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

4. Results

1. Absolute Relative Error mean (RE) and Standard Deviation of the Relative Error mean (SDRE)

A significant difference was detected between FT and IT trials for RE (Z = 2.02, p = .04). The participants showed a better performance, as far as intonation goes, in the Integrated Trials than in the Free Trial (Figure 4). A marginal difference between trials was found in the SDRE analysis (Z = -0.85, p = .06), indicating a tendency of the Integrated Trial to be more consistent compared to the Free Trial (Figure 3).

Figure 4 — Comparisons of RE (Absolute Relative Error) and SDRE (Standard Deviation of the Relative Error) between Free Trials (in white) and Integrated Trials (in grey) of double bassists trying to reach target notes in descending, ascending and overall movements of the left hand.

2. Signed Relative Error mean (SRE)

The analysis of trials regardless of movement direction showed a significant difference between trials (Z = 2.19, p = .02). It became evident that the participants exhibited in the Free Trial an undershoot pattern (-0.94%) in relation to target notes, while an overshoot pattern (0.31%) was observed in the Integrated Trial (Figure 4). The overshoot of 0.31% is not relevant in the perception of melodic intervals, because the just noticeable difference of consecutive tones is approximately 0.7% (nearly a tenth of a semitone, an irrelevant interval for the perception of human ears).

In the analysis of descending movements, the average of SRE between trials was marginally different (Z=1.85, p = 0.6) and an undershoot pattern was observed in the Free Trial condition, while a small magnitude overshoot pattern was observed in the Integrated Trial (Figure 5).

The same result was found in the analysis of ascending movements. The average of SRE between trials was marginally different (Z=1.85, p = 0.6) and an undershoot pattern was observed in the Free Trial condition, while a small magnitude overshoot pattern was observed in the Integrated Trial (Figure 5).

Figure 5 — Comparisons SRE (Signed Relative Error) between Integrated Trials (in grey) and Free Trials (in white) of double bassists trying to reach target notes in descending and ascending movements of the left hand.