Eye Movement in Music Reading - Tempo

Tempo

Smith (1988) found that when tempo is increased, fixations are fewer in number and shorter in mean duration, and that fixations tend to be spaced further apart on the score. Kinsler & Carpenter (1995) investigated the effect of increased tempo in reading rhythmic notation, rather than real melodies. They similarly found that increased tempo causes a decrease in mean fixation duration and an increase in mean saccade amplitude (i.e., the distance on the page between successive fixations). Souter (2001) used novel theory and methodology to investigate the effects of tempo on key variables in the sight reading of highly skilled keyboardists. Eye movement studies have typically measured saccade and fixation durations as separate variables. Souter (2001) used a novel variable: pause duration. This is a measure of the duration between the end of one fixation and the end of the next; that is, the sum of the duration of each saccade and of the fixation it leads to. Using this composite variable brings into play a simple relationship between the number of pauses, their mean duration, and the tempo: the number of pauses factored by their mean duration equals the total reading duration. In other words, the time taken to read a passage equals the sum of the durations of the individual pauses, or nd = r, where n is the number of pauses, d is their mean duration, and r is the total reading time. Since the total reading duration is inversely proportional to the tempo—double the tempo and the total reading time will be halved—the relationship can be expressed as nd is proportional to r, where t is tempo.

This study observed the effect of a change in tempo on the number and mean duration of pauses; thus, now using the letters to represent proportional changes in values,

nd = 1⁄_t, where n is the proportional change in pause number, d is the proportional change in their mean duration, and t is the proportional change in tempo. This expression describes a number–duration curve, in which the number and mean duration of pauses form a hyperbolic relationship (since neither n nor d ever reaches zero). The curve represents the range of possible ratios for using these variables to adapt to a change in tempo. In Souter (2001), tempo was doubled from the first to the second reading, from 60 to 120 MM; thus, t = 2, and the number–duration curve is described by nd = 0.5 (Figure 2). In other words, factoring the proportional change in the number and mean duration of pauses between these readings will always equal ½. Each participant’s two readings thus corresponded to a point on this curve.

Irrespective of the value of t, all number–duration curves pass through three points of theoretical interest: two ‘sole-contribution’ points and one ‘equal-contribution’ point. At each sole-contribution point, a reader has relied entirely on one of the two variables to adapt to a new tempo. In Souter's study, if a participant adapted to the doubling of tempo by using the same number of pauses and halving their mean duration, the reading would fall on the sole-contribution point (1.0,0.5). Conversely, if a participant adapted by halving the number of pauses and maintaining their mean duration, the reading would fall on the other sole-contribution point (0.5,1.0). These two points represent completely one-sided behaviour. On the other hand, if a reader’s adaptation drew on both variables equally, and factoring them gives 0.5, they must both equal the square root of t (since t = 2 in this case, the square root of 2). The adaptation thus fell on the equal-contribution point:

(, ), equivalent to (0.707,0.707).

Predicting where performers would fall on the curve involved considering the possible advantages and disadvantages of using these two adaptive resources. A strategy of relying entirely on altering pause duration to adapt to a new tempo—falling on (1.0,0.5)—would permit the same number of pauses to be used irrespective of tempo. Theoretically, this would enable readers to use a standardised scanpath across a score, whereas if they changed the number of their pauses to adapt to a new tempo, their scanpath would need to be redesigned, sacrificing the benefits of a standardised approach. There is no doubt that readers are able to change their pause duration and number both from moment to moment and averaged over longer stretches of reading. Musicians typically use a large range of fixation durations within a single reading, even at a stable tempo. Indeed, successive fixation durations appear to vary considerably, and seemingly at random; one fixation might be 200 ms, the next 370 ms, and the next 240 ms. (There are no data on successive pause durations in the literature, so mean fixation duration is cited here as a near-equivalent.)

In the light of this flexibility in varying fixation duration, and since the process of picking up, processing and performing the information on the page is elaborate, it might be imagined that readers prefer to use a standardised scanpath. For example, in four-part, hymn-style textures for keyboard, such as were used in Souter (2001), the information on the score is presented as a series of two-note, optically separated units—two allocated to an upper stave and two to a lower stave for each chord. A standardised scanpath might consist of a sequence of ‘saw-tooth’ movements from the upper stave to the lower stave for a chord, then diagonally across to the upper stave and down to the lower stave of the next chord, and so on. However, numerous studies have shown that scanpaths in the reading of a number of musical textures—including melody, four-part hymns, and counterpoint—are not predictable and orderly, but are inherently changeable, with a certain ragged, ad-hoc quality. Music readers appear to turn their backs on the theoretical advantage of standardised scanpath: they are either flexible or ad hoc when it comes to the number of pauses—just as they are with respect to their pause durations—and do not scan a score in a strict, predetermined manner.

Souter hypothesised that the most likely scenario is that both pause duration and number are used to adapt to tempo, and that a number–duration relationship that lies close to the equal-contribution point allows the apparatus the greatest flexibility to adapt to further changes in reading conditions. He reasoned that it may be dysfunctional to use only one of two available adaptive resources, since that would make it more difficult to subsequently use that direction for further adaptation. This hypothesis—that when tempo is increased, the mean number–duration relationship will be in the vicinity of the equal-contribution point—was confirmed by the data in terms of the mean result: when tempo doubled, both the mean number of pauses per chord and the mean pause duration overall fell such that the mean number–duration relationship was (0.705,0.709), close to the equal-contribution point of (0.708, 0.708), with standard deviations of (0.138,0.118). Thus, the stability of scanpath—tenable only when the relationship is (0.5,1.0)—was sacrificed to maintain a relatively stable mean pause duration.

This challenged the notion that scanpath (largely or solely) reflects the horizontal or vertical emphasis of the musical texture, as proposed by Sloboda (1985) and Weaver (1943), since these dimensions depend significantly on tempo.