Various - Harvard Psychological Studies, Volume 1

V >> Various >> Harvard Psychological Studies, Volume 1

Pages:
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 | 51 | 52 | 53 | 54 | 55

This reinforcing influence is greater--according to the figures just
given--in the case of the element preceding the accent than in that of
the reaction which follows it. It may be, therefore, that the position
of maximal stress in the preceding table is due to the close average
relation in which the third position stands to the accented element.
This proximity it of course shares with the second reaction of the
group, but the underlying trochaic tendency depreciates the value of
the second reaction while it exaggerates that of the third. This
reception of the primitive accent the third element of the group
indeed shares with the first, and one might on this basis alone have
expected the maximal value to be reached in the initial position, were
it not for the influence of the accentual stress on adjacent members
of the group, which affects the value of the third reaction to an
extent greater than the first, in the ratio 1.000:0.571.

The average intensity of the reactions in each of the four forms--all
subjects and positions combined--is worthy of note.

TABLE XXV.

Stress. Initial. Secondary. Tertiary. Final.
Value, 1.000 1.211 1.119 1.151

The first and third forms, which involve initial accents--in the
relation of the secondary as well as primary accent to the
subgroups--are both of lower average value than the remaining types,
in which the accents are final, a relation which indicates, on the
assumption already made, a greater ease and naturalness in the former
types. Further, the second form, which according to the subjective
reports was found the most difficult of the group to execute--in so
far as difficulty may be said to be inherent in forms of motor
reaction which were all relatively easy to manipulate--is that which
presents the highest intensive value of the whole series.

In the next group of experiments, the subject was required to execute
a series of reactions in groups of alternating content, the first to
contain two uniform beats, the second to consist of a single reaction.
This second beat with the interval following it constitutes a measure
which was to be made rhythmically equivalent to the two-beat group
with which it alternated. The time-relations of the series were
therefore left to the adjustment of the reactor. The intensive
relations were separated into two groups; in the first the final
reaction was to be kept uniform in strength with those of the
preceding group, in the second it was to be accented.

The absolute and relative intensive values for the two forms are given
in the following table:

TABLE XXVI.

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

Syncopated Measures 13.00 15.12 16.50 Absolute.
Unaccented, 1.000 1.175 1.269 Relative.

Syncopated Measures 10.95 11.82 16.11 Absolute.
Accented, 1.000 1.079 1.471 Relative.

These averages hold for every individual record, and therefore
represent a thoroughly established type. In both forms the reaction of
the syncopated measure receives the greatest stress. In the first
form, while the stress is relatively less than in the second, it is at
the same time absolutely greater. The whole set of values is raised
(the ratio of average intensities in the two forms being 1.147:1.000),
as it has already been found to be raised in other forms difficult to
execute. To this cause the preponderance is undoubtedly to be
attributed, as the reports of every subject describe this form as
unnatural, in consequence of the restraint it imposes on an impulse to
accent the final reaction, _i.e._, the syncopated measure.

In the next set of experiments the series of reactions involved the
alternation of a syncopated measure consisting of a single beat with a
full measure of three beats. The same discrimination into accented and
unaccented forms in the final measure was made as in the preceding
group. The series of absolute and relative values are given in the
following table.

TABLE XXVII.

Rhythm. 1st Beat. 2d Beat. 3rd Beat. 4th Beat. Value.

Syncopated Measures 9.77 8.96 9.61 13.78 Absolute.
Unaccented, 1.000 0.915 0.983 1.165 Relative.

Syncopated Measures 11.57 11.07 11.53 21.50 Absolute.
Accented, 1.000 0.957 0.996 1.858 Relative.

These averages hold for every subject where the syncopated measure
receives accentuation, and for two out of three reactors where it is
unaccented. The latter individual variation shows a progressive
increase in intensity throughout the series.

Here, as in the preceding forms, a well-established type is presented.
Not only when accentuation is consciously introduced, but also when
the attempt is made--and in so far as the introspection of the reactor
goes, successfully made--to maintain a uniformity among the reactions
of the full and syncopated measures, the emphasis on the latter is
unconsciously increased. In the accented form, as before, there is a
clear discrimination into two grades of intensity (ratio of first
three elements to final, 1.000:1.888) while in the unaccented no such
broad separation exists (ratio of first three elements to final,
1.000:1.156).

The type of succession in each of these forms of reaction is a
transformed dactylic, in which group should now be included the simple
four-beat rhythm with final accent, which was found to follow the same
curve. The group begins with a minor stress in both of the present
forms, this stress being greater in the unaccented than in the
accented type. This preponderance I believe to be due to the endeavor
to repress the natural accent on the syncopated measure. In both forms
the intensive value of the second element is less than that of the
third, while the intensity of the initial reaction is greater than
that of either of these subsequent beats. This form of succession I
have called a _transformed dactylic_. It adheres to the dactylic type
in possessing initial accentuation; it departs from the normal
dactylic succession in inverting the values of the second and third
members of the group. This inversion is not inherent in the rhythmic
type. The series of three beats decreasing in intensity represents the
natural dactylic; the distortion actually presented is the result of
the proximity of each of these groups to a syncopated measure which
follows it. This influence I believe to be reducible to more
elementary terms. The syncopated measure is used to mark the close of
a logical sequence, or to attract the hearer's attention to a striking
thought. In both cases it is introduced at significant points in the
rhythmical series and represents natural nodes of accentuation. The
distortion of adjacent measures is to be attributed to the increase in
this elementary factor of stress, rather than to the secondary
significance of the syncopation, for apart from any such change in the
rhythmical structure we have found that the reactions adjacent to that
which receives accentual stress are drawn toward it and increased in
relative intensity.

Further quantitative analysis of rhythmical sequences, involving a
comparison of the forms of successive measures throughout the higher
syntheses of verse, couplet and stanza, will, I believe, confirm this
conception of the mutable character of the relations existing between
the elements of the rhythmical unit, and the dependence of their
quantitative values on fixed points and modes of structural change
occurring within the series. An unbroken sequence of dactyls we shall
expect to find composed of forms in which a progressive decrease of
intensity is presented from beginning to end of the series (unless we
should conceive the whole succession of elements in a verse to take
shape in dependence on the point of finality toward which it is
directed); and when, at any point, a syncopated measure is introduced
we shall look for a distortion of this natural form, at least in the
case of the immediately preceding measure, by an inversion of the
relative values of the second and third elements of the group. This
inversion will unquestionably be found to affect the temporal as well
as the intensive relations of the unit. We should likewise expect the
relations of accented and unaccented elements in the two-beat rhythms
to be similarly affected by the occurrence of syncopated measures, and
indeed to find that their influence penetrates every order of rhythm
and extends to all degrees of synthesis.

To the quantitative analysis of the intensive relations presented by
beaten rhythms must be added the evidence afforded by the apprehension
of auditory types. When a series of sounds temporally and
qualitatively uniform was given by making and breaking an electric
circuit in connection with a telephone receiver, the members of a
group of six observers without exception rhythmized the stimuli in
groups--of two, three and four elements according to rate of
succession--having initial accentuation, however frequently the
series was repeated. When the series of intervals was temporally
differentiated so that every alternate interval, in one case, and
every third in another, stood to the remaining interval or intervals
in the ratio, 2:1, the members of this same group as uniformly
rhythmized the material in measures having final accentuation. In
triple groups the amphibrachic form (in regard to temporal relations
only, as no accentuation was introduced) was never heard under natural
conditions. When the beginning of the series was made to coincide with
the initiation of an amphibrachic group, four of those taking part in
the investigation succeeded in maintaining this form of apprehension
for a time, all but one losing it in the dactylic after a few
repetitions; while the remaining two members were unable to hold the
amphibrachic form in consciousness at all.

(_b_) The Distribution of Durations.

The inquiry concerning this topic took the direction, first, of a
series of experiments on the influence which the introduction of a
louder sound into a series otherwise intensively uniform exerts on the
apparent form of the series within which it occurs. Such a group of
experiments forms the natural preliminary to an investigation of the
relation of accentuation to the form of the rhythm group. The
apparatus employed was the fourth in the series already described. The
sounds which composed the series were six in number; of these, five
were produced by the fall of the hammer through a distance of 2/8
inch; the sixth, louder sound, by a fall through 7/8 inch. In those
cases in which the intensity of this louder sound was itself varied
there was added a third height of fall of two inches. The succession
of sounds was given, in different experiments, at rates of 2.5, 2.2,
and 1.8 sec. for the whole series. The durations of the intervals
following and (in one or two cases) preceding the louder sound were
changed; all the others remained constant. A longer interval
intervened between the close and beginning of the series than between
pairs of successive sounds. After hearing the series the subject
reported the relations which appeared to him to obtain among its
successive elements. As a single hearing very commonly produced but a
confused impression, due to what was reported as a condition of
unpreparedness which made it impossible for the hearer to form any
distinct judgment of such relations, and so defeated the object of the
experiment, the method adopted was to repeat each series before asking
for judgment. The first succession of sounds then formed both a signal
for the appearance of the second repetition and a reinforcement of the
apperception of its material.

In order to define the direction of attention on the part of the
observer it was made known that the factors to be compared were the
durations of the intervals adjacent to the louder sound in relation to
the remaining intervals of the series, and that all other temporal and
intensive values were maintained unchanged from experiment to
experiment. In no instance, on the other hand, did any subject know
the direction or nature of the variation in those quantities
concerning which he was to give judgment. In all, five subjects shared
in the investigation, C., E., F., H. and N. Of these C only had
musical training. In the tables and diagrams the interval preceding
the louder sound is indicated by the letter B, that following it by
the letter A. Totals--judgment or errors--are indicated by the letter
T, and errors by the letter E. The sign '+' indicates that the
interval against which it stands is judged to be greater than the
remaining intervals of the series, the sign '=' that it is judged
equal, and the sign '-' that it is judged less.

The first series of changes consisted in the introduction of
variations in the duration of the interval following the loud sound,
in the form of successive increments. This loud sound was at the third
position in the series. All intensive relations and the duration of
the interval preceding the louder sound remained unchanged. The
results of the experiment are presented in the following table.

TABLE XXVIII.

Ratio of A to B A Errors Total Per cent.
Other Intervals. + = - + = - B A T judgts. of errors

1.000 : 0.625 2 2 2 4 2 0 4 2 6 12 50
1.000 : 0.666 4 2 0 1 3 2 4 5 9 12 75
1.009 : 0.714 5 3 0 2 2 4 5 6 11 16 69
1.000 : 0.770 5 4 0 1 1 7 5 8 13 18 72
1.000 : 0.833 1 5 0 0 0 6 1 6 7 12 50

Totals, 17 16 2 8 8 19 19 27 46 70

The value of the interval following the louder sound is correctly
reported eight times out of thirty; that preceding it is correctly
reported sixteen times out of thirty. The influence which such a
change in intensive value introduced at a single point in a series of
sounds exerts on the apparent relation of its adjacent intervals to
those of the remainder of the series is not equally distributed
between that which precedes and that which follows it, but affects the
latter more frequently than the former in a ratio (allowing latitude
for future correction) of 2:1. In the case of interval A the error is
one of underestimation in twenty-seven cases; in none is it an error
of overestimation. In the case of interval B the error is one of
overestimation in seventeen instances, of underestimation in two. The
influence of the introduction of such a louder sound, therefore, is to
cause a decrease in the apparent duration of the interval which
follows it, and an increase in that of the interval which precedes it.
The illusion is more pronounced and invariable in the case of the
interval following the louder sound than of that preceding it, the
proportion of such characteristic misinterpretations to the whole
number of judgments in the two cases being, for A, 77 per cent.; for
B, 54 per cent. The effect on interval A is very strong. In the second
group, where the ratio of this interval to the others of the series is
3:2, it is still judged to be equal to these others in 50 per cent. of
the cases, and less in 35 per cent. Further, these figures do not give
exhaustive expression to the whole number of errors which may be
represented in the judgments recorded, since no account is taken of
greater and less but only of change of sign; and an interval might be
underestimated and still be reported greater than the remaining
intervals of the series in a group of experiments in which the
relation of the interval in question to these remaining intervals
ranged from the neighborhood of equivalent values to that in which one
was double the other. If in a rough way a quantitative valuation of
errors be introduced by making a transference from any one sign to
that adjacent to it (_e.g._, - to =, or = to +) equal to _one_, and
that from one extreme sign to the other equal to _two_, the difference
in the influence exerted on the two intervals will become still more
evident, since the errors will then have the total (quantitative)
values of A 46, and B 19, or ratio of 1.000:0.413.

Next, the position of the louder sound in the series of six was
changed, all other conditions being maintained uniform throughout the
set of experiments. The series of intervals bore the following
relative values: A, 0.900; B, 1.100; all other intervals, 1.000. The
louder sound was produced by a fall of 0.875 inch; all others by a
fall of 0.250 inch. The louder sound occurred successively in the
first, second, third, fourth and fifth positions of the series. In the
first of these forms it must of course be remembered that no interval
B exists. The results of the experiment are shown in the following
table:

TABLE XXIX.

Position Apparent Values. Errors. % of Errors Ditto
in B A B A T in tot. judg. quant.
Series + = - + = - B A B A
1 2 6 6 0 12 12 85.7 85.7
2 2 8 2 1 7 4 10 11 21 83.3 91.6 73.3 91.6
3 1 9 3 1 8 3 10 11 21 76.9 91.6 71.9 91.6
4 1 8 4 2 6 5 9 11 20 69.2 84.6 52.8 84.6
5 0 12 0 0 4 8 12 12 24 100.0 100.0 60.0 100.0
Totals, 4 37 9 6 31 26 41 57 98 82.3 90.7 64.5 90.7

Total judgments, 113; Errors (B = 31), A = 57.

The relatively meager results set forth in the preceding section are
corroborated in the present set of experiments. That such a variation
of intensity introduced into an otherwise undifferentiated auditory
series, while it affects the time-values of both preceding and
following intervals, has a much greater influence on the latter than
on the former, is as apparent here as in the previous test. The number
of errors, irrespective of extent, for the two intervals are: B, 82.3
per cent, of total judgments; A, 90.7 per cent. When the mean and
extreme sign displacements are estimated on the quantitative basis
given above these percentages become B, 64.5; A, 90.7, respectively--a
ratio of 0.711:1.000.

The direction of error, likewise, is the same as in the preceding
section. Since the actual values of the two intervals here are
throughout of extreme sign--one always greater, the other always
less--only errors which lie in a single direction are discriminable.
Illusions lying in this direction will be clearly exhibited, since the
differences of interval introduced are in every case above the
threshold of discrimination when the disturbing element of variations
in intensity has been removed and the series of sounds made
intensively uniform. In case of a tendency to underestimate B or
overestimate A, errors would not be shown. This problem, however, is
not to be met here, as the results show; for there is recorded a
proportion of 82.3 per cent. of errors in judgment of interval B, and
of 90.7 per cent. in judgment of interval A, all the former being
errors of overestimation, all of the latter of underestimation.

The influence of position in the series on the effect exerted by such
a change of intensity in a single member can be stated only
tentatively. The number of experiments with the louder sound in
position five was smaller than in the other cases, and the relation
which there appears cannot be absolutely maintained. It may be also
that the number of intervals following that concerning which judgment
is to be given, and with which that interval may be compared, has an
influence on the accuracy of the judgment made. If we abstract from
this last set of results, the tendency which appears is toward an
increase in accuracy of perception of comparative durations from the
beginning to the end of the series, a tendency which appears more
markedly in the relations of the interval preceding the louder sound
than in those of the interval which follows it. This conclusion is
based on the succession of values which the proportion of errors to
total judgments presents, as in the annexed table.

TABLE XXX.

Percentage of Errors for Each Position.

Interval. I II III IV V
B. 83.3 76.9 69.2 (100) Irrespective
A. 85.7 91.6 91.6 84.6 (100) of extent.
B. 73.3 71.9 53.8 (60) Estimated
A. 85.7 91.6 91.6 84.6 (100) quantitatively.

Next, the relation of the amount of increase in intensity introduced
at a single position in such a series to the amount of error thereby
occasioned in the apprehension of the adjacent intervals was taken up.
Two sets of experiments were carried out, in each of which five of
the sounds were of equal intensity, while one, occurring in the midst
of the series, was louder; but in one of the sets this louder sound
was occasioned by a fall of the hammer through a distance of 0.875
inch, while in the other the distance traversed was 2.00 inches. In
both cases the extent of fall in the remaining hammers was uniformly
0.25 inch. The results are given in the following table:

TABLE XXXI.

Interval B.¹ Interval A.
Ratio of Interval 0.875 in. 2.00 in. 0.875 in. 2.00 in.
B to Interval A. + = - + = - + = - + = -
1.000 : 1.000 0 6 0 0 4 2 0 5 1 0 0 6
0.909 : 1.000 2 4 0 0 4 2 0 2 4 2 2 2
0.833 : 1.000 0 6 0 0 4 2 4 0 2 1 3 2
0.770 : 1.000 0 6 0 2 2 2 2 4 0 4 0 2
0.714 : 1.000 0 6 0 1 5 0 6 0 0 2 2 2
Totals, 2 28 3 19 8 12 11 7 9 7 14
T.E., T.J., 2 30 11 30 13 30 21 30
and per cent., 6.6% 36.6% 60.0% 70.0%

¹Interval B in these experiments is of the same duration as all
others but that following the louder sound; hence, judgments in
the second column are correct.

Again the markedly greater influence of increased intensity on the
interval following than on that preceding it appears, the percentage
of errors being, for B (both intensities), 21.6 per cent.; for A, 56.6
per cent. Also, in these latter experiments the direction of error is
more definite in the case of interval A than in that of interval B.

The influence of changes in intensity on the amount of error produced
is striking. Two intensities only were used for comparison, but the
results of subsequent work in various other aspects of the general
investigation show that this correlation holds for all ranges of
intensities tested, and that the amount of underestimation of the
interval following a louder sound introduced into an otherwise uniform
series is a function of the excess of the former over the latter. The
law holds, but not with equal rigor, of the interval preceding the
louder sound. So far as these records go, the influence of such an
increase of intensity is more marked in the case of interval B than in
that of interval A. It is to be noted, however, that the absolute
percentage of errors in the case of A is several times greater than in
that of B. I conclude that A is much more sensitive than B to such
influences, and that there is here presented, in passing from
intensity I. to intensity II., the rise of conditions under which the
influence of the louder sound on B is first distinctly felt--that is,
the appearance of a threshold--and that the rate of change manifested
might not hold for higher intensities.

Lastly, the rate at which the sounds of the series succeeded one
another was varied, in order to determine the relation which the
amount of influence exerted bore to the absolute value of the
intervals which it affected. Three rates were adopted, the whole
series of sounds occupying respectively 2.50 secs., 2.20 secs, and
1.80 secs. The results are summed in the following table:

TABLE XXXII.

Rate: 2.5 secs. Rate: 2.2 secs. Rate: 1.8 secs.

Ratio of Interval B B A B A B A
to Interval A. + = - + = - + = - + = - + = - + = -

1.000 : 1.000 2 8 0 0 8 2 0 8 2 0 2 8 0 4 0 0 2 2
0.917 : 1.000 0 8 2 4 6 0 3 8 0 0 8 3 2 2 0 0 2 2
0.846 : 1.000 1 9 0 5 4 1 3 8 0 3 7 1 6 5 0 1 8 2
0.786 : 1.000 1 10 0 11 0 0 6 6 0 7 3 4 6 2 2 2 6 2
0.733 : 1.000 4 2 0 4 0 2 4 6 0 8 0 2
0.687 : 1.000 5 3 1 6 1 2 2 6 0 7 0 1

Totals 4 35 2 20 18 3 21 35 3 20 21 20 20 25 2 18 18 11*

*Transcriber's Note: Original "1".

These results are converted into percentages of the total number of
judgments in the following table:

TABLE XXXIII.

Rate of B A
Success. + = - Errors. + = - Errors.
2.5 secs 10 85 5 15 49 44 7 51
2.2 " 36 59 5 41 33 34 33 67
1.8 " 43 53 4 47 38 38 24 62