Sixteen Experimental Investigations from the Harvard Psychological Laboratory by Hugo Münsterberg (100 books to read .txt) 📕

consistently began with the initial reaction of the series.

An analysis of the constituent 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 coördination 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 quantitative results follow, arranged as in the

preceding experiment.

TABLE XXXVI.

Quantity. 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 retardation. 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 substitution

for this of a temporal form of differentiation.

In this trochaic rhythm the phases of variation in the constituent

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 retardation 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 quantitative values of the measure and its constituent

intervals, taken in series of ten successive repetitions, are as

follow:

TABLE XXXVII.

Quantity 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 passes 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 XXXVIII.

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 anapæstic—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 XXXIX.

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

Anapæs., 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 retardations presents sharply differentiated terms and a

curve uninverted at any point.

A separate analysis 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 constituent having a strongly marked

functional character, the process of change becomes unlike that of

true retardation. 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

constituting 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.

In the amphibrachic form the changes manifested by the constituents of

the unit group are more obscure. No progressive retardation of the

accented element is apparent. In the initial and final intervals the

difference in duration between the first and last members of the

series is small and appears early in the process. If we assume the

general application of the laws of change presented in the preceding

section, there should be here two influences concerned in the

determination of the relations presented, the factors, namely, of

position and accent. The falling of the accentual stress on the median

interval eliminates one of the two factors of progressive reduction in

that element and replaces it by a factor of increase, thereby doing

away with the curve of change; while at the same time it decreases the

changes which occur in the bounding intervals of the group by removing

the accent from the first and by the proximate position of its own

accent tending to reduce the last interval.

Under this same assumption there should be expected in the anapæstic

form of rhythm an exaggeration of the progressive increase in the

final interval, together with a further reduction in the duration of

the initial; since from the falling of the accent on the final

interval two factors of increase combine, while in the initial, which

immediately follows the accented interval in the series, a positive

factor of reduction appears. This is actually the type of change

presented by the quantitative relations, which are given as

proportional values in the following table.

TABLE XLI.

Interval. I II III IV V VI VII VIII IX X

First, 1.000 0.950 1.000 0.950 1.000 0.950 1.000 1.000 1.000 1.050

Second, 1.000 1.100 1.000 1.050 1.100 1.000 1.000 1.050 1.100 1.000

Third, 1.000 1.073 1.073 1.024 1.024 1.122 1.098 1.098 1.098 1.146

Between its first and last terms the first interval shows a departure

slightly less than that of the previous rhythm from the rate of change

which characterizes the dactylic type; but if the average values of

the whole series of intervals be taken in each of the three cases, the

progressive reduction will be seen clearly to continue in passing from

the second to the third form. The figures annexed give these averages

as proportions of the first interval in the series.

TABLE XLII.

1st Av. of

Rhythm. Interv. all others.

Dactylic, 1.000 : 1.188

Amphibrachic, 1.000 : 1.019

Anapæstic, 1.000 : 1.000

The relations of the various intervals in the three forms are put

together here for comparison:

TABLE XLIII.

Rhythm. 1st Interval. 2d Interval. 3d Interval.

Dactylic, 1.000 : 1.231 1.000 : 1.000 1.000 : 1.066

Amphibrachic, 1.000 : 1.045 1.000 : 1.000 1.000 : 1.054

Anapæstic, 1.000 : 1.050 1.000 : 1.000 1.000 : 1.146

An analysis of the factors of accentual stress and of position in the

rhythmical group in isolation from each other, confirms the

assumptions already made as to their influence in defining the form of

the rhythmic unit. Table XLIV. exhibits the series of temporal changes

taking place in accented and unaccented intervals, respectively, for

the three forms combined, and therefore independent of position in the

group.

TABLE XLIV.

Interval. I II III IV V VI VII VIII IX X

Accented. 1.000 1.064 1.064 1.064 1.064 1.094 1.094 1.064 1.094 1.129

Unaccented, 1.000 1.000 1.000 1.080 1.040 1.040 1.040 1.040 1.040 1.040

Similarly, in Table XLV. are given the proportional values of the

series of intervals in order of their position in the group and

independent of accentual stress:

TABLE XLV.

Interval. I II III IV V VI VII VIII IX X

First, 1.000 1.043 1.087 1.043 1.087 1.043 1.043 1.121 1.043 1.121

Second, 1.000 1.000 1.000 1.043 1.000 0.956 1.000 0.956 1.000 0.956

Third, 1.000 1.028 1.028 1.055 1.028 1.083 1.083