Various - Harvard Psychological Studies, Volume 1

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A similar displacement occurs if the periodic accentuations within the
series be increased or decreased in intensity. The impression of
rhythm from a strongly accented series persists longer, as retardation
of its rate proceeds, than does that of a weakly accented series; the
rhythm of a weakly accented series, longer than that of a uniform
succession. The sensation, in the case of a greater intensive accent,
is not only stronger but also more persistent than in that of a
weaker, so that the members of a series of loud sounds succeeding one
another at any given rate appear to follow in more rapid succession
than when the sounds are faint. But the threshold at which the
intervals between successive sounds become too great to arouse any
impression of rhythm does not depend solely on the absolute loudness
of the sounds involved; it is a function also of the degree of
accentuation which the successive measures possess. The greater the
accentuation the more extended is the temporal series which will hold
together as a single rhythmic group.

This relation appears also in the changes presented in beaten rhythms,
the unit-groups of which undergo a progressive increase in the number
of their components. The temporal values of these groups do not remain
constant, but manifest a slight increase in total duration as the
number of component beats is increased, though this increase is but a
fraction of the proportional time-value of the added beats. Parallel
with this increase in the time-value of the unit-group goes an
increase in the preponderance of the accented element over the
intensity of the other members of the group. Just as, therefore, in
rhythms that are heard, the greatest temporal values of the simple
group are mediated by accents of the highest intensity, so in
expressed rhythms those groups having the greatest time-values are
marked by the strongest accentuation.

Above the superior limit a rhythm impression may persist, but neither
by an increase in the number of elements which the unit group
contains, nor by an increase in the rate at which these units follow
one another in consciousness. The nature of the unit itself is
transformed, and a totally new adjustment is made to the material of
apprehension. When the number of impressions exceeds eight or ten a
second--subject to individual variations--the rhythmical consciousness
is unable longer to follow the individual beats, a period of confusion
ensues, until, as the rate continues to increase, the situation is
suddenly clarified by the appearance of a new rhythm superimposed on
the old, having as its elements the structural units of the preceding
rhythm. The rate at which the elements of this new rhythm succeed one
another, instead of being more rapid than the old, has become
relatively slow, and simple groups replace the previous large and
complex ones. Thus, at twelve beats per second the rhythms heard by
the subjects in these experiments were of either two, three or four
beats, the elements entering into each of these constituent beats
being severally three and four in number, as follows:

TABLE I.

> >
Simple Trochaic, four beats per second: 1 2 3, 4 5 6; 7 8 9,10 11 12.
\___/ \___/ \___/ \______/
>
________ ___________
/ \ / \
Dipodic Trochaic, " " " " 1 2 3, 4 5 6; 7 8 9,10 11 12.
\__/ \__/ \___/ \________/
>>>
Simple Dactylic, three " " " 1 2 3 4, 5 6 7 8, 9 10 11 12.
\____/ \____/ \_______/

The only impression of rhythm here received was of a trochaic or
dactylic measure, depending upon an accent which characterized a group
and not a single beat, and which recurred only twice or thrice a
second. Sometimes the subjects were wholly unaware that the elements
of the rhythm were not simple, a most significant fact, and frequently
the number reported present was one half of the actual number given.
During the continuance of such a series the rhythm form changes
frequently in the apprehension of the individual subject from one to
another of the types described above.

It cannot be too strongly insisted on that the perception of rhythm is
an _impression_, an immediate affection of consciousness depending on
a particular kind of sensory experience; it is never a construction, a
reflective perception that certain relations of intensity, duration,
or what not, do obtain. If the perception of rhythm in a series of
impressions were dependent on intellectual analysis and
discrimination, the existence of such temporal limits as are actually
found would be inconceivable and absurd. So long as the perception of
the uniformity or proportion of time-relations were possible, together
with the discrimination of the regular recurrence in the series of
points of accentuation, the perception of rhythm should persist,
however great or small might be the absolute intervals which separated
the successive members of the series. If it were the conception of a
certain form of relation, instead of the reception of a particular
impression, which was involved, we should realize a rhythm which
extended over hours or days, or which was comprehended in the fraction
of a second, as readily as those which actually affect us.

The rate at which the elements of a series succeed one another affects
the constitution of the unit groups of which the rhythmical sequence
is composed. The faster the rate, the larger is the number of
impressions which enter into each group. The first to appear in
subjective rhythm, as the rate is increased from a speed too slow for
any impression of rhythm to arise, are invariably groups of two beats;
then come three-beat groups, or a synthesis of the two-beat groups
into four, with major and minor accents; and finally six-and
eight-beat groups appear. When objective accentuation is present a
similar series of changes is manifested, the process here depending on
a composition of the unit-groups into higher orders, and not involving
the serial addition of new elements to the group.

The time relations of such smaller and larger units are dependent on
the relative inertia of the mechanism involved. A definite subjective
rhythm period undoubtedly appears; but its constancy is not maintained
absolutely, either in the process of subjective rhythmization or in
the reproduction of ideal forms. Its manifestation is subject to the
special conditions imposed on it by such apprehension or expression.
The failure to make this distinction is certain to confuse one's
conception of the temporal rhythmic unit and its period. The
variations of this period present different curves in the two cases of
subjective rhythmization and motor expression of definite rhythm
forms. In the former the absolute duration of the unit-group suffers
progressive decrease as the rate of succession among the stimuli is
accelerated; in the latter a series of extensions of its total
duration takes place as the number of elements composing the unit is
increased. The series of relative values for units of from two to
eight constituents which the finger reactions presented in this
investigation is given in the following table:

TABLE II.

No. of Elements. Proportional Duration.
Two, 1.000
Three, 1.109
Four, 1.817
Five, 1.761
Six, 2.196
Seven, 2.583
Eight, 2.590

This progressive extension of the rhythm period is to be explained by
the mechanical conditions imposed on the expression of rhythm by
processes of muscular contraction and release. Were it possible freely
to increase the rate of such successive innervations, we should expect
to find a much greater constancy in the whole period occupied by the
series of reactions which composes the unit. The comparatively
unsatisfactory quality of these larger series, and the resolution of
them into subgroups described elsewhere in this paper, are due to this
inability to accommodate the series of motor reactions to the
subjective rhythm period.

On the other hand, the temporal value of the unit which appears as the
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 cooerdinated 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 aesthetic 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 _Gestaltsqualitaet_ of the passage or the
stanza is thus frequently appreciated and reproduced without an
awareness of its sequential relations, though with the keenest sense
of what is necessary to, or inconsistent with, its structure; so that
the slightest deviation from its form is remarked and the whole
sequence accurately reproduced.

In order to isolate and exhibit the tendency toward rhythmization in
regularly repeated motor reactions, one should examine series of
similar movements made at different rates both as an accompaniment to
a recurrent auditory stimulus and as free expressions of the motor
impulse independent of such objective control. In the former of these
cases the series of stimuli should be undifferentiated in quality as
well as uniform in time. The rhythm which appears in such a case will
contradict the phases of an objective series which prescribes its
form, and the evidence of its existence, presented under such adverse
conditions, should be indubitable.

As preliminary to their special work the members of the experimental
group were tested in regard to the promptness and regularity of their
reactions (by finger flexion) in accompanying a periodically recurrent
stimulus given by the beating of a metronome; records were taken also
of their capacity to estimate and maintain constant time relations by
freely tapping at intervals of one, two and five seconds. Of the
latter type of reaction the records show that a temporal grouping of
the reactions is presented in every rate of tapping. This, owing to
the large absolute intervals, is uniformly in groups of two, the first
member of which is of shorter, the second of longer duration. There is
likewise an intensive differentiation of the alternate reactions. Thus
a double rhythmical treatment appears, but while with intervals of two
seconds the phases of temporal and intensive rhythm coincide, at rates
of one and five seconds they are opposed, that is, the accentuation
falls on the initial reaction which is followed by the shorter
interval. This doubtlessly marks the emergence of that tendency to
initial accentuation which was subsequently found to prevail in all
expression of rhythm.

The types of reaction which these records afford leave no doubt that a
fuller investigation of the matter would show the constant presence,
in all such forms of activity, of a rhythmical automatization of the
series. The special problems which such an investigation should first
resolve, relate to the dependence of the amount of rhythmical
differentiation on the rate of succession among the reactions; the
relation of the form of this reaction series to factors of attention
and control; and the significance, in connection with the process of
rhythmization, of auditory stimuli produced by and accompanying the
reaction series, that is, the comparison of soundless and sounded
reactions.

In the second set of experiments the reactor was directed simply to
accompany the beating of a metronome by a light tapping with the
forefinger on a rubber-surfaced tambour connected with a pneumographic
registering pen, with which was aligned an electrical time-marker also
actuated by the metronome. Three rates of tapping were adopted, 60, 90
and 120 beats per minute. No specific instructions were given as to
direction or keenness of attention on the part of the reactor; the
most natural and simple accompaniment was desired. Occasionally, for
comparison, the reactor was directed to attend closely to each
successive beat as it occurred.

Certain questions as to the applicability of the material here
interpreted to the point in question, and as to its relation to the
objective conditions of experimentation, must be met at the outset.
The first of these is as to the actual uniformity of the metronome
series. Objective determination of its temporal regularity is
unnecessary (in so far as such a determination looks toward an
explanation of the form of tapping by reference to inequality in the
metronomic intervals). That the rhythmical phases which appear in the
accompaniment are not due to inequality in the stimulation intervals,
is shown by the reversal of relations between the metronome and its
accompaniment which occur in the midst of a continuous series of taps.
To speak roughly, a break occurs every twentieth beat. I do not refer
to minor irregularities occurring within the single group but not
affecting the form of the rhythmical accompaniment. The latter
appeared with surprising rarity, but when found were included in the
continuous calculation of averages. But in every score or so of beats
a stroke out of series would be interpolated, giving the form
| 1 >2 [1] 2 >1 |; the accompaniment being cooerdinated during the
second portion of the whole series with opposite phases of the
metronome from those with which its elements were connected in the
earlier part. Moreover, the dependence of this grouping of the sounds
on subjective attitudes may readily be made to appear. When attention
is turned keenly on the process its phases of rhythmical
differentiation decline; when the accompaniment becomes mechanical
they mount in value. When the observer tries to mark the ticking as
accurately as possible, not only does the index of his motor reactions
become more constant, but the sounds of the instrument likewise appear
more uniform. The observers report also that at one and the same time
they are aware of the regularity of the metronome and the rhythmical
nature of their tapping, while yet the conviction remains that the
accompaniment has been in time with the beats. Furthermore, if the
phases of ticking in the metronome were temporarily unlike, the motor
accompaniment by a series of observers, if accurate, should reproduce
the time-values of the process, and if inaccurate, should present only
an increase of the mean variation, without altering the characteristic
relations of the two phases. On the other hand, if the series be
uniform and subjectively rhythmized by the hearer, there should be
expected definite perversions of the objective relations, presenting a
series of increasing departures from the original in proportion as the
tendency to rhythmize varied from individual to individual.