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

this curve to say, however, that the subjective rhythmization of

uniform material becomes more pronounced in proportion as the

intervals between the successive stimulations increase. Below a

certain rapidity the series of sounds fails wholly to provoke the

rhythmizing tendency; and it is conceivable that a change in the

direction of the curve may occur at a point beyond the limits included

within these data.

The introduction from time to time of a single extra tap, with the

effect of transposing the relations of the motor accompaniment to the

phases of the metronome, has been here interpreted as arising from a

periodically recurring adjustment of the reaction process to the

auditory series which it accompanies, and from which it has gradually

diverged. The departure is in the form of a slow retardation, the

return is a swift acceleration. The retardation does not always

continue until a point is reached at which a beat is dropped from, or

an extra one introduced into, the series. In the course of a set of

reactions which presents no interpolation of extra-serial beats

periodic retardation and acceleration of the tapping take place. This

tertiary rhythm, superimposed on the differentiation of simple phases,

has, as regards the forms involved in the present experiments, a

period of ten single beats or five measures.

From the fact that this rhythm recurs again and again without the

introduction of an extra-serial beat it is possible to infer the

relation of its alternate phases to the actual rate of the metronome.

Since the most rapid succession included was two beats per second, it

is hardly conceivable that the reactor lost count of the beats in the

course of his tapping. If, therefore, the motor series in general

parallels the auditory, the retardations below the actual metronome

rate must be compensated by periods of acceleration above it. Regarded

in this light it becomes questionable if what has been called the

process of readjustment really represents an effort to restore an

equilibrium between motor and auditory processes after an involuntary

divergence. I believe the contrasting phases are fundamental, and that

the changes represent a free, rhythmical accompaniment of the

objective periods, which themselves involve no such recurrent

differentiation.

Of the existence of higher rhythmic forms evidence will be afforded by

a comparison of the total durations of the first and second

five-groups included in the decimal series. Difference of some kind is

of course to be looked for; equivalence between the groups would only

be accidental, and inequality, apart from amount and constancy, is

insignificant. In the results here presented the differentiation is,

in the first place, of considerable value, the average duration of the

first of these groups bearing to the second the relation of

1.000:1.028.

Secondly, this differentiation in the time-values of the respective

groups is constant for all the subjects participating. The ratios in

their several cases are annexed:

TABLE XVIII.

Subject. Ratio.

J. 1.000:1.042

K. 1.000:1.025

N. 1.000:1.010

It is perhaps significant that the extent of this differentiation—and

inferably the definition of rhythmical synthesis—corresponds to the

reported musical aptitudes of the subjects; J. is musically trained,

K. is fond of music but little trained, N. is without musical

inclination.

The relations of these larger rhythmical series repeat those of their

constituent groups—the first is shorter, the second longer. The two

sets of ratios are brought together for comparison in the annexed

table:

TABLE XIX.

Subject. Unit-Groups. Five Groups.

J. 1.000:1.354 1.000:1.042

K. 1.000:1.388 1.000:1.025

N. 1.000:1.326 1.000:1.010

It is to be noted here, as in the case of beating out specific

rhythms, that the index of differentiation is greater in simple than

in complex groups, the ratios for all subjects being, in simple

groups, 1.000:1.356, and in series of five, 1.000:1.026.

There is thus present in the process of mechanically accompanying a

series of regularly recurring auditory stimuli a complex rhythmization

in the forms, first, of a differentiation of alternate intervals, and

secondly, of a synthesis of these in larger structures, a process here

traced to the third degree, but which may very well extend to the

composition of still more comprehensive groups. The process of

reaction is permeated through and through by rhythmical

differentiation of phases, in which the feeling for unity and

equivalence must hold fast through really vast periods as the long

slow phases swing back and forth, upon which takes place a swift and

yet swifter oscillation of rhythmical values as the unit groups become

more limited, until the opposition of single elements is reached.

III. THE CHARACTERISTICS OF THE RHYTHMICAL UNIT.

A. The Number of Elements in the Group and its Limits.

The number of elements which the rhythmical group contains is related,

in the first place, to the rate of succession among the elements of

the sequence. This connection has already been discussed in so far as

it bears on the forms of grouping which appear in an undifferentiated

series of sounds in consequence of variations in the absolute

magnitude of the intervals which separate the successive stimuli. In

such a case the number of elements which enter into the unit depends

solely on the rate of succession. The unit presents a continuous

series of changes from the lowest to the highest number of

constituents which the simple group can possibly contain, and the

synthesis of elements itself changes from a succession of simple forms

to structures involving complex subordination of the third and even

fourth degree, without other change in the objective series than

variations in tempo.

When objectively defined rhythm types are presented, or expression is

given to a rhythm subjectively defined by ideal forms, these simple

relations no longer hold. Acceleration or retardation of speed does

not unconditionally affect the number of elements which the rhythm

group contains. In the rhythmization of an undifferentiated series the

recurrence of accentuation depends solely on subjective conditions,

the temporal relations of which can be displaced only within the

limits of single intervals; for example, if a trochaic rhythm

characterizes a given tempo, the rhythm type persists under conditions

of progressive acceleration only in so far as the total duration of

the two intervals composing the unit approximates more closely to the

subjective rhythm period than does that of three such intervals. When,

in consequence of the continued reduction of the separating intervals,

the latter duration presents the closer approximation, the previous

rhythm form is overthrown, accentuation attaches to every third

instead of to alternate elements, and a dactylic rhythm replaces the

trochaic.

In objective rhythms, on the other hand, the determination of specific

points of increased stress makes it impossible thus to shift the

accentuation back and forth by increments of single intervals. The

unit of displacement becomes the whole period intervening between any

two adjacent points of accentuation. The rhythm form in such cases is

displaced, not by those of proximately greater units, but only by such

as present multiples of its own simple groups. Acceleration of the

speed at which a simple trochaic succession is presented results thus,

first, in a more rapid trochaic tempo, until the duration of two

rhythm groups approaches more nearly to the period of subjective

rhythmization, when—the fundamental trochaism persisting—the

previous simple succession is replaced by a dipodic structure in which

the phases of major and minor accentuation correspond to the

elementary opposition of accented and unaccented phases. In the same

way a triplicated structure replaces the dipodic as the acceleration

still continues; and likewise of the dactylic forms.

We may say, then, that the relations of rate to complexity of

structure present the same fundamental phenomena in subjective

rhythmization and objectively determined types, the unit of change

only differing characteristically in the two cases. The wider range of

subjective adjustment in the latter over the former experience is due

to the increased positive incentive to a rhythmical organic

accompaniment afforded by the periodic reinforcement of the objective

stimulus.

An investigation of the limits of simple rhythmical groups is not

concerned with the solution of the question as to the extent to which

a reactor can carry the process of prolonging the series of elements

integrated through subordination to a single dominant accentuation.

The nature of such limits is not to be determined by the introspective

results of experiments in which the observer has endeavored to hold

together the largest possible number of elements in a simple group.

When such an attempt is made a wholly artificial set of conditions,

and presumably of mechanisms, is introduced, which makes the

experiment valueless in solving the present problem. Both the

direction and the form of attention are adverse to the detection of

rhythmical complications under such conditions. Attention is directed

away from the observation of secondary accents and toward the

realization of a rhythm form having but two simple phases, the first

of which is composed of a single element, while within the latter

fall all the rest of the group. Such conditions are the worst possible

for the determination of the limits of simple rhythm groups; for the

observer is predisposed from the outset to regard the whole group of

elements lying within the second phase as undifferentiated. Thus the

conditions are such as to postpone the recognition of secondary

accents far beyond the point at which they naturally arise.

But further, such an attempt to extend the numerical scope of simple

rhythm groups also tends to transform and disguise the mechanism by

which secondary stresses are produced, and thereby to create the

illusion of an extended simple series which does not exist. For we

have no right to assume that the process of periodic accentuation in

such a series, identical in function though it be, involves always the

same form of differentiation in the rhythmical material. If the

primary accentuation be given through a finger reaction, the fixating

of that specific form of change will predispose toward an overlooking

of secondary emphases depending on minor motor reactions of a

different sort. The variety of such substitutional mechanisms is very

great, and includes variations in the local relations of the finger

reaction, movements of the head, eyes, jaws, throat, tongue, etc.,

local strains produced by simultaneous innervation of flexor and

extensor muscles, counting processes, visual images, and changes in

ideal significance and relation of the various members of the group.

Any one of these may be seized upon to mediate the synthesis of

elements and thus become an unperceived secondary accentuation.

Our problem is to determine at what point formal complication of the

rhythmical unit tends naturally to arise. How large may such a group

become and still remain fundamentally simple, without reduplication of

accentual or temporal differentiation? The determination of such

limits must be made on the basis of quantitative comparison of the

reactions which enter into larger and smaller rhythmical series, on

the one hand, and, on the other, of the types of structure which

appear in subjective rhythmization and the apprehension of objective

rhythms the forms of which are antecedently unknown to the hearer. The

evidence from subjective rhythms is inconclusive. The prevailing

types are of two and three beats. Higher forms appear which are

introspectively simple, but introspection is absolutely unable to

solve the problem as to the possible composite nature of these

extended series. The fact that they are confined to even numbers, the

multiples of two, and to such odd-numbered series as are multiples of

three, without the appearance of the higher primes, indicates the

existence in all these groups of secondary accentuation, and the

resolution of their forms into structures which are fundamentally

complications of units of two and three elements only. The process of

positive accentuation which appears in every higher rhythmical series,

and underlying its secondary changes exhibits the same reduction of

their elementary structure to double and triple groups, has been

described elsewhere