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

interval following a louder sound introduced into a series. The

influence of this second factor cannot be analyzed in detail, since

the amount of underestimation is not recorded unless it be sufficient

to displace the sign of the interval; but if such a quantitative

method be applied as has already been described, the results show a

continuous decrease in the amount of underestimation of this interval

from the first position to the fourth, or penultimate, which presents

the following relative values: 92, 66, 50, 40. A phase of rapid

increase in the amount of underestimation appears in the fifth or

final position, represented on the above scale of relative values by

120. This falling off at the end of the series, which appeared also in

previous experiments, can be attributed only to an interference with

the functions which the several measures bear in the process of

comparison, and indicates that the accuracy of judgment is dependent

on a comparison of the measure or element in question with those which

follow as well as with those which precede it.

The results presented in the preceding section form the statement of

but one half the evidence of higher rhythmical synthesis afforded by

the material of the present investigation. We turn now to the second

set of results. It deals, in general, with the quantitative relations

of rhythmic forms which find expression through finger reactions.

Portions of this evidence have already been presented, through motives

of economy, in connection with the discussion of the phases of

differentiation in intensity and duration which such beaten rhythms

manifest. The burden of it, however, is contained in the results of an

analysis, form by form, of the proportional mean variations which

characterize these types of rhythmic expression. This method has been

applied to a study (a) of the characters of the constituent

intervals of the unit, in their relation to accentuation and position;

(b) of the simple group which these elements compose; and (c) of

the forms of higher synthesis manifested by the variations in

successive groups. The first of these relations concerns, indeed, only

the internal organization of the simple group, and has no direct

bearing on the combination of such groups in higher syntheses; but,

again for the sake of economy, the items are included with the rest of

the material.

The application of such a method, as in all treatment of material by

mean variations, involves much labor,[12] and on that account alone

the lack of its employment to any considerable extent in previous

investigations may be excused; but to this method, as it seems to me,

must the final appeal be made, as an indisputable means by which all

questions concerning the refined features of rhythmical organization,

the definition of units and the determination of the forms in which

they enter into larger rhythmic quantities, are to be settled.

[12] In connection with this work some 48,000 individual measurements

were made (for the transcription of which I am indebted to the patient

assistance of my wife). Half of these were measurements of the

intensity of the successive reactions; the other half, of the

intervals which separated them. The former series has been employed in

obtaining the averages which appear in the section on the distribution

of intensities; the latter in that on the distribution of durations.

The determination of mean variations was made in connection with the

second series only (24,000). These quantities were combined in series

of single groups, and in series of two, four, eight and ten groups,

and for each of these groupings severally the mean variation of the

series was computed.

Of all the possible forms of rhythmic apprehension or expression, the

material for such a statistical inquiry is most readily obtainable in

the form of a series of finger reactions, and to such material the

application of the method in the present investigation has been

restricted.

In the first experiment of this group the reactor was asked to tap out

a series in which temporal, but not intensive variations were

introduced; the strokes were to be of uniform strength but separated

into groups of two beats. No directions as to length of pause between

the successive groups were given, but the whole form of the groups was

to be kept absolutely constant. The reports of the subjects were

uniformly to the effect that no accent had been introduced. At a

cursory examination no intensive grouping was apparent. These records

were the earliest analyzed, when only time relations were in mind, and

no measurements were made of variations in strength. Only the mean

variations of the intervals, therefore, will here be taken up.

A word first as to the relative value of the two intervals and its

significance. The form of a rhythmical series is determined in every

part by subordination to principles of strict temporal arrangement.

Every suppression of elements in such a series, every rest and

syncopated measure has as positive and well-defined a function as have

the successive reactions and their normal intervals. If such a pause

is made as we find introduced in the present case, its value must be a

fixed function of the system of durations of which it forms a part,

whether it replace an element in a rhythmical unit, or a subgroup in a

higher rhythmical quantity. In general, the value of such a rest is

less than the duration of a corresponding full measure or interval.

For example, the syncopated forms | >q % | and | >q % %_| are

demonstrably of shorter average duration than the corresponding

measures| >q q | and | >q q q_|; and the pause occurring at the close

of a syncopated line—such as that in the middle of a catalectic

trochaic tetrameter—should be found of less value than that of the

regular foot.

In the present instance two reactions are made, a pause follows, then

the reactions take place again, and so on. The intervals separating

successive groups of reactions thus result from the coalescence of two

periods, the interval which would regularly follow the reaction and

the additional pause at its close. The value of the latter I interpret

as functionally equivalent to a group of two beats and not to a single

interval; that is, the rhythm beaten out is essentially quadruple, the

second member of each composite group being suppressed, as follows:

>

| q q; % % |.

______/

To estimate the proper value of such a rest the average relative

duration of first and second intervals was taken in a continuous

series of two-beat measures, in which the first member was accented

sufficiently to define the rhythmical groups. The ratio was

1.000:0.760. In the present instance the values of the simple initial

interval and the composite interval which follows it are, in terms of

the linear measurement, 1.55 mm. and 3.96 mm. Assuming the above ratio

to hold, the duration of a period which included the second

beat-interval and a group-rest should be 1.16 + 1.55 + 1.16 = 3.87 mm.

This is slightly less than the actual value of the period, whereas it

should be greater. It must be remembered, however, that the disparity

between the two intervals increases with initial accentuation, and in

consequence the proportional amounts here added for the second

interval (1.16 to 1.55) should be greater. This interval is not

rhythmically ‘dead’ or insensitive. The index of mean variation in all

reactors is greater for the first than for the second interval (or

interval + pause) in the ratio 1.000:0.436, that is, the value of the

latter is more clearly defined than that of the former, and the

reactor doubly sensitive to variations occurring within it.

An analysis of the variations of these intervals separately in series

of four groups reveals a secondary reciprocal rhythm, in which the

changes in value of the mean variation at any moment are in opposite

directions in the two intervals. These values in percentages of the

total duration of the periods are given in the following table.

TABLE LXI.

Interval. 1st Group. 2d. Group. 3d Group. 4th Group.

First, 15.4 per cent. 26.4 per cent. 13.8 per cent. 30.3 per cent.

Second, 12.4 ” 7.0 ” 9.6 ” 7.5 “

Without measurement of their intensive values, interpretation of these

variations is speculative. They indicate that the pairs of beats are

combined in higher groups of four; that the differences of mean

variation in the first interval are functions of an alternating major

and minor accentuation, the former occurring in the second and fourth,

the latter in the first and third; and that the inversely varying

values of the mean variation in the second interval are functions of

the division into minor and major groups, the reduced values of the

second and fourth of these intervals being characteristic of the

greater sensitiveness to variations occurring in the group pause than

to changes occurring within the group.

The fixity of the group is markedly greater than that of the simple

interval. In the one case in which the mean variation of the group is

greater than that of the elementary period the material involved was

meager (five instead of ten repetitions) and the discrepancy therefore

insignificant.

The difference in the mean variation of the first and second intervals

respectively rises to an individual maximum of 3.000:1.000, and

averages for all subjects 2.290:1.000; the fixity, that is to say, of

the inter-group interval in this form of tapping is more than twice as

great as that of the intra-group interval. The fixity of the larger

rhythmical quantities is greater than that of the smaller, whether the

relation be between the elementary interval and the unit group, or

between the synthetic unit and its higher composite. The average mean

variation of the beat intervals exceeds that of the whole group in the

relation of 1.953:1.000. The differentiation of larger and smaller

groups is less clear. When the material is taken in groups of eight

successive beats the mean variation is less in the case of every

subject than when taken in fours, in the ratio 1.000:1.521. The

comparative values for groups of two and four beats is reversed in two

thirds of the cases, yet so that an average for all subjects gives the

ratio 1.000:1.066 between groups of four and two beats. The whole

series of values arranged on the basis of unity for the mean variation

of the beat interval is given in Table LXII.

TABLE LXII.

Proportional. Single Beat. 2-Beat Group. 4-Beat Group. 8-Beat Group.

M.V. 1.000 0.512 0.480 0.320

The persons taking part in the investigation were next required to

make a series of reactions composed of unit groups of two beats, in

each of which the first member received accentuation, a simple

trochaic rhythm. In this type the relation of intra-group to

inter-group interval remains unchanged. In all subjects but one the

mean variation of the first interval exceeds that of the second in the

average ratio 1.722:1.000. The amount of difference is less than in

the preceding type of reaction. In the former there is presented not

an intensively uniform series, but an irregularly rhythmical grouping

of intensities, in dependence on the well-defined parallel types of

temporal differentiation; in the latter such intensive differentiation

is fundamental and constant in its form. Assuming the character of the

second interval to remain unchanged, there is in the intensive fixity

of the initial accented element, on the one hand, and the alternate

assertion of the impulse to accentuation and repression of it in the

attempt to preserve uniformity, on the other, an occasion for the

difference in the relation of the mean variation of this interval to

that of the following in the two cases. It is to be expected that

there should be less irregularity in a series of reactions