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

1.000 : 1.400 39.0 ” 46.0 ” 15.0 “

1.000 : 1.182 60.0 ” 37.2 ” 2.8 “

1.000 : 1.000 85.4 ” 12.2 ” 2.4 “

1.000 : 0.846 89.2 ” 10.8 “

1.000 : 0.714 100.0 “

1.000 : 0.660 96.0 ” 4.0 “

The increase in the number of inverted forms which occur is

coördinated percentually in the following table with the successive

increments of difference between the accented and unaccented intervals

of the group:

TABLE LI.

Rhythm. 2.428 2.000 1.769 1.666 1.571 1.400 1.222 1.182 1.118 1.000

Trochaic, 93.7 74.0 44.2 25.0 25.0 2.9

Datylic, 93.6 54.0 39.4 18.4

These figures are corroborative of the preceding conclusions. The

dactylic figure is maintained in the presence of much greater

differences in the relative durations of accented and unaccented

intervals than is the trochaic. In the latter, inversions not only

appear earlier in the series, but become the (practically) exclusive

mode of apprehension at a point where not fifty per cent, of the

dactyls have suffered transformation. At a certain definite stage in

the process the tendencies toward the two forms of apprehension

balance each other, so that with the slightest change in direction of

attention the rhythmical figure inverts and reverts to the original

form indifferently. These points are defined, in the case of the two

rhythms here reported on, by the following (or intermediate) ratios:

Trochaic-Iambic, (1.400-1.571): 1.000; Dactylic-Anapæstic,

(1.666-2.000): 1.000.

The temporal conditions of such equilibrium are a strict function of

the degree of accentuation which the rhythm group presents. The

location of the indifference point must, therefore be independently

determined for each intensive value through which the accented element

may pass. Its changes are given for five such increments in the

following table, in which the values of the various intervals are

represented as proportions of the absolute magnitudes which appear in

the first, or undifferentiated series.

TABLE LII.

Intensive Form. 1st Interval. 2d Interval. 3d Interval.

1/8 1/8 1/8 1.000 1.000 1.000

3/8 1/8 1/8 1.042 1.010 0.948

7/8 1/8 1/8 1.142 1.021 0.862

15/8 1/8 1/8 1.146 1.042 0.808

24/8 1/8 1/8 1.291 1.000 0.708

IV. THE COMBINATION OF RHYTHMICAL GROUPS IN HIGHER SYNTHESES AND THEIR

EQUIVALENCES.

In the elaboration of higher rhythmical forms the combination of

formally identical groups is rather the rule than the exception, since

in poetical structures the definition of the metrical form and the

maintenance of its proper relations depend on a clear preponderance of

its own particular unit-type over local variants. In the experimental

investigation of composite rhythm forms the temporal relations of

structures presenting such likeness in their constituent groups were

first taken up. In the conduct of the research those differences of

intensity which are actually expressed and apprehended in the

utterance of a rhythmic sequence were uniformly employed. While there

is no doubt that a succession of perfectly identical forms would,

under the requisite temporal conditions, be apprehended as presenting

major and minor phases of accentuation, yet in the expression of

rhythmic relations the subordination of accents is consistently

observed, and all our ordinary apprehension of rhythm, therefore, is

supported by an objective configuration which fulfils already the form

of our own subjective interpretation.

The temporal relations of these major and minor phases cannot be

considered apart from the index of their respective accentuations. As

the distribution of elements within the simple group fluctuates with

the changes in intensive accentuation, so does the form of temporal

succession in larger structures depend on the relations of intensity

in their primary and secondary accentuations. The quantitative values

hereafter given apply, therefore, only to those specific intensities

involved in the experiment. Two types were chosen, the trochee and the

dactyl. The series of sounds was given by successive hammer-falls of

7/8 and 1/8 inch for the major, and 3/8 and 1/8 inch for the minor

phase. The distribution of time-values within each group was made on

the basis of previous experimentation to determine those relations

which support psychological uniformity. These internal relations were

maintained unchanged throughout the series of ratios which the

durations of the two groups presented. Four subjects took part in the

experiment. The quantitative results in the composition of trochaic

forms are given in the following tables (LIII., LIV.), the figures of

which present, in the form of percentages of total judgments, the

apprehension of sensible equality or disparity in the two groups.

In the earlier set of experiments the series of ratios diverged in

both directions from unity; in the later it departed in one only,

since every divergence in the opposite direction had, in the previous

experiments, been remarked at once by the observer. In this second set

the series of differences is more finely graded than in the former;

otherwise the two sets of figures may be considered identical. Using

the equilibrium of errors as an index of sensible equality, the two

trochaic groups are perceptually uniform when the temporal ratio of

major and minor lies between 1.000:0.757 and 1.000:0.779.

TABLE LIII.

Ratio of Duration 2d Group Judged to be

of 1st Group to 2d. + = -

1.000 : 1.250 100 per cent.

1.000 : 1.116 100 “

1.000 : 1.057 100 “

1.000 : 1.000 100 “

1.000 : 0.895 68 ” 22 per cent.

1.000 : 0.800 25 ” 75 “

1.000 : 0.714 100 per cent.

TABLE LIV.

Ratio of Duration 2d Group Judged to be

of 1st Group to 2d. + = -

1.000 : 1.000 100.0 per cent.

1.000 : 0.973 87.5 ” 12.5 per cent.

1.000 : 0.870 66.6 ” 33.3 “

1.000 : 0.823 33.3 ” 22.2 ” 44.4 per cent.

1.000 : 0.777 50.0 ” 50.0 “

1.000 : 0.735 33.3 ” 33.3 ” 33.3 “

1.000 : 0.694 33.3 ” 66.6 “

In the dactylic form, as in the second trochaic series, ratios varying

from unity in one direction only were employed. The results follow:

TABLE LV.

Ratio of Duration Second Group Judged to be

of 1st Group to 2d. + = -

1.000 : 1.000 100.0 per cent.

1.000 : 0.946 62.5 ” 37.5 per cent.

1.000 : 0.915 33.3 ” 66.6 “

1.000 : 0.895 8.3 ” 33.3 ” 58.3 per cent.

1.000 : 0.800 40.0 ” 60.0 “

As in the preceding case, when relations of equality obtained between

the two subgroups, the secondary period in every instance appeared

longer than the primary. This prolongation was uniformly reported as

displeasing. The distribution of values which here support

psychological uniformity lies between 1.000:0.915 and 1.000:0.895,

that is to say, the difference of phases is less marked than in the

case of the simpler trochaic composite. This is a structural principle

which penetrates all rhythmical forms. The difference in the case of

both of these composites is less than in the opposition of phases

within the simple group, in which for identical intensities and

(practically) the same group of observers these presented the ratio

1.000:0.714. It is evident that the relative differentiation of

accented and unaccented intervals due to specific variations in

intensity is greater than is that of successive groups characterized

by similar differences of accentual stress; and if still more

extensive groups were compared it would unquestionably be found that a

further approximation to equality had taken place.

In the integration of rhythmical groups this subordination of the

intensive accents which characterize them is not the sole mechanism of

higher synthesis with which we are presented. Another mode is the

antithesis of rhythmical quantities through verse catalepsis. Such

variation of the rhythmical figure can take place in two directions

and in two only: by an increase in the number of constituents, giving

what may be called redundancy to the measure, and by a decrease in

their number, or syncopation. Each of these forms of departure from

the typical figure fulfils a specific rhythmic function which

determines its temporal and intensive characters, and its local

position in the rhythmical sequence.

(a) Redundant Measures.—The position of such a measure is

uniformly initial. On rare occasions individual observers reported an

inversion of this order in the earlier portion of the series,[8] but

in no case were subjectively formulated series concluded in this way;

and when the objective succession ended with the redundant measure the

experience was rhythmically displeasing. In accentual stress the

redundant measure is of secondary rank, the chief intensity falling

upon the shorter, typical groups. Variation from the type does not,

therefore, unconditionally indicate a point of accentual stress,

though the two are commonly connected.

[8] This was probably due to beginning the series of

stimulations with the typical measure. Such beginning was

always made by chance.

In regard to the relative duration of the redundant measure the

subjective reports indicate a large variability. The dactylic form

appears to be slightly longer than the trochaics among which it

appears; but not infrequently it is shorter.[9] These variations are

probably connected with differences in stress due to the relation

which the measure bears to the accentual initiation of the whole

series; for this accent apparently may fall either within the

redundant measure itself or on the first element of the succeeding

___ _____

>/ > | | > >

group, thus: | q q q; q q; |, or | e e e q q; q q |.

_/

[9] The only form taken up was the occurrence of dactylic

measures in trochaic series.

Two rhythm forms were analyzed, the trochaic and the dactylic, the

series of sounds being given by hammer-falls of 7/8 and 1/8 inch for

accented and unaccented elements respectively. In each experiment full

and syncopated measures alternated regularly with each other in

continuous succession, giving the forms

> > > >

| q. q; q % | and | q. q q; q. % % |.

_____/ ____________/

The initiation of the series was in every case determined by chance.

Six observers took part in the work with trochaic forms, five in that

with dactylic. The quantitative results are given in the following

tables, in each of which the relations of duration, position and

stress are included.

TABLE LVI.

TROCHAIC FORM.

Apparent Accentuation

Ratio of 1st Second Group Judged to be 2d Group of Second Group.

to 2d Group. + = - Final + = -

1.000:1.000 55.5% 44.4% 100% 71.5% 28.5%

1.000:0.946 83.3 16.6% 100 30.0 70.0

1.000:0.895 66.6 11.1 22.2 100 30.0 60.0 10.0%

1.000:0.846 16.6 41.6 41.6 100 40.0 60.0

1.000:0.800 16.6 41.6 41.6 100 40.0 60.0

1.000:0.756 49.9 24.9 24.9 100 40.0 60.0

1.000:0.714 16.6 41.6 41.6 100 20.0 80.0

TABLE LVII.

DACTYLIC FORM.

Apparent Accentuation

Ratio of 1st Second Group Judged to be 2d Group of Second Group.

to 2d Group. + = - Final + = -

1.000:1.000 100.0% 100% 40.0% 60.0%

1.000:0.946 83.3% 16.6% 100 40.0 60.0

1.000:0.895 66.6 33.3 100 20.0 80.0

1.000:0.846 37.5 62.5 100 40.0 60.0

1.000:0.800 100.0 100 40.0 60.0

The syncopated measure, like the redundant, bears to the acatalectic

group specific relations of duration, accentual stress, and position

in the rhythmical sequence. In position it is final. This relation is

independent of the factor of duration, on which the order of elements

in the simple measure depends. Even the excessive shortening which

occurs in the trochaic form, when the full measure has a duration

almost one and one half times as great as the syncopated, brings about

no inversion of the order.

In duration the syncopated group is a shortened measure. The amount of

reduction necessary to preserve rhythmical proportion with the rest of

the sequence is greater in the trochaic than in the dactylic form, as

in the relation of accented to unaccented elements in the simple

measure it is greater than in the case of the trochaic, a principle of