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

to be compared, the distribution of time values within them, the

position of accents, rests, and the like—does not in any way affect

the sense of equivalence between the unlike units. Against a group of

two, three, four, or even five elements may be balanced a syncopated

measure which contains but one constituent, with the sense of full

rhythmical equivalence in the functional values of the two types.

Indeed, in the case of five-beat rhythms the definition of values is

greater when such opposition finds place than when the five-beat

group is continuously repeated. This is to be explained doubtlessly by

the more definite integration into a higher rhythmical unity which is

afforded under the former conditions.

The number and the distribution of elements are factors variable at

will, and are so treated in both musical and poetical expression. The

condition which cannot be transgressed is the maintenance of strict

temporal relations in the succession of total groups which constitute

the rhythmical sequence. These relations are, indeed, not invariable

for either the single interval or the duration of the whole group, but

they are fixed functions of the dynamic values of these elements and

units. Two identically figured groups (e.g., | >q. q q | >q. q q |

), no more possess rhythmically substitutionary values than does the

opposition of a single beat to an extended series (e.g.,

| >q. | >q. q q | ), apart from this factor of temporal proportion.

Those groups which are identical in figure must also be uniform in

duration if they are to enter as substitutionary groups into a

rhythmical sequence.[5] When the acatalectic type is alternately

departed from and returned to in the course of the rhythmical

sequence, the metrical equivalents must present total time-values

which, while differing from that of the full measure in direction and

degree, in dependence on the whole form of their structure, maintain

similar fixed relations to the primary type. The changes which these

flexible quantities undergo will here only be indicated. If the

substitutionary groups be of different figures, that which comprises

the larger number of elements will occupy the greater time, that which

contains fewer, the less.

[5] Theoretically and strictly identical; this abstracts from

the coördination of such identical groups as major and minor

components of a higher rhythmical synthesis, which is really

never absent and in virtue of which the temporal values of the

groups are also differentiated.

I do not forget the work of other observers, such as Brücke, who finds

that dactyls which appear among trochees are of less duration than the

latter, nor do I impugn their results. The rhythmical measure cannot

be treated as an isolated unit; it must always be considered in its

structural relations to the rhythmical sequence of which it forms a

part. Every non-conforming measure is unquestionably affected by the

prevailing type of the rhythmical sequence in which it occurs. Brücke

points out the converse fact that those trochees and iambs are longest

which appear in dactylic or other four-measures; but this ignores the

complexity of the conditions on which the character of these intrusive

types depends. The time-values of such variants are also dependent on

the numerical preponderance of the typical form in the whole series.

When a single divergent form appears in the sequence the dynamic

relations of the two types is different from that which obtains when

the numbers of the two approach equality, and the effect of the

prevailing form on it is proportionally greater. Secondly, the

character of such variants is dependent on the subordinate

configuration of the sequence in which they appear, and on their

specific functions within such minor rhythmical figures. The relative

value of a single dactyl occurring in an iambic pentameter line cannot

be predicated of cases in which the two forms alternate with each

other throughout the verse. Not only does each type here approximate

the other, but each is affected by its structural relation to the

proximately higher group which the two alternating measures compose.

Thirdly, the quantitative values of these varying forms is related to

their logical significance in the verse and the degree of accentuation

which they receive. Importance and emphasis increase the duration of

the measure; the lack of either shortens it. In this last factor, I

believe, lies the explanation of the extreme brevity of dactyls

appearing in three-rhythms. When a specific rhythm type is departed

from, for the purpose of giving emphasis to a logically or metrically

important measure, the change is characteristically in the direction

of syncopation. Such forms, as has been said elsewhere, mark nodes of

natural accentuation and emphasis. Hence, the dactyl introduced into

an iambic or trochaic verse, which, so far as concerns mere number of

elements, tends to be extended, may, in virtue of its characteristic

lack of accentuation and significance, be contracted below the value

of the prevailing three-rhythm. Conversely the trochee introduced into

a dactylic sequence, in consequence of its natural accentuation or

importance, may exceed in time-value the typical four-rhythm forms

among which it appears. The detailed examination of the relation of

temporal variations to numerical predominance in the series, to

subordinate structural organization, and to logical accentuation, in

our common rhythms, is a matter of importance for the general

investigation which remains still to be carried out. In so far as the

consideration of these factors entered into the experimental work of

the present research, such quantitative time relations are given in

the following table, the two types in all cases occurring in simple

alternation:

TABLE XXI.

Rhythm. 1st Meas. 2d Meas. Rhythm. 1st Meas. 2d Meas.

. > > > > .

q q q; q q % 1.000 1.091 q q %; q q q 1.000 1.140

. > > .

q q q; q q % 1.000 1.159 q q %; q q q 1.000 1.021

. > > .

q q q; q q % 1.000 1.025 q q %; q q q 1.000 1.267

> . . >

q q q; q q % 1.000 0.984 q q %; q q q 1.000 1.112

> . . >

q q q; q q % 1.000 0.766 q q %; q q q 1.000 1.119

As the disparity in numerical constitution increases, so will also the

divergence in time-value of the two groups concerned. When

differentiation into major and minor phases is present, the duration

of the former will be greater than that of the latter. Hence, in

consequence of the combination of these two factors—e.g., in a

syncopated measure of unusual emphasis—the characteristic time-values

may be inverted, and the briefer duration attach to that unit which

comprises the greater number of elements. Intensive values cannot take

the place of temporal values in rhythm; the time form is fundamental.

Through all variations its equivalences must be adhered to. Stress

makes rhythm only when its recurrence is at regular intervals. The

number of subordinate factors which combine with the accented element

to make the group is quite indifferent. But whether few or many, or

whether that element on which stress falls stands alone (as it may),

the total time values of the successive groups must be sensibly

equivalent. When a secondary element is absent its place must be

supplied by a rest of equivalent time-value. If these proper temporal

conditions be not observed no device of intensive accentuation will

avail to produce the impression of metrical equivalence among the

successive groups.

B. The Distribution of Elements Within the Group.

(a) The Distribution of Intensities.

In the analysis of the internal constitution of the rhythmic unit, as

in other parts of this work, the investigation follows two distinct

lines, involving the relations of rhythm as apprehended, on the one

hand, and the relations of rhythm as expressed, on the other; the

results in the two cases will be presented separately. A word as to

the method of presentation is necessary. The fact that in connection

with each experiment a group of questions was answered gives rise to

some difficulty in planning the statement of results. It is a simple

matter to describe a particular set of experiments and to tell all the

facts which were learned from them; but it is not logical, since one

observation may have concerned the number of elements in the rhythmic

unit, another their internal distribution, and a third their

coalescence in a higher unity. On the other hand, the statement of

each of these in its own proper connection would necessitate the

repetition of some description, however meager, of the conditions of

experimentation in connection with each item. For economy’s sake,

therefore, a compromise has been made between reporting results

according to distribution of material and according to distribution of

topics. The evidence of higher grouping, for example, which is

afforded by variations in duration and phases of intensity in

alternate measures, will be found appended to the sections on these

respective classes of material.

In all the following sections the hammer-clang apparatus formed the

mechanism of experimentation in sensory rhythms, while in reactive

rhythms simple finger-tapping was employed.

In comparing the variations in stress which the rhythmical material

presents, the average intensities of reaction for the whole group has

been computed, as well as the intensities of the single reactions

which compose it. This has been done chiefly in view of the unstable

intensive configuration of the group and the small amount of material

on which the figures are based. The term is relative; in ascertaining

the relations of intensity among the several members of the group, at

least ten successive repetitions, and in a large part of the work

fifty, have been averaged. This is sufficient to give a clear

preponderance in the results to those characteristics which are really

permanent tendencies in the rhythmical expression. This is especially

true in virtue of the fact that throughout these experiments the

subject underwent preliminary training until the series of reactions

could be easily carried out, before any record of the process was

taken. But when such material is analyzed in larger and smaller series

of successive groups the number of reactions on which each average is

based becomes reduced by one half, three quarters, and so on. In such

a case the prevailing intensive relations are liable to be interfered

with and transformed by the following factor of variation. When a

wrong intensity has accidentally been given to a particular reaction

there is observable a tendency to compensate the error by increasing

the intensity of the following reaction or reactions. This indicates,

perhaps, the presence of a sense of the intensive value of the whole

group as a unity, and an attempt to maintain its proper relations

unchanged, in spite of the failure to make exact coördination among

the components. But such a process of compensation, the disappearance

of which is to be looked for in any long series, may transpose the

relative values of the accented elements in two adjacent groups when

only a small number of reactions is taken into account, and make that

seem to receive the major stress which should theoretically receive

the minor, and which, moreover, does actually receive such a minor

stress when the value of the whole group is regarded, and not solely

that member which receives the formal accentuation.

The quantitative analysis of intensive relations begins with triple

rhythms, since its original object was to compare the relative

stresses of the unaccented elements of the rhythmic group. These

values for the three forms separately are given in Table XXII., in

which the value of the accented element in each case is represented by

unity.

TABLE XXII.

Rhythm. 1st Beat. 2d Beat. 3d Beat.

Dactylic, 1.000 0.436 0.349

Amphibrachic, 0.488 1.000 0.549

Anapæstic, 0.479 0.484 1.000

The dactylic form is characterized by a progressive decline in

intensity throughout