Sixteen Experimental Investigations from the Harvard Psychological Laboratory, Hugo Münsterberg [top fiction books of all time TXT] 📗

in this report. Here it is in place to point out

certain indirect evidence of the same process of resolution as

manifested in the treatment of longer series of elements.

 

The breaking up of such series into subgroups may not be an explicitly

conscious process, while yet its presence is indispensable in giving

rhythmical form to the material. One indication of such

undiscriminated rhythmical modification is the need of making or

avoiding pauses between adjacent rhythmical groups according as the

number of their constituents varies. Thus, in rhythms having units of

five, seven, and nine beats such a pause was imperative to preserve

the rhythmical form, and the attempt to eliminate it was followed by

confusion in the series; while in the case of rhythms having units of

six, eight, and ten beats such a pause was inadmissible. This is the

consistent report of the subjects engaged in the present

investigation; it is corroborated by the results of a quantitative

comparison of the intervals presented by the various series of

reactions. The values of the intervals separating adjacent groups for

a series of such higher rhythms are given in Table XX. as proportions

of those following the initial, accented reaction.

 

TABLE XX.

 

Rhythm. Initial Interval. Final Interval

Five-Beat, 1.000 1.386

Six ” 1.000 0.919

Seven ” 1.000 1.422

Eight ” 1.000 1.000

Nine ” 1.000 1.732

Ten ” 1.000 1.014

 

The alternate rhythms of this series fall into two distinct groups in

virtue of the sharply contrasted values of their final intervals or

group pauses. The increased length of this interval in the

odd-numbered rhythms is unquestionably due to a subdivision of the

so-called unit into two parts, the first of which is formally

complete, while the latter is syncopated. In the case of five-beat

rhythms, this subdivision is into threes, the first three of the five

beats which compose the so-called unit forming the primary subgroup,

while the final two beats, together with a pause functionally

equivalent to an additional beat and interval, make up the second, the

system being such as is expressed in the following notation:

| .q. q q; >q. q % |. The pause at the close of the group is

indispensable, because on its presence depends the maintenance of

equivalence between the successive three-groups. On the other hand,

the introduction of a similar pause at the close of a six-beat group

is inadmissible, because the subdivision is into three-beat groups,

each of which is complete, so that the addition of a final pause would

utterly unbalance the first and second members of the composite group,

which would then be represented by the following notation:

| >q. q q; .q. q q % |; that is, a three-group would alternate with a

four-group, the elements of which present the same simple time

relations, and the rhythm, in consequence, would be destroyed. The

same conditions require or prevent the introduction of a final pause

in the case of the remaining rhythm forms.

 

The progressive increase in the value of the final interval, which

will be observed in both the odd-and even-numbered rhythms, is

probably to be attributed to a gradual decline in the integration of

the successive groups into a well-defined rhythmical sequence.

 

This subdivision of material into two simple phases penetrates all

rhythmical structuring. The fundamental fact in the constitution of

the rhythmical unit is the antithesis of two phases which we call the

accented and the unaccented. In the three-beat group as in the

two-beat, and in all more complex grouping, the primary analysis of

material is into these two phases. The number of discriminable

elements which enter each phase depends on the whole constitution of

the group, for this duality of aspect is carried onward from its point

of origin in the primary rhythm group throughout the most complex

combination of elements, in which the accented phase may comprise an

indefinitely great number of simple elements, thus:

 

______ __________ ______________

/

> . > . >> .

| q q ; q q |, | q q q; q q q |, | q q q q; q q q q |, etc.

_/

>

 

An indication of this process of differentiation into major and minor

phases appears in the form of rhythm groups containing upwards of four

elements. In these the tendency is, as one observer expresses it, ‘to

consider the first two beats as a group by themselves, with the others

trailing off in a monotonous row behind.’ As the series of elements

thus bound up as a unit is extended, the number of beats which are

crowded into the primary subgroup also increases. When the attempt was

made to unite eleven or twelve reactions in a single group, the first

four beats were thus taken together, with the rest trailing off as

before. It is evident that the lowest groups with which attention

concerned itself here were composed of four beats, and that the actual

form of the (nominally) unitary series of eleven beats was as follows:

 

_______________________

/

>> > >

| q q q q; q q q q; q q q q |.

…

 

The subscripts are added in the notation given above because it is to

be doubted if a strictly simple four-beat rhythm is ever met with. Of

the four types producible in such rhythm forms by variation in the

accentual position, three have been found, in the course of the

present investigation, to present a fundamental dichotomy into units

of two beats. Only one, that characterized by secondary accentuation,

has no such discriminable quality of phases. Of this form two things

are to be noted: first, that it is unstable and tends constantly to

revert to that with initial stress, with consequent appearance of

secondary accentuation; and second, that as a permanent form it

presents the relations of a triple rhythm with a grace note prefixed.

 

The presence of this tendency to break up the four-rhythm into

subgroups of two beats explains a variety of peculiarities in the

records of this investigation. The four-beat rhythm with final accent

is found most pleasant at the close of a rhythmical sequence. The

possibility of including it in a continuous series depends on having

the final interval of ‘just the right length.’ If one keeps in mind

that a secondary initial accent characterizes this rhythm form, the

value required in this final interval is explained by the resolution

of the whole group into two units of three beats each, the latter of

the two being syncopated. The pause is of ‘just the right length’ when

it is functionally equal to two unaccented elements with their

succeeding intervals, as follows: | .q. q q; .q % % |.

 

Likewise in four-rhythms characterized by initial stress there appears

a tendency to accent the final beat of the group, as well as that to

accent the third. Such a series of four may therefore break up in

either of two ways, into | >q. q; .q q | on a basis of two-beat units,

or into | .q. q q; >q % %| on a basis of three-beat units.

 

The persistence of these simple equivalences appears also in the

treatment of syncopated measures and of supplementary or displaced

accents. Of the form | >q. q >q. | one reactor says, and his

description may stand for all, “This deliberate introduction of a

third accent on the last beat is almost impossible for me to keep. The

single group is easy enough and rather agreeable, but in a succession

of groups the secondarily accented third beat comes against the first

of the next group with a very disagreeable effect.” This is the case

where no pause intervenes between the groups, in which case the rhythm

is destroyed by the suppression, in each alternate simple group, of

the unaccented phase; thus, | >q. q >q. | alone is pleasant, because

it becomes | .q. q; >q % |, but in combination with preceding and

succeeding groups it is disagreeable, because it becomes in reality

| >q. q; .q % |, etc. A long pause between the groups destroys this

disagreeableness, since the lacking phase of the second subgroup is

then restored and the rhythm follows its normal course.

 

The amphibrachic form, | >q q. q |, is more difficult to maintain than

either the dactylic or the trochaic, and in a continuous series tends

to pass over into one of these, usually the former. ‘With sufficient

pause,’ the reactors report, ‘to allow the attitude to die away,’ it

is easily got. The same inability to maintain this form in

consciousness appears when a continuous series of clicks is given,

every third of which is louder than the rest. Even when the beginning

of the series is made coincident with the initial phase of the

amphibrachic group the rhythmic type slips over into the dactylic, in

spite of effort. In this, as in the preceding type of reaction, if the

interval separating adjacent groups be lengthened, the rhythm is

maintained without trouble. The ‘dying away’ of the attitude lies

really in such an arrangement of the intervals as will formally

complete a phrase made up of simple two-beat units.

 

The positive evidence which this investigation affords, points to the

existence of factors of composition in all rhythms of more than three

beats; and a variety of peculiarities which the results present can be

explained—and in my estimation explained only—on the basis of such

an assumption. I conclude, therefore, that strictly stated the

numerical limit of simple rhythm groups is very soon reached; that

only two rhythmical units exist, of two and three beats respectively;

that in all longer series a resolution into factors of one of these

types takes place; and, finally, that the subordination of higher

rhythmical quantities of every grade involves these simple relations,

of which, as the scope of the synthesis increases, the opposition of

simple alternate phases tends more and more to predominate over

triplicated structures.

 

Variation in the number of elements which enter into the rhythmic

unit does not affect the sense of equivalence between successive

groups, so long as the numerical increase does not reach a point at

which it lessens the definiteness of the unit itself. For the purpose

of testing this relation the reactors beat out a series of rhythm

forms from ‘one-beat’ rhythms to those in which the group consisted of

seven, eight and nine elements, and in which the units were either

identical with one another or were made up of alternately larger and

smaller numbers of elements. Two questions were to be answered in each

case; the manner in which these various changes affected the sense of

rhythmical equivalence in the alternate groups, and the variations in

affective quality which these changes introduced into the experience.

With the former of these problems we are here concerned. From

‘one-beat’ to four-beat rhythms the increase in number of constituents

in no way affects the sense of rhythmical equivalence. Beyond this

point there is a distinct falling off. ‘The first part of the rhythm

begins to fade away before the end of the second,’ says one; and

another: ‘The series then reverts to a monotonous succession without

feeling of rhythm.’ This decline marks those groups composed of an odd

number of elements much earlier and more strongly than those which

contain an even number. The sense of equivalence has fallen off at

five and practically disappears at seven beats, while groups of six

and eight retain a fairly definite value as units in a rhythmical

sequence. This peculiar relation must be due to the subconscious

resolution of the larger symmetrical groups into smaller units of

three and four constituents respectively.

 

Likewise the introduction of variations in the figure of the

group—that is, in the number of elements which enter