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

result of subjective rhythmization undergoes a progressive decrease in

absolute magnitude as the rate of succession among the undifferentiated

stimuli is accelerated. The series of values for units containing from

two to eleven constituents is given in the following table:

TABLE III.

No. of Elements. Duration in Seconds.

Two, 2.00

Three, 1.75

Four, 1.66

Seven, 1.75

Nine, 1.50

Eleven, 0.97

If the time-value of the simple rhythm group here depended solely on

the relation of the successive stimuli to the subjective rhythm

period, no progressive diminution should be presented, for in

proportion as the absolute value of the separating intervals decreases

the true nature of this period should be more clearly manifested. It

is scarcely to be doubted that the complexity of its content is

likewise a determinant of the temporal value of this period, and that

to this factor is to be attributed the changes which are here

presented.[4]

[4] Bolton reports a similar decrease in the temporal value of

the unit, and gives the following quantitative relations:

Average length of 2-group, 1.590 secs.

” ” ” 3-group, 1.380 “

” ” ” 4-group, 1.228 “

” ” ” 6-group, 1.014 “

” ” ” 8-group, 1.160 “

In subjective rhythmization the number of elements which compose the

unit is dependent solely on the relation of the subjective rhythm

period to the rate of succession among such elements. In objective

rhythm, as has been pointed out, a free treatment of the material is

rendered impossible by the determination of specific points of

increased stress, in virtue of which a new unit of change appears,

namely, the whole period elapsing from any one occurrence of

accentuation to its return.

But this is not the sole determinant of the numerical limits of the

simple group in such objective rhythms. The structural unit must

indeed adhere to the scheme given by the period of the recurrent

accentuation; but the point at which simple successions of this figure

give place to complex structures (at which | >q. q q_| is replaced by

| >q. q q;_q. q q_|, for example) may conceivably be hastened or

retarded by other factors than that of the simple rate of succession.

The degrees of segregation and accentuation which characterize the

rhythmic unit are elements which may thus affect the higher synthesis.

Increase in either of these directions gives greater definition to the

rhythmic figure and should tend to preserve the simple group in

consciousness. The latter relation was not made the subject of special

investigation in this research. The former was taken up at a single

point. The sounds were two in number, alternately accented and

unaccented, produced by hammer-falls of 7/8 and 1/8 inch respectively.

These were given at three rates of succession, and three different

degrees of segregation were compared together. In the following table

is given, for six subjects, the average number of elements entering

into the group-form, simple or complex, under which the rhythm was

apprehended:

TABLE IV.

Ratio of Beat-interval Value in Seconds of Average Interval,

to Group-interval. 5/12 3/12 2/12

1.000: 1.400 3.5 5.3 9.0

1.000: 1.000 4.0 5.4 9.6

1.000: 0.714 5.2 8.4 10.8

The quantitative relations presented by these figures are consistent

throughout. For every rate of speed the average rhythmic group is

smallest when the interval separating the successive groups is at its

maximum; it is largest when this interval is at its minimum; while in

each case a median value is presented by the relation of uniformity

among the intervals. In the second as well as the first of the ratios

included in the foregoing table the interval which separates adjacent

groups is felt to be distinctly longer than that internal to the

group; in the third the relative durations of the two intervals are

those which support psychological uniformity. In the latter case, in

consequence of the freer passage from group to group, the continuity

of the rhythmical series is more perfectly preserved than in the

former, and the integration of its elements into higher syntheses more

extended.

The extension of the numerical limits of the rhythm group in

subjective rhythm which appear in consequence of progressive

acceleration in the rate of succession is given for a series of six

different values of the separating intervals in the following table,

the figures of which represent the average for six observers:

TABLE V.

HIGHEST UNITS WHICH APPEAR.

Value of interval in secs.: 12/12 7/12 5/12 3/12 2/12 1/12

No. of el’s in rhythm group: 2.5 3.0 4.0 7.0 9.0 11.0

Average duration of group: 2.500 1.750 1.666 1.750 1.500 0.917

SIMPLE UNITS.

No. of els. in simplest group: 2.5 2.3 2.9 3.7 4.7 5.0

Duration of simplest group: 2.50 1.34 1.21 0.92 0.78 0.41

The rate of increase here presented in the number of elements is not

sufficiently rapid to counterbalance the acceleration of speed and

maintain a constancy in the duration of the group. The greatest value

of this period is coördinated with the slowest rate of succession, the

lowest with the most rapid. As the speed increases, the duration of

the rhythmic unit is shortened. Its average duration for all rates

here included is 1.680 sec., or, without the first of the series

(one-second intervals, at which only two of the observers received the

impression of rhythm), 1.516 sec. These values are not for the

simplest combinations, but for the highest synthetical unit which was

immediately apprehended in the series of stimulations. This

compounding becomes more pronounced as the rate of succession is

accelerated, but even at intervals of 5/12 and 7/12 sec. it is the

characteristic mode of apprehension.

The number of elements in the simple groups of which these higher

units are composed, and their average duration, are also given in the

table. These likewise show a progressive increase in number, but of a

much slower rate than that manifested by the total synthesis of

elements. That is to say, in subjective rhythm as well as in

objectively figured series, subordinate rhythmical differences in the

material sink out of consciousness less rapidly than the inclusion of

fresh elements takes place; in other words, the organic complexity of

the rhythmic unit increases with every acceleration in the rate of

succession. The duration of these simple structural groups, as may be

inferred, decreases with such acceleration, but at a much more rapid

rate than is the case with the total reach of rhythmical apprehension,

the value of that unit which appears in connection with the highest

speed here included being less than half a second. The ‘liveliness’ of

such rapid measures is thus a resultant of several factors. It is not

a consequence solely of the more rapid rate at which the individual

stimuli succeed one another, but depends also on the shortening of the

periods of both these rhythmical units and on the progressive

divergence of the simple from the complex group.

The influence of the rate of succession on the rhythmical unit is not

confined to its segregation from adjacent groups, but affects the

internal configuration of the measure as well. With every acceleration

in rate the relative preponderance of the interval following the

accented element (in rhythms having initial stress) increases; as the

rate is retarded, smaller and smaller degrees of difference in the

values of accented and unaccented intervals are discriminated. In this

regard the influence of reduction in the absolute value of the

separating intervals is analogous to that of increased accentuation

within the group. In fast tempos and with high degrees of emphasis the

interval following the initial accent is relatively longer, that

following the unaccented relatively shorter, than at slow tempos and

with weak emphasis. This is but another way of expressing the fact

that as the elements of the auditory series succeed one another more

and more slowly the impression of rhythm fades out and that as their

succession increases in rapidity the impression becomes more and more

pronounced. The following table presents these relations in a

quantitative form for trochaic rhythm. The figures represent the

number of times the second, or group interval, was judged to be

greater than, equal to, or less than the first or internal interval of

the group. Three rates were compared together, having average

intervals of 5/12, 3/12 and 2/12 sec. Six observers took part, but

only a small number of judgments was made by each, to which fact is

probably to be attributed the irregularities of form which appear in

the various curves:

TABLE VI.

Ratio of 1st to 2d 5/12 3/12 2/12

Interval + = - + = - + = -

1.000: 1.057 95.0 0.0 5.0 100.0 0.0 0.0 100.0 0.0 0.0

1.000: 1.000 94.7 5.3 0.0 86.0 10.5 3.5 87.5 12.5 0.0

1.000: 0.895 40.0 60.0 0.0 46.2 49.6 3.3 74.1 18.5 7.4

1.000: 0.846 41.0 50.0 9.0 39.4 54.6 6.0 40.0 52.0 8.0

1.000: 0.800 20.0 60.0 20.0 13.0 70.0 17.0 53.8 46.2 0.0

1.000: 0.756 29.4 23.5 47.1 21.8 43.4 34.8 28.0 72.0 0.0

Av. for all ratios, 53.3 33.1 13.5 51.1 38.0 10.8 63.9 33.5 2.6

Within the limits of its appearance, as the figures just presented

indicate, the force, definition and persistency of the rhythmical

impression do not continue uniform. At the lowest rates at which

rhythm appears the integration of the successive groups is weak and

their segregation indistinct. As the rate increases the definition of

the rhythmic form grows more precise, group is separated from group by

greater apparent intervals, and the accentuation of the groups

becomes more pronounced. In subjective rhythmization of an

undifferentiated series, likewise, the impression of segregation and

periodic accentuation grows more forcible and dominating as the rate

increases. The sensitiveness to form and dynamic value in the

successive groups also increases up to a certain point in the process

of acceleration. As expressed in the capacity to discriminate

departures from formal equivalence among the groups, this function

reached its maximum, for those concerned in this investigation, at

rates varying individually from 0.3 sec. to 0.6 sec. in the value of

their intervals.

It is in virtue of its nature as an impression, as opposed to a

construction, that every structural unit, and every rhythmical

sequence into which it enters, possesses a distinct individual

quality, by which it is immediately apprehended and discriminated from

other forms, as the face of an acquaintance is remembered and

identified without detailed knowledge of the character of any feature

it possesses. For what persists from the reception of a rhythm

impression and becomes the basis of future recognition and

reproduction of it, is not the number of beats in a unit or sequence,

nor the absolute or relative intensity of the components of the group;

it is the quality of the groups as individuals, and the form of the

sequence as a whole. The phrase and verse are as vividly conceived as

the unit group; the stanza or the passage is apprehended as

immediately and simply as the bar or the measure. Of the number and

relation of the individual beats constituting a rhythmical sequence

there is no awareness whatever on the part of the æsthetic subject. I

say this without qualification. So long as the rhythmical impression

endures the analytic unit is lost sight of, the synthetic unit, or

group, is apprehended as a simple experience. When the rhythm function

is thoroughly established, when the structural form is well integrated

or familiar, it becomes well-nigh impossible to return to the analytic

attitude and discern the actual temporal and intensive relations which

enter into the rhythm. Even the quality of the organic units may lapse

from distinct consciousness, and only a feeling of the form of the

whole sequence remain. The Gestaltsqualität of the passage or the

stanza is thus frequently appreciated and reproduced without an

awareness of its sequential relations, though with