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Becky Saletan, publisher of the adult trade division, will leave next week in a sign of further unraveling at the publisher.

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Various - Harvard Psychological Studies, Volume 1

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





A comparison of the second and third columns of the table shows an
excess of mean variation of the smaller group over that of the larger
in each of the three forms. It is true also of the individual subjects
except in two instances, in each of which the two indices are equal.
This proportion is broken in the relation of the primary interval to
the unit group in the dactylic rhythm form. A similar diversity of the
individual records occurred in the two-beat rhythms.

The same indication of higher groupings appears here as in the case of
previous rhythms. Rhythmical variations are presented in the amount of
the mean variations for alternate groups of three beats.
Chronologically in the records, as well as in dependence on
theoretical interpretation, the first member of each higher group is
characterized by the greater instability. The amounts of this
difference in cooerdination between the first and last halves in series
of six beats is set down for the three rhythm forms in the following
table:


TABLE LXVIII.

Stress. First Half. Second Half
Initial, 1.000 0.794¹
Median, 1.000 0.668
Final, 1.000 0.770

¹These figures are made up from the records of three out of
four subjects. In the exceptional results of the fourth
subject no mean variation appears in the first half and 6.3
per cent, in the second, making the average for the whole
group 1.000:1.023.


There is still other evidence of higher rhythmical grouping than these
oscillations in the amount of the mean variation of alternate groups.
Exactness of cooerdination between the individual intervals of
successive groups might undergo development without affecting the
relative uniformity of such total groups themselves. But, throughout
these results, an increase in cooerdination between the periods of the
whole group takes place in passing from the first to the second member
of a composite group. The relation here is not, however, so uniform as
in the preceding case. The series of proportional values is given on
page 403.

TABLE LXIX.

Stress. First Half. Second Half.
Initial, 1.000 0.846¹
Median, 1.000 1.064
Final, 1.000 0.742

¹ Here also the records of three subjects only are involved,
the results of the same reactor as in the preceding cases
being discarded. Including this, the ratio becomes
1.000:1.016.

The index of mean variation for the individual elements of the group
also shows a progressive decrease from first to last as follows:


TABLE LXX.

Stress. Interval I. Interval II. Interval III.
Initial, 5.82 per cent. 6.45 per cent. 4.65 per cent.
Median, 9.95 " 7.87 " 4.70 "
Final, 11.95 " 9.77 " 7.15 "


The relation holds in all cases except that of I. to II. in the rhythm
with initial stress. From this table may be gathered the predominance
of primacy of position as a factor of disturbance over that of stress.
Indeed, in this group of reactions the index of variation for the
accented element, all forms combined, falls below that of the
unaccented in the ratio 6.95 per cent. : 7.91 per cent.

In rhythms of four beats, as in those of three, the estimation of
values is made on the basis of an average of the mean variations for
the three intra-group intervals, which is then compared with the final
or inter-group interval. As in those previous forms, sensitiveness to
variations in duration is greater throughout in the case of the latter
than in that of the former. The proportional values of their several
mean variations are given in the annexed table:


TABLE LXXI.

Interval. Initial Stress. Secondary Stress. Tertiary Stress. Final Stress.
Intra-group, 1.000 1.000 1.000 1.000
Inter-group, 0.941 0.775 0.725 0.713


This relation, true of the average of all intra-group intervals, is
not, as in the preceding forms, true of each of the three constituent
intervals in every case. In the second and fourth forms, those marked
by secondary and final stress, it holds for each member of the group
of intervals; in the first form it fails for the second and third
intervals, while in the third form it fails for the last of the three.

The proportional amount of this difference in mean variation
continuously increases from beginning to end of the series of
rhythmical forms. This cannot be interpreted as directly indicative of
a corresponding change in the definition which the four forms possess.
The absolute values of the several mean variations must simultaneously
be taken into account. First, then, in regard to the final pause there
is presented the following series of values:


TABLE LXXII.

Stress. Initial. Secondary. Tertiary. Final.
M.V. 6.57 per cent. 9.50 per cent. 4.90 per cent. 15.70 per cent.


A very striking rhythmical alternation in the magnitude of the mean
variation thus occurs according as the accents fall on the first
member of the subgroups when its amount is smaller or on the second
member when it is larger. Further, the cases noted above, the second
and fourth forms, in which each of the intra-group intervals is
severally of greater mean variation than the final pause, are just
those in which the index of mean variation in the final pause itself
is at a maximum.

The average mean variations of the earlier intervals thus present
changes which are analogous to and synchronous with those of the final
pause. Their values in proportion to the whole duration of the
intervals are as follows[13]:

[13] In the second line of figures has been added the series of
values of the average mean variation for all four intervals of
the group.


TABLE LXXIII.

Stress. Initial. Secondary. Tertiary. Final.
M.V. 6.98 per cent. 12.25 per cent. 6.57 per cent. 22.0 per cent.
M.V. 6.87 " 11.56 " 6.15 " 20.45 "


Those rhythmical forms having their accentual stress initial, or on
the initial elements of the subgroups, are marked by a sensitiveness
almost twice as great as those in which the stress is final, or on the
final elements of the subgroups.

Finally, if we take the whole series of intervals severally, we shall
find that this rhythmical variation holds true of each element
individually as it does of their average. The whole series of values
is given in the table annexed.


TABLE LXXIV.

Stress.
Interval. Initial. Secondary. Tertiary. Final.

First, 9.57 per cent. 13.23 per cent. 9.00 per cent. 11.45 per cent.
Second, 5.53 " 10.60 " 8.70 " 9.00 "
Third, 5.83 " 12.93 " 2.00 " 12.90 "
Fourth, 6.57 " 9.50 " 4.90 " 7.85 "


It is an obvious inference from these facts that the position of the
accent in a rhythmical group is of very great significance in relation
to the character of the rhythmical movement. The initial accent gives
incomparably greater cooerdination and perfection to the forms of
uttered (produced) rhythm than does the final. It is in this sense the
natural position of the accent, because on the success and fluency of
this cooerdination the aesthetic value of the rhythm depends.

In general, though not so unequivocally, the four-beat rhythms show a
progressive increase of stability in passing from the simple interval
to the group, and from the smaller group to the larger. The series of
values for the four accentual positions follows.


TABLE LXXV.

Stress. Single Interval. 4-Beat Group. 2-Beat Group.
Initial, 7.27 per cent. 8.20 per cent. 8.17 per cent.
Secondary, 11.60 " 9.60 " 6.25 "
Tertiary, 3.20 " 3.40 " 2.25 "
Final, 10.22 " 6.30 " 6.00 "
Average, 8.07 " 6.87 " 5.67 "


Here, as in the preceding rhythmical forms, the most constant relation
is that of smaller and larger groups, in which no exception occurs to
the excess of mean variation in the former over the latter. The cases
in which this relation is reversed are found, as before, in comparing
the simple interval with the duration of the unit group; and the
exceptional instances are just those, namely the first and third
forms, in which the mean variation of this uncompounded interval is
itself at a minimum. This means that the simple interval presents a
more mobile character than that of the group; and while in general it
is less stable than the latter, it is also the first to show the
influence of increased cooerdination. Training affects more readily the
single element than the composite measure, and in the most highly
cooerdinated forms of rhythm the simple interval is itself the most
perfectly integrated unit in the system of reactions.

Here, as in the preceding rhythmical forms, evidence of higher
grouping appears in the alternate increase and decrease of mean
variation as we pass from the first to the second subgroup when the
material is arranged in series of eight beats. The proportional values
of the indices are given in the following table:


TABLE LXXVI.

Subgroups Init. Stress Sec. Stress Tert. Stress Fin. Stress
1st Four, 1.000 1.000 1.000 1.000
2d Four, 0.950 0.762 0.984 0.790


The first member of the larger group, in the case of every rhythm form
here in question, is less exactly cooerdinated than the second, the
interpretation of which fact need not here be repeated. Several
additional points, however, are to be noted. The differences in
stability of cooerdination which are encountered as one passes from the
first to the last of the four rhythm forms, extends, when the
reactions are analyzed in series of eight beats, to both members of
the compound group, but not in equal ratios. The mean variation of the
second and fourth forms is greater, both in the first and second
subgroups, than that of the corresponding subgroups of the first and
third forms; but this increase is greatest in the first member of the
composite group. That is, as the group grows more unstable it does so
mainly through an increase in variation of its initial member; or, in
other words, the difference in variability of the beat intervals of
the first and last subgroups reaches its maximum in those rhythmic
types in which the indices of mean variation for these intervals are
themselves at their maxima.

This process of cooerdination, with its indication of a higher
rhythmical synthesis, appears also in the transformations in the value
of the mean variations in duration of the total groups, when the
material is treated in series of eight beats, as in table LXXVII.


TABLE LXXVII.

Subgroups. Init. Stress. Sec. Stress. Tert. Stress. Final Stress.
1st Four, 1.000 1.000 1.000 1.000
2d Four, 0.773 0.768 0.943 0.579


The total initial group, therefore, as well as each of its constituent
intervals, is less stable than the second.

Within the unit group itself the values of the mean variation show
here, as in the preceding forms, a progressive increase in
sensitiveness to temporal variations from first to last of the
component intervals. The proportional values for the four intervals in
order are, 1.000, 0.786, 0.771, 0.666. The distribution of these
relative values, however, is not uniform for all four rhythmical
forms, but falls into two separate types in dependence on the position
of the accents as initial or final, following the discrimination
already made. The figures for the four forms separately are as
follows:


TABLE LXXVIII.

Stress. 1st Interval. 2d Interval. 3d Interval. 4th Interval.

Initial, 9.57 per cent. 5.53 per cent. 5.83 per cent. 6.57 per cent.
Secondary, 13.23 " 10.60 " 12.93 " 9.50 "
Tertiary, 9.00 " 8.70 " 2.00 " 4.90 "
Final, 11.45 " 9.00 " 12.60 " 7.85 "


In the first type (Rhythms I. and III.) appear a descending curve
followed by an ascending; in the second type (Rhythms II. and IV.) a
second descending curve follows the first. The changes in the first
type are not cooerdinated with a similar curve of variation in the
intensive magnitude of the beats. It is to be noted here that the
smallest mean variation presented in this whole set of results is
found in that element of the first form which receives the stress, an
exception to the general rule. The variations in the contrasted type
have their maxima at those points on which the group initiation--
primary or secondary--falls, namely, the first and third.

As in preceding rhythmical forms, while the separation of accentual
stress from primacy in the series tends to increase the mean variation
of that element on which this stress falls and to raise the index of
mean variation for the whole group, yet the mean variation of the
initial element is also raised, and to a still greater degree,
reinforcing the evidence that primacy of position is a more important
factor of instability than the introduction of accentual stress.

In the investigation of mean variations for units (if we may call them
such) of more than four beats only a modicum of material has been
worked up, since the types of relation already discovered are of too
definite a character to leave any doubt as to their significance in
the expression of rhythm. The results of these further experiments
confirm the conclusions of the earlier experiments at every point.

These higher series were treated in two ways. In the first the reactor
beat out a rhythm consisting in the simple succession of groups of
reactions, each of which contained one and only one accent. These
units in each case were marked by initial stress, and were composed of
five, six, seven, eight and ten beats respectively. The results are
given in the following table, which contains the series of mean
variations in duration both for single intervals and for total groups.


TABLE LXXIX.

No. Med. Unac'td
of Beats. Acc'td Beat. Beats. Final Beat. Average. Group.
Five, 12.2% 6.8% 7.1% 7.9% 6.3%
Six, 9.2 10.6 6.9 9.7 8.3
Seven, 7.1 5.2 7.9 5.8 3.6
Eight, 12.4 9.5 8.8 9.7 8.0
Ten, 7.5 6.6 7.3 6.8


The averages for the combined, median, unaccented intervals are given
separately from those of the final interval, for the reason that the
mean variation of the latter is greater in three cases out of five
than that of the former, a relation which apparently contradicts what
has already been said concerning the sensitiveness to variations which
marks the intervals separating rhythmical groups. The reason for this
final increase in variation appears when the relative intensities of
the series of reactions are considered. They are given in Table LXXX.


TABLE LXXX.

No. of Beats. Acc. Beat. Av. Unacc. Final. Pre-final.
Five, 1.000 0.543 0.518 0.500
Six, 1.000 0.623 0.608 0.592
Seven, 1.000 0.515 0.544 0.437
Eight, 1.000 0.929 0.949 0.863
Ten, 1.000 0.621 0.640 0.545


In every case the final element is marked by an increase over that
which precedes it (see last two columns of table) of the average value
for all rhythms of 1.000:0.900; an increase which raises it above the
average value of the whole series of preceding unaccented beats in
three cases out of five. To this final accentuation the increase in
variation is to be attributed. Yet despite the additional element of
disturbance due to this increased final stress the average value of
the mean variation for this final interval is lower than that of the
median unaccented intervals in the ratio (all rhythms combined) of
0.992:1.000.

Turning, then, to Table LXXIX., there is presented, firstly, an excess
of variation in the accented element over that of the average
unaccented elements in every case but one (the six-beat rhythm in
which the values are nearly identical), which for the whole series of
rhythms has a value of 1.000:0.794. Secondly, in every completed case
(part of the figures in the last rhythm are inadvertently lacking),
the average mean variation of the single interval preponderates over
that of the total group.

The second form of rhythmical tapping, in which the longer series were
beaten out as pairs of equal subgroups, was added in order to
determine the quantitative relations of the mean variations for
alternate subgroups when such groups were purposely intended, instead
of appearing in the form of unconscious modifications of the
rhythmical treatment, as heretofore. At the same time the results
present an additional set of figures embodying the relations here in
question. They are as follows:


TABLE LXXXI.
Intervals. Groups.
Number Av. 1st 2d 1st 2d
of Beats. Acc. Unacc. Half. Half. Half. Half. Average Totals
Six, 27.9% 20.9% 23.4% 23.0% 14.6% 13.3% 13.9% 13.8%
Eight, 16.6 14.8 13.2 17.3 6.2 3.3 4.7 2.7
Ten, 7.9 2.6 3.4 4.0 5.9 5.2 5.5 3.1


No exception here occurs to the characteristic predominance in
instability of the accented element. As regards simple intervals, the
relation of first and second groups is reversed, the reason for which
I do not know. It may be connected with the rapid speed at which the
series of reactions was made, and its consequent raising of the
threshold of perceptible variation, proportional to the value of the
whole interval, to which is also due the higher absolute value of the
variations which appear in both tables.

These inversions disappear when we compare the relative stability of
the first and second subgroups, in which the excess of variation in
the former over the latter is not only constant but great, presenting
the ratio for all three rhythms of 1.000:0.816. The characteristic
relation of lower to higher rhythmical syntheses also is here
preserved in regard to the two subgroups and the total which they
compose.

The points here determined are but a few of the problems regarding the
structure of larger rhythmical sequences which are pressing for
examination. Of those proximate to the matter here under
consideration, the material for an analysis of the mean variation in
intensity of a series of rhythmical reactions is contained in the
measurements taken in the course of the present work, and this may at
a future time be presented. The temporal variations having once been
established it becomes a minor point.

Such conclusions, however, are only preliminary to an investigation of
the characteristic structure of the ordinary metrical forms, and to
these attention should next be turned. The configuration of the common
meters should be worked out both in relation to the whole formal
sequence, and to the occurrence within the series of characteristic
variations. There can be no question that each metrical structure, the
iambic trimeter or dactylic tetrameter line, for example, composes a
definite rhythmical melody within which each measure is shortened or
prolonged, subdued or emphasized, according to its position and
connections in the series of relations which constitute the rhythmical
sequence.

These several metrical forms should be explored and the characters of
each measure in the series quantitatively determined. Such an
investigation would include an ascertainment of the proportional
time-value of each successive measure, its average force, and its
sensitiveness to variations, temporal and intensive. It should include
an examination of the configuration of the single measure and the
changes in distribution of accents and intervals which it undergoes as
the rhythmical series advances. For the rhythm group must not be
conceived as a simple unchanging form; both intensively and temporally
it is moulded by its function in the whole sequence, the earlier
iambic of a heroic measure being unlike the later, the dactyl which
precedes a measure of finality different from that which introduces
the series. Such a set of determinations will give the pure
characteristic curves of our common poetical meters.

But these meters are no more simple forms than are their constituent
measures. At every point their structure is subject to modification by
factors which appear in the rhythmic utterance in virtue of its use as
a medium for the free expression of thought and emotion; and the
manner in which the characteristic form is altered by these factors of
variation must be studied. Of these variations the more important are
the effects of the introduction of variants--of spondees among
dactyls, of anapaests among iambics, and the like--and the occurrence
of points of origin, emphasis, interruption, and finality in special
accentuations, syncopated measures, caesural pauses and elisions. These
factors influence the structure both of those measures within which
they appear and of those adjacent to them. The nature and extent of
this wave of disturbance and its relation to the configuration of the
whole sequence call for examination.

Finally, this process of investigation should be applied to the larger
structures of the couplet and stanza, that the characteristic
differences in the pair or series of verses involved may be
determined. These characters include the whole time occupied by each
verse of the stanza, the relative values of acatalectic and catalectic
verses occurring within the same stanza structure, differences in
rhythmical melody between the latter forms, the variations of average
intensity in the accentual elements of such lines, and a determination
of the values of rests of higher and lower degrees--mid-line, verse,
and couplet pauses--which appear in the various stanza forms, and
their relation to other structural elements.

* * * * *




RHYTHM AND RHYME.

BY R.H. STETSON.


I. INTRODUCTION.


The psychological theory of rhythm has its beginnings in the work of
Herbart,[1] who inaugurated the treatment of rhythm as a species of
time perception and suggested an explanation of its emotional effects.
While Herbart had simply pointed out the effect of a whole rhythmic
series in giving rise to an emotion of expectation, delay, or haste,
Lotze[2] applied the principle severally to each unit group (each
foot) in the rhythm, and made the emotional effect of rhythm depend on
these alternate feelings of strain, expectation, and satisfaction
produced by every repetition of the unit group. Vierordt[3] did the
first experimental work on rhythm, determining the period of greatest
regularity in the tapping of rhythms. But the first important
experiments were carried on by von Bruecke.[4] By tapping out rhythms
on a kymograph, he determined the well-known 'Taktgleichheit' of the
feet in scanned verse, and noted a number of facts about the time
relations of the different unit groups. Mach[5] added to the previous
knowledge about rhythm certain observations on the subjective
accentuation of an objectively uniform series, and specially he noted
that the process is involuntary. With a much clearer understanding of
the facts of rhythm than his predecessors had had, he really provided
the foundation for the theories which follow. His most important
contribution, for some time overlooked, was his emphasis of the
essentially motor nature of the phenomena of rhythm, and his motor
theory therefor.

[1] Herbart, J.F.: 'Psychol. Untersuchungen' (Saemmt. Werk,
herausgeg. von Hartenstein), Leipzig, 1850-2, Bd. VII., S. 291
ff.

[2] Lotze, R.H.: 'Geschichte der AEsthetik,' Muenchen, 1863, S.
487 ff.

[3] Vierordt, K.: 'Untersuchungen ueber d. Zeitsinn,' Tuebingen,
1868.

[4] von Bruecke, E.W.: 'Die physiol. Grundlagen d.
neuhochdeutschen Verskunst,' Wien, 1871.

[5] Mach, Ernst: 'Unters. ue. d. Zeitsinn d. Ohres,' _Wiener
Sitz. Ber., mathem. naturw. Classe_, 1865, Bd. 51, II., S. 133.
_Beitraege zur Physiol. d. Sinnesorgane_, S. 104 ff.

Many of the recent theories of rhythm are based on Wundt's analysis.
The work of Wundt and Dietze,[6] was concerned with rhythmic series;
but it may be noted that the 'span of consciousness' and the
'synthetic activity of consciousness' were the subjects actually under
investigation. Rhythm was considered as a special temporal form of
this 'psychic synthesis.' There are three different elements in a
sound series, declared these writers, which contribute to this
synthesis: qualitative changes, intensive changes and melodic changes.
Of these the intensive changes are the most important. Every increase
in intensity, that is, every beat ('Hebung') is followed by a
decrease, and the next increase which follows is recognized as a
repetition of the preceding beat and as the forerunner of the beat
which is to follow. From this comes the synthetic power of the rhythm.
Just as the simple unit groups are built up by this synthesizing
power, so they in turn are combined into larger phrases and periods.
The motor factor has little place in Wundt's own discussion,[7] the
'mental activity' is the all-important thing. Bolton[8] also made a
very important contribution to the experimental knowledge of rhythm.
His work was based entirely on Wundt's theory. His method of
experimentation was accurate and his observations copious. The
arrangement of his apparatus, however, led him to emphasize objective
uniformity as a condition of rhythmic grouping; so that Meumann's
criticism of his application of this principle to poetry is quite
just. Nevertheless Bolton established the essential facts of
subjective accentuation and apparent temporal displacement. It is
noteworthy that he laid great emphasis on the motor aspect of rhythm,
and made many careful observations on the 'motor accompaniment.' While
inclining strongly to a motor interpretation he did not attempt to cut
loose from the Wundtian 'apperceptive process' as the primary factor.

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