumentalists may feel less uncomfortable performing these ascending pair of pitches that did not achieved the target pitch due to their auditory perception and because they did not have to activate antagonistic muscles and initiate an opposite movement and, thus, produce a stronger frequency interference in the process. This would also corroborate the idea in which smaller temporal and energy costs prevail (Lyons et al., 2006).

The interaction of these interfering factors in the production of undershoot or overshoot patterns can be summarized in the complex intonation scenario which Applebaum and Applebaum (1973, p. 15), as mentioned above, called "the universal problem" in orchestral string playing. Lage et al (2007) investigated the role of sensorial information in the control of the non-tempered intonation on the double bass and found greater precision and lower variability when tactile and visual cues were simultaneously available in its performance. These findings corroborate results of other studies on the efficiency of vision and haptic information in motor control (Elliott et al., 2014; Khan & Franks, 2003; Rabin & Gordon, 2004).

On the double bass, undershoot in descending movements (proximal-to-distal) means an achieved frequency below the target pitch, while overshoot refers to an achieved frequency above the target pitch (Figure 2). Thus, undershoot here means a shorter distance covered (in mm) and corresponds to a smaller frequency (in Hz) achieved. On the other hand, in ascending movements, the reasoning is the opposite: undershoot means an achieved frequency above the target pitch, while overshoot refers to an achieved frequency below the target pitch. In other words, undershoot in ascending movements on the double bass means a shorter distance covered but a higher frequency achieved. In this article, undershoot and overshoot were inferred from the frequency achieved related to movement direction (ascending or descending).

Figure 2 — Intonation problems in shifting on the double bass: undershoot (below-target frequency) and overshoot (above-target frequency) in both descending (proximal-to-distal) and ascending (distal-to-proximal) left hand movements.

In short, sensorial constraints and movement direction may play an important role on undershoot and overshoot patterns in musical performance on the double bass. To extend Lage et al. (2007) findings, it was investigated how sensorial guidance influences undershoot and overshoot patterns (1) on overall measurement of performance independent of movement direction, (2) on descending movements and (3) on ascending movements. Moreover, it also observed the role of sensorial guidance on performance accuracy and variability.

In the overall analysis, it was hypothesized that the integration of specific visual and tactile cues (1) improves the accuracy and consistency of musical performance and (2) creates a less pronounced undershoot pattern compared to the no-guidance performance. Furthermore, in the analysis of movement direction, it was expected that the no-guidance condition in descending movements, compared to the sensorial guidance condition, produces a more pronounced undershoot pattern (achieving a frequency below the target pitch). On the other hand, the no-guidance condition in ascending movements should create a more pronounced undershoot pattern due to the uncertainty of movement control in association with gravitational constraints (achieving a frequency above the target pitch). In other words, resorting to vision and tact not only would improve intonation in general on the double bass but also would prevent patterns within the common fear to not reach the target note in shifts to the high register of the instrument.

¹Sense of body position and orientation signaled by muscles, joint receptors, and receptors located in the inner ear (Schmidt and Lee, 1999).