Sixteen Experimental Investigations from the Harvard Psychological Laboratory, Hugo Münsterberg [top fiction books of all time TXT] 📗

98 82.3 90.7 64.5 90.7

 

Total judgments, 113; Errors (B = 31), A = 57.

 

The relatively meager results set forth in the preceding section are

corroborated in the present set of experiments. That such a variation

of intensity introduced into an otherwise undifferentiated auditory

series, while it affects the time-values of both preceding and

following intervals, has a much greater influence on the latter than

on the former, is as apparent here as in the previous test. The number

of errors, irrespective of extent, for the two intervals are: B, 82.3

per cent, of total judgments; A, 90.7 per cent. When the mean and

extreme sign displacements are estimated on the quantitative basis

given above these percentages become B, 64.5; A, 90.7, respectively—a

ratio of 0.711:1.000.

 

The direction of error, likewise, is the same as in the preceding

section. Since the actual values of the two intervals here are

throughout of extreme sign—one always greater, the other always

less—only errors which lie in a single direction are discriminable.

Illusions lying in this direction will be clearly exhibited, since the

differences of interval introduced are in every case above the

threshold of discrimination when the disturbing element of variations

in intensity has been removed and the series of sounds made

intensively uniform. In case of a tendency to underestimate B or

overestimate A, errors would not be shown. This problem, however, is

not to be met here, as the results show; for there is recorded a

proportion of 82.3 per cent. of errors in judgment of interval B, and

of 90.7 per cent. in judgment of interval A, all the former being

errors of overestimation, all of the latter of underestimation.

 

The influence of position in the series on the effect exerted by such

a change of intensity in a single member can be stated only

tentatively. The number of experiments with the louder sound in

position five was smaller than in the other cases, and the relation

which there appears cannot be absolutely maintained. It may be also

that the number of intervals following that concerning which judgment

is to be given, and with which that interval may be compared, has an

influence on the accuracy of the judgment made. If we abstract from

this last set of results, the tendency which appears is toward an

increase in accuracy of perception of comparative durations from the

beginning to the end of the series, a tendency which appears more

markedly in the relations of the interval preceding the louder sound

than in those of the interval which follows it. This conclusion is

based on the succession of values which the proportion of errors to

total judgments presents, as in the annexed table.

 

TABLE XXX.

 

Percentage of Errors for Each Position.

 

Interval. I II III IV V

B. 83.3 76.9 69.2 (100) Irrespective

A. 85.7 91.6 91.6 84.6 (100) of extent.

B. 73.3 71.9 53.8 (60) Estimated

A. 85.7 91.6 91.6 84.6 (100) quantitatively.

 

Next, the relation of the amount of increase in intensity introduced

at a single position in such a series to the amount of error thereby

occasioned in the apprehension of the adjacent intervals was taken up.

Two sets of experiments were carried out, in each of which five of

the sounds were of equal intensity, while one, occurring in the midst

of the series, was louder; but in one of the sets this louder sound

was occasioned by a fall of the hammer through a distance of 0.875

inch, while in the other the distance traversed was 2.00 inches. In

both cases the extent of fall in the remaining hammers was uniformly

0.25 inch. The results are given in the following table:

 

TABLE XXXI.

 

Interval B.¹ Interval A.

Ratio of Interval 0.875 in. 2.00 in. 0.875 in. 2.00 in.

B to Interval A. + = - + = - + = - + = -

1.000 : 1.000 0 6 0 0 4 2 0 5 1 0 0 6

0.909 : 1.000 2 4 0 0 4 2 0 2 4 2 2 2

0.833 : 1.000 0 6 0 0 4 2 4 0 2 1 3 2

0.770 : 1.000 0 6 0 2 2 2 2 4 0 4 0 2

0.714 : 1.000 0 6 0 1 5 0 6 0 0 2 2 2

Totals, 2 28 3 19 8 12 11 7 9 7 14

T.E., T.J., 2 30 11 30 13 30 21 30

and per cent., 6.6% 36.6% 60.0% 70.0%

 

¹Interval B in these experiments is of the same duration as all

others but that following the louder sound; hence, judgments in

the second column are correct.

 

Again the markedly greater influence of increased intensity on the

interval following than on that preceding it appears, the percentage

of errors being, for B (both intensities), 21.6 per cent.; for A, 56.6

per cent. Also, in these latter experiments the direction of error is

more definite in the case of interval A than in that of interval B.

 

The influence of changes in intensity on the amount of error produced

is striking. Two intensities only were used for comparison, but the

results of subsequent work in various other aspects of the general

investigation show that this correlation holds for all ranges of

intensities tested, and that the amount of underestimation of the

interval following a louder sound introduced into an otherwise uniform

series is a function of the excess of the former over the latter. The

law holds, but not with equal rigor, of the interval preceding the

louder sound. So far as these records go, the influence of such an

increase of intensity is more marked in the case of interval B than in

that of interval A. It is to be noted, however, that the absolute

percentage of errors in the case of A is several times greater than in

that of B. I conclude that A is much more sensitive than B to such

influences, and that there is here presented, in passing from

intensity I. to intensity II., the rise of conditions under which the

influence of the louder sound on B is first distinctly felt—that is,

the appearance of a threshold—and that the rate of change manifested

might not hold for higher intensities.

 

Lastly, the rate at which the sounds of the series succeeded one

another was varied, in order to determine the relation which the

amount of influence exerted bore to the absolute value of the

intervals which it affected. Three rates were adopted, the whole

series of sounds occupying respectively 2.50 secs., 2.20 secs, and

1.80 secs. The results are summed in the following table:

 

TABLE XXXII.

 

Rate: 2.5 secs. Rate: 2.2 secs. Rate: 1.8 secs.

 

Ratio of Interval B B A B A B A

to Interval A. + = - + = - + = - + = - + = - + = -

 

1.000 : 1.000 2 8 0 0 8 2 0 8 2 0 2 8 0 4 0 0 2 2

0.917 : 1.000 0 8 2 4 6 0 3 8 0 0 8 3 2 2 0 0 2 2

0.846 : 1.000 1 9 0 5 4 1 3 8 0 3 7 1 6 5 0 1 8 2

0.786 : 1.000 1 10 0 11 0 0 6 6 0 7 3 4 6 2 2 2 6 2

0.733 : 1.000 4 2 0 4 0 2 4 6 0 8 0 2

0.687 : 1.000 5 3 1 6 1 2 2 6 0 7 0 1

 

Totals 4 35 2 20 18 3 21 35 3 20 21 20 20 25 2 18 18 11*

 

*Transcriber’s Note: Original “1”.

 

These results are converted into percentages of the total number of

judgments in the following table:

 

TABLE XXXIII.

 

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 passing 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 XXXIV.

 

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 quantitative

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 quantitative results of an analysis

of the material in series of ten successive pairs of reactions, upon

the basis of unity as the value of the first element.

 

TABLE XXXV.

 

Quantities. 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 retardation, 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