Harvard Psychological Studies Part 43

These results are converted into percentages of the total number of judgments in the following table:

TABLE x.x.xIII.

Rate of B A Success. + = - Errors. + = - Errors.

2.5 secs 10 85 5 15 49 44 7 51 2.2 " 36 59 5 41 33 34 33 67 1.8 " 43 53 4 47 38 38 24 62

In the case of interval A the direction of the curve of error changes in pa.s.sing from Rate II. to Rate III. In the case of interval B the increase is continuous.

This increase in the percentage of error is, further, distinctly in the direction of an accentuation of the overestimation of the interval B, as is shown in the percentage of cases in which this interval appeared greater than the rest of the series for each of the three rates.

If the three rates be combined in the one set of results, the difference in the effects produced on the interval following the louder sound and on that which precedes it becomes again apparent.

This is done in the table below.

TABLE x.x.xIV.

B A B A Ratio + = - + = - T.E. T.J. % T.E. T.J. % I. 2 20 2 0 12 12 2 24 8.5 12 24 50.0 II. 5 18 2 4 16 5 5 25 20.0 21 25 84.4 III. 10 22 0 9 19 4 10 32 31.0 23 32 72.0 IV. 13 18 2 20 9 8 13 33 39.0 17 37 46.0 V. 8 8 0 12 0 4 8 16 50.0 4 16 25.0 VI. 7 9 1 13 1 3 7 17 41.0 4 17 24.0

The overestimation of the interval before the louder sound also tends to increase in extent with the actual increase in duration of the interval following that sound over the other intervals of the series.

Thus, the form which the sensible time-relations of such a limited series of sounds present is found to be intimately dependent on the intensive preponderance of certain elements within it, on the degree of increased stress which such elements receive, on their local position in the series, and on the rate at which the stimulations succeed one another. The knowledge of these facts prepares us for the whole series of relations manifested in the special quant.i.tative investigations reported in the sections which follow. In the first of these is presented the time-relations obtaining among the successive reactions of the various rhythm types discussed in the preceding division of this part, the section, namely, on the distribution of intensities.

In the first group of reactions the series was not to be consciously accented, nor to be divided into groups by the introduction of pauses.

The reactor was required only to conceive it as a succession of two-beat groups continuously repeated, the way in which the groups should be defined, whether by counting or otherwise, being left to his own discretion. The experimental group was composed of five subjects.

The following table presents the quant.i.tative results of an a.n.a.lysis of the material in series of ten successive pairs of reactions, upon the basis of unity as the value of the first element.

TABLE x.x.xV.

Quant.i.ties. I II III IV V VI VII VIII IX X Whole Meas., 1.000 0.894 1.035 0.912 1.000 0.877 1.070 0.877 1.070 0.841 First Inter., 1.000 1.142 1.071 1.142 1.000 1.285 1.000 1.214 1.000 1.214 Second Inter., 1.000 0.837 1.023 0.860 1.000 0.744 1.093 0.767 1.093 0.790

Within the limits of the calculation no progressive change appears, either of acceleration or of r.e.t.a.r.dation, whether in general or on the part of individual reactors. In narrower ranges the inconstancy of the periods is very marked, and their variations of clearly defined rhythmical character. The duration of the total measures of two beats is throughout alternately longer and shorter, the average of their values presenting a ratio of 1.000:0.847. The order of this arrangement, namely, that the longer period precedes the shorter in the larger group, is drawn from the fact that measurements consistently began with the initial reaction of the series.

An a.n.a.lysis of the const.i.tuent intervals of the unit group, as shown in the second and third lines of the table, reveals the existence of a complex subordinate rhythm. The two components of the rhythmical group do not increase and decrease concomitantly in temporal value in composing the alternate long and short measures of the fluent rhythm.

The movement involves a double compensating rhythmical change, in which the two elements are simultaneously in opposite phases to each other. A measure which presents a major first interval contains always a minor second; one introduced by a minor first concludes with a major second. The ratios of these two series of periodic variations must themselves manifestly be different. Their values are, for the first interval of the measure, 1.000:1.214; and for the second interval, 1.000:0.764. The greater rhythmical differentiation marks the second of the two intervals; on the variations of this second interval, therefore, depends the appearance of that larger rhythm which characterizes the series. The ratios of these primary intervals are less consistently maintained than are those of the rhythmical measures built out of them. It will be noted that in both intervals there is a tendency for the value of the difference between those of alternate groups to increase as the tapping progresses. This change I have interpreted as indicative of a progressive definition in the process of rhythmization, depending on an increase in coordination and differentiation of the reactions as the series advances.

A simple stress on alternate elements was next introduced in the series, forming a simple trochaic measure repeated without interruption. The quant.i.tative results follow, arranged as in the preceding experiment.

TABLE x.x.xVI.

Quant.i.ty. I II III IV V VI VII VIII IX X Measure, 1.000 1.035 1.070 1.035 1.087 1.070 1.071 1.052 1.070 1.070 1st Int., 1.000 1.000 1.111 1.000 1.055 1.111 1.166 1.111 1.111 1.111 2d Int., 1.000 1.025 1.051 1.051 1.102 1.051 1.025 1.025 1.051 1.051

Here again there is no progressive acceleration or r.e.t.a.r.dation. The rhythmical differentiation of alternate measures is very slight--the average ratio of the first to the second being 1.000:0.993--but is of the same type as in the preceding. The excess in the amount of this differentiation presented by the first type of reaction over the second may be due to the presence of a tendency to impart rhythmical character to such a series of reactions, which, prohibited in one form--the intensive accent--finds expression through the subst.i.tution for this of a temporal form of differentiation.

In this trochaic rhythm the phases of variation in the const.i.tuent intervals of the measure are concomitant, and their indices of differentiation almost identical with each other. Their values are, for the first, 1.000:0.979; and for the second, 1.000:0.995. The higher index is that of the first interval, that, namely, which follows the accented beat of the measure, and indicates that the rhythmical change is due chiefly to a differentiation in the element which receives the stress.

In iambic measures similarly beaten out there is likewise no acceleration nor r.e.t.a.r.dation apparent in the progress of the tapping.

The temporal differentiation of alternate measures is of the same extent as in the preceding group, namely, 1.000:0.991. the proportional quant.i.tative values of the measure and its const.i.tuent intervals, taken in series of ten successive repet.i.tions, are as follow:

TABLE x.x.xVII.

Quant.i.ty I II III IV V VI VII VIII IX X Measure, 1.000 0.979 1.000 0.979 1.020 0.979 0.979 1.020 0.979 0.979 1st Int., 1.000 0.941 0.941 1.000 1.000 0.941 8.082 0.941 0.941 0.941 2d Int., 1.000 1.000 1.032 0.967 1.032 1.000 1.000 1.032 1.000 0.967

The alternation of greater and less duration in the rhythm groups is due to a variation in the time-value of the second interval only, the index of average change in the first member being zero. That is, the greater index of instability again attaches to that element which receives the stress. Though this holds true throughout these experiments, the amount of difference here is misleading, since on account of the smaller absolute value of the first interval the proportional amount of change within it which pa.s.ses unrecorded is greater than in the case of the second interval.

In general, the larger temporal variations of the trochaic and iambic rhythm forms are too slight to be significant when taken individually.

The evidence of rhythmical treatment in such a series of reactions, which is strongly marked in the unaccented form, nevertheless receives reinforcement from these inconsiderable but harmonious results.

The proportional values of the variations in alternate measures for accented and unaccented elements are given in the following table, in which the figures for the trochaic and iambic forms are combined:

TABLE x.x.xVIII.

Interval I II III IV V VI VII VIII IX X Accented, 1.000 1.000 1.083 1.000 1.041 1.000 1.083 1.000 1.041 1.000 Unacc. 1.000 1.000 1.000 1.035 1.071 1.000 0.964 1.000 1.000 1.000

It is perhaps worthy of note that in this table a still higher rhythmical synthesis of regular form appears in the accented elements if the figures be taken in series of four consecutive pairs of reactions.

In the group of triple rhythms next taken up--the dactylic, the amphibrachic and the anapaestic--each type presents an increase in the duration of the unit group between the beginning and end of the series, but without any regular curve connecting these terms. Neither the average results nor those of the individual subjects show anywhere a decrease of duration in the progress of the tapping. The proportional results for each of the three rhythm forms, and their averages, are given in the following table.

TABLE x.x.xIX.

Rhythm. I II III IV V VI VII VIII IX X Datyl., 1.000 1.062 1.062 1.087 1.087 1.075 1.125 1.112 1.125 1.112 Amphib., 1.000 1.000 1.000 1.069 1.085 1.046 1.046 1.046 1.046 1.035 Anapaes., 1.000 1.012 1.023 1.012 1.037 1.037 1.023 1.059 1.023 1.084

Average, 1.000 1.024 1.036 1.060 1.060 1.060 1.072 1.072 1.072 1.084

When all types and subjects are thus combined the summation of these inconstant r.e.t.a.r.dations presents sharply differentiated terms and a curve uninverted at any point.

A separate a.n.a.lysis of the components of the rhythmical group shows, for the dactylic form, an important increase in duration in only one of the three intervals, namely, that following the element which receives accentual stress. The proportional values for these intervals follow.

TABLE XL.

Interval. I II III IV V VI VII VIII IX X First, 1.000 1.153 1.153 1.153 1.153 1.231 1.193 1.193 1.231 1.231 Second, 1.000 0.917 0.917 1.000 0.917 0.917 0.917 0.917 0.917 0.917 Third 1.000 1.000 1.033 1.066 1.055 1.066 1.133 1.066 1.066 1.066

Since the progressive variation does not penetrate the whole measure, but affects only a single const.i.tuent having a strongly marked functional character, the process of change becomes unlike that of true r.e.t.a.r.dation. In such a case, if the increase in duration be confined to a single element and parallel the changes in a simultaneous variant of a different order, we should regard them as functionally connected, and therefore interpret the successively greater periods of time occupied by the rhythmical measures as const.i.tuting no real slowing of the tempo. The measure of relative tempo in such a case consists in the ratios of the successive durations of the rhythmical units after the subtraction of that element of increase due to this extraneous source. Here, since the increase is confined to that member of the group which receives accentual stress, and since the increase of accentuation is typically accompanied by an extension of the following interval, the changes presented do fulfil the conditions of a progressively increased accentuation of the rhythm group, and to this origin I think it is undoubtedly to be attributed. It is to be noted that the final interval also undergoes a slight increase, while the median suffers a similarly slight decrease in duration as the series progresses.