repetitions alone, where both have a definite outline, and one or
both varies to a greater or lesser extent. The effort will be to show
that the unit which for some reason is of principal importance in the
rhythm, is the one chosen to vary, and if not that the repetition
suffers thereby.
125 EXAMPLES
A. Variations in Principal Unit alone: 87.
I. Content alone:
a. Metopes and Tryglyphs in Friezes: 9.
b. Arches and Columns: 2.
c. Statues in niches alternating with supports: 37.
d. Windows alternating with supports or decorations: 12.
e. Paintings or mosaics: 7.
f. Carved designs in screens or ceilings: 17.
II. Size and Content.
a. Doors, paintings and reliefs on façades.
Vary in size to emphasize symmetry: 4.
b. Statues or shields over arcades.
Vary in size to complicate rhythm: 1.
B. Variations in Principal Unit AND Alternate: 37.
I. Content alone:
a. Windows and decorations on façades.
Alternates vary in design to emphasize symmetry: 4.
b. Windows and turrets. Vary alternately in design to complicate
rhythm: 2.
c. Reliefs alternating with tablets; reliefs or statues and
pillars: Alternates vary in design to give richer effect: 11.
d. Alternate unit is human figure: 9.
e. Alternate unit varies in design, but is on a different level: 3.
f. Irregular variation in alternates (windows, shields, and
railings): 3.
II. Of Size of Alternate Unit.
a. Windows and supports. Vary in size to emphasize symmetry: 1.
b. Statues and pillars; windows and pilasters.
Alternates vary in size to complicate rhythm: 3.
c. Vary in size irregularly. Disorder: 1.
C. Variation of Distance.
Row of windows--Distance between first two is wider: 1.
The 125 illustrations of alternating repetition which were taken at
random among 5000 photographs show a decided compliance with the
principles already laid down. But there are many divergences as well,
which it is necessary to consider, to see whether they are really
contrary in principle or fall under its wider application. Eighty-two
accord exactly with the principles with which we started. The distances
between each set of units are equal and invariable; one unit varies in
content but not in size or including shape; the alternating unit is
invariable.
There is an interesting modification of this principle in the case of
the metopes and triglyphs of the Greek friezes. Here the triglyphs are
unquestionably the principal units structurally, and to many observers
the principal beat of the rhythm when taken rhythmically. But the
triglyphs never vary and the metopes do, which would seem at first to
violate the rule that principal units alone, and not alternates, should
vary. This difficulty is obviated in two ways. With the spatial type of
observer, the triglyph is indeed the principal beat of the rhythm when
the series is at such a distance that the difference in the metopes (if
there is such) cannot be detected. When, however, the series is nearer
at hand, there ceases to be any rhythm, but each carved relief is
taken for itself without regard to the others. With the rhythmic type
of observer, if the triglyph has been the principal unit before, the
principal beat changes on nearer approach to the metope and the whole
series shifts its accent. It is impossible for any observer to keep
the triglyph as the principal unit of the rhythm, when so near that
differences in the metope are easily perceived.
There are still thirty-eight cases which vary from these rules, and
many of them vary in more than one respect. These exceptions fall into
several classes, quite distinctly marked off from one another, and will
be taken up in turn.
In five cases, the _size_ of the principal unit varies as well as the
content, but in four cases the variation of size is either at each end,
or in the centre unit, to emphasize bilateral symmetry of the series as
a whole. The series in this case is taken as a larger unity of which
the separate units are parts; and hence they are not only repeated with
respect to themselves, but are symmetrical with respect to the whole.
In the other case where the size of the principal unit varies, it
varies on _every other one_, thereby complicating but not confusing the
rhythm, _i. e._, a stronger accent comes on every other principal unit.
There are also five cases in which the alternate spaces vary in size.
Three vary regularly, thereby enriching the rhythm by introducing
alternate heavy beats, and one varies at each end of the series to
emphasize bilateral symmetry of the whole, with regard to the central
unit. In the other case the alternates vary in both shape and size,
with no regularity and from the point of view of repetition alone,
disorder is all that results. This is on the Palazzo Pretoria in
Pistoia, where carved shields occur at equal distances between windows.
These shields are not component parts of the building, but were added
with some other kind of significance; hence they express nothing so far
as repetition for its own sake is concerned.
The other variations are all in the _content_ of the alternate, minor
space. Four vary _symmetrically_ in the designs on each side of the
central point, so as to accent the bilateral symmetry of the whole
taken as a unity. Two vary rhythmically in design, _i. e._, there are
two sets of designs which alternate with each other in the unaccented
spaces. When they vary regularly in design, the rhythm of the whole
is _enriched_ not confused, provided there are only _two_ sets, not
three or more. The alternate spaces are passed over on the way to
the principal unit, but by having an alternating design between them
(varying only in detail, but of the same general character) a more
complex rhythm is introduced which is good, since in both cases the
alternates and principal units are so different they could not possibly
be confused with each other, even though both varied. (In one case,
turrets and statues vary with windows of the same shape but different
decorations; in the other, arched windows and arched spaces alternate
with statues.)
Eleven more cases of variation in the minor as well as major spaces
fall under another head. These do not vary with regularity, but are
different in each case--the detail of the design varying, while the
shape, size, and distance remain unchanging. It is interesting to
notice that these examples of variations of alternates were almost all
taken from examples of Renaissance architecture, where a richness of
effect was desired, even at the expense of regular rhythm. This could,
indeed, be attained in no other way so well as this. In all these
eleven cases, the conditions are alike: both of the repeated units
are enclosed by limiting lines of unchanging outline. The principal
units are more prominent than the others on account of greater size or
interest, but the alternates, instead of retiring entirely into the
background, have slight variations in decoration. This variation is
always only in detail: the tracery on the pillars of the tomb of Louis
XII, of the Loggia dei Novoli, in the Chiesi di Frari, Venice, etc. So
unimportant in fact is the variation that it is not observed until one
attends closely to it, and yet the rhythm is just enough disturbed by
its presence to give a feeling of _extra sensation_ or _luxuriance_
which cannot be attained through variation of the major units alone.
It is in the alternate spaces that the _feeling_ of repetition lies.
Any material change in them destroys the series, but a slight variation
in the lines of decoration, a little rearrangement of the conventional
curves in each alternate, gives, even though unattended to, in fact
partly _because_ unattended to, a vague feeling of variety, of some
superfluous sensation being brought into consciousness, although the
regular shape, size, and distance of the objects remains unchanged. It
is this feeling of superfluity and slight disturbance which constitutes
the peculiar richness of certain styles. These examples, then, far
from falling outside of the laws of repetition, owe their opulence of
sensations to the very principles of regular rhythm which they violate.
Another set of exceptions will involve more searching analysis. Nine
of the examples described have the human form for the alternate unit,
and in every case where this happens, the alternate varies. In the
majority of cases where statues of the human form alternate with any
other object, the statue is taken as the principal unit on account of
its superior interest, but this is not always the case. In the Padua
Basilica, and in the Church of St. Guistiana, cherubs alternate with
conventional decorations, but the latter are so much larger and more
elaborate that they would naturally be taken as the principal units. In
the other seven cases, statues alternate with bas-reliefs which also
have human figures in them; hence, since the bas-reliefs equal the
statues in interest and exceed them in size and importance, they are
taken as principal units.
It might at first be expected from the previous discussion that, in
order not to shatter the repetition, the alternate statues must be
alike, must be conventionalized into identity; but this is not the
case. Another principle now comes into play. We demand variation in
the human form whatever its place in art, even in the unimportant
position of alternate in a repetition, and although they are kept as
much alike in pose, size, level of head and feet, general character
(_i. e._, cherubs do not alternate with old men, nor draped figures
with undraped), yet there is some variation of pose or direction of
glance, to keep them from being duplicates. We should expect this
variety of repetition to be in danger of becoming fatiguing because of
its lack of an unchanging rest-phase, but this difficulty was evidently
felt in building them, for in every case _some unchanging element_
has been supplied to the series to bind it together and to keep the
constant changes of attention from upsetting the series. The cherubs
of the Padua Basilica are in high relief against a uniform rectangular
background which does not vary, and which furnishes an alternate
just in character with the principal unit, the bas-relief. In the
Cantoria of Donatello, although the dancing children move across the
whole space, uniform double columns occur at intervals, and supply an
unchanging alternate, while the children vary in position behind them.
Around the pulpit of Lincoln Cathedral, although both units, reliefs,
and statues vary, the pilasters behind the statues are invariable and
supply a constant, unchanging factor in the series. In the alternating
reliefs and statues of the Milan Cathedral or in the paintings of
different sizes in All Souls Church, Oxford, an unchanging element
is supplied in the frame, which is of like design in every case,
so that in passing from one to the other an unvarying alternate is
always present. In the Sienna font, and in the statue to Leonardo da
Vinci, which are types of a vast quantity of repeated forms, there is
uniformity in the minor pedestals and in the frames of the alternating
bas-reliefs, which supplies the unchanging factor.
Moreover, another factor is noticeable in this kind of repeated
series,--it is never long. The fatigue which would certainly result
from a too long continuance of varied alternates, even with unvarying
factors in the way of supports, pillars, and frames, is obviated in
various ways. The series is either short and the whole has a definite
bilateral symmetry, as in the Padua Basilica, and in the Oxford church;
or, as in a great number of cases, the series goes around a fixed
central point so that only three units are seen at a time. It is thus
especially that this method is used in fonts, pulpits, and monuments,
where from the circular arrangement enough can never be brought into
the field at once to fatigue the attention.
This consideration of alternates which vary widely, as do human
figures, even when they are alike in size, general shape, and
character, and, moreover, the discovery that there is almost without
exception an invariable element _between_ the other alternating units,
_i. e._, a third alternate; or _behind_ them, as in the case of the
pilaster behind the statue, may well bring up two questions:
(1) When the unchanging factor comes _between_ the other two units,
is not _it_ in reality the alternate, and the two other units either
variations of shape and size of one principal unit or two sets of
principal units? In other words, do we not actually apperceive the two
principal objects as the units of importance, and take the unvarying
factor which comes between, no matter how slight it may be, as the
alternate? Do we not demand the unvarying as our alternate, no matter
how many variations may be in the other figures?
(2) When the unchanging factor comes _behind_ the alternating statue,
in the same plane with the bas-relief, do we not inevitably take _it_
as the alternate in the series, and regard the statues more as episodes
or attendants on the series but with real values of their own? Is not
the fact that the unvarying factor and principal units are in the same
plane an indication that they constitute a real series, while the
statues or paintings which are in a plane by themselves make a series,
harmonizing with the other, it is true, and in part coinciding with
it, but felt in a different way? Therefore the actual repeated series
conforms to the given conditions and is made to do so in every case by
its unchanging alternate in the same plane; while human figures with
values of their own never can be considered quite as alternates, but
are really felt to be a series by themselves.
This introduces another question. In two more cases of varying
alternates, there was variation in decoration above the level of the
rest of the series. In the Borghese Casino, there is variation in the
busts placed _over_ the alternate windows. In the Venice rood-screens,
there is variation in the carving of the alternating supports, which
rise _above_ the rest of the series. Is that part of the series above
the level of the principal units really included in its perception? It
would seem rather that when the series as a whole is being taken, those
variations above the level of the main units (if they are not very
marked, and they were not in either of these two cases) are ignored
or only felt in a vague way as added richness. When, however, the
attention is turned toward them especially, they form a series of their
own, in which they become the principal units, and alternate with empty
spaces. There is no limit to the changes possible in apperception,
according to the _level_ and _plane_ of the alternating units.
There are three cases left; two where alternates vary in content
with no system, and one with variation in distance. The first two
are differently carved sections of railing on the side of Freiburg
Cathedral, and a differently decorated frieze of squares and circles in
the S. Lorenzo Cloisters, Rome. The effect is only of disconnected and
fragmentary series in both cases, and especially in the latter case it
is impossible to feel it as a repetition at all unless the variations
are ignored, and the attention fixed on the unvarying factor of size.
The variation of distance is in the Beauvais Palais de Justice, where
the first window is at an unequal distance from the others in the
series. The effect is only of disorder and accident.
We have, then, surveyed all our examples of alternate repetition, and
found that in the exceptions to the general principles laid down some
other effect than repetition as such was sought. Either (1) symmetry
for the series as a unity was required, which demanded variation of the
end or central units. In so far, then, as it fulfilled the requirements
of symmetry, those of repetition were disregarded.
(2) Richness of effect was accomplished by those slight variations
in decoration of alternates as well as the principal units. These by
their vague suggestions of different combinations of similar elements,
and minor differences felt but not attended to, gave a superfluity of
experience which made up its peculiar richness.
(3) When the human form (or any other form of especial meaning in
itself) makes the alternate unit, some variation is demanded as in
keeping with its own significance, since in proportion as a thing
has meaning in itself, it must not be exactly duplicated. But an
invariable alternate is always supplied in the way of a frame, or
background, which is felt as the real rest-phase of the rhythm, while
the varying alternate forms have a place in a series of their own.
Also, since such a complex attitude would be fatiguing, such series are
always short, or circular, so that few units are in the field at once.
(4) Regular variations in size or content, in either major or minor
which recur at fixed intervals, give a heightened rhythmical effect by
making certain beats heavier than the rest. As has been stated before,
the major unit holds within it the real significance of the _content_
of the experience; the minor unit holds the secret of the _rhythmic_
effect.
(5) Only 4 examples of the 125 were found to repeat themselves
alternately with irregular variation of alternates and violation of the
other principles laid down at the start. These can only be regarded as
accidents, as faulty examples of art, whose virtue lies in some other
part of the work as a whole, and not by any beauty they possess in
themselves as repeated series.
SUMMARY
125 _Illustrations._
I. Variations in Principal Unit alone, 87
82 Content
5 Size 4 Symmetry
1 Rhythm
II. Variations in Alternate Unit (and Principal Unit)
32 Content 11 Richness
9 Human figure
2 Rhythm
4 Symmetry
3 Different level
3 Disorder
5 Size 1 Symmetry
3 Rhythm
1 Disorder
III. Variation in Distance
1 Disorder
Several questions have been raised in this discussion of variations,
but one which seems directly leading from it will be considered next.
When is variation _necessary_ in a repeated series? We have considered
the numerous cases where variation is _possible_, and the different
ways in which a series may vary according to the idea to be expressed.
Moreover, what appeared to be exceptions to the rule were shown to be
guided by a desire for some other effect than repetitions as such.
But when do we demand variation in a series? Is there any case where
variation of the unit is not only allowable, but positively necessary
to its æsthetic value?
There were no experiments on this question, for it will be seen from
what follows that they would have been impracticable. But observation
of several thousand photographs has made the following clear: When the
series consists of objects having an æsthetic significance of their
own, not depending on something else for their value, then variation
is demanded. In other words, when a thing is an end in itself, we do
not tolerate an _exact_ duplicate. It may have a place in a series
of others similar to it, but its own meaning loses force if another
is beside it precisely alike. When, however, an object has no great
significance by itself, or when however great its value, it be regarded
as means to something greater, hence not an end in itself, it may be
repeated without variation.
This principle may be stated from another point of view: Any work
of art, of the _highest_ significance in itself alone, must not be
repeated at all. There must not be even the suggestion of repetition.
The highest values are individual, and to have a copy or a series
defeats its whole reason for being. Thus, a second Sistine Madonna, or
a series of Venuses, would shock our whole æsthetic feeling. Moreover,
we do not want a _suggestion_ of repetition; even a series of different
Madonnas in similar frames would take away from the significance of
each, in so far as they were regarded as a series, and not as a mere
collection of detached units.
But grading down from these works of the highest value in art, there
comes a point where an object, although possessing considerable value
in itself, is not so intensely individual but that it can gain somewhat
by a place in a series of others like it _in some respects_, but
differing enough so that each still keeps its own meaning distinct from
the rest.
The balance between these two artistic aims, _i. e._, the significance
of the unit, and the rhythm of the series, must be adjusted with
great nicety, and certain principles obtain wherever such series are
found. It would be useless to cite the numberless cases where such
series occur. Many have already been given in the examples of statues
of saints, paintings on altar-pieces, and reliefs alternating with
statues. One such series is a type of all. The human form represents
that which has the most significance in itself, so when it is used
in a rhythmic series, its individuality must be toned down and
conventionalized; it must have no marked feature in one unit that does
not appear in another; the head and feet must be on the same level, or
vary with regularity; the general character and spirit of all must be
similar, but never identical.
The reducing to a common type is the demand of the rhythmic series; the
difference in attitude and arrangement of detail is the demand of the
unit.
Thus, the subjects chosen for repetition of this kind are in the
majority of cases apostles and saints, whose spirit and general
conception are the same; typical representations of abstract qualities,
such as Virtue, Courage, etc.; or conventionalized cherubs, and even
animals. As has been stated before, a long series of this kind is
impossible without fatigue. In proportion as the object is repeated
the individual units lose their own meaning, and they must have their
individuality definitely toned down and conventionalized to avoid the
clash between the two artistic values. Yet their essential peculiarity
must always be maintained, for we refuse to admit or allow the total
identity of any expression of living values, especially as expressed in
the human form.
It may be urged that statues are often arranged at regular intervals
around a building, where the effect of repetition is distinct, and
yet each statue is distinctly valuable for itself. But a distinction
must be insisted upon. The statues form a repeated series as regards
uniformity in position, height, pedestal, and color, so that the direct
sensuous effect may be called rhythmic. But as the attention fastens on
each for itself and takes it for its own meaning, it ceases to be part
of a series at all, but becomes a unit in a world of its own.
But what of the cases where the human form is repeated in a series,
and does not vary? Examples of this are rare, but they do occur, and
are interesting, since they throw light on what has been already said.
In the whole collection of photographs only two were found where a
series of identical statues of the human form occurred,--_The Porch
of the Maidens_ in the Erectheum of Athens, and the _Baths of the
Forum_ in Pompeii. In the former case the left knee of the caryatids
on the right of the centre, and the right knee of those on the left
of it, are raised a little; but aside from this slight variation the
six statues are exactly alike. In the latter case a row of titans all
around the interior bear the ceiling on their uplifted forearms and are
all alike. These two examples are very perfect of their kind, and, far
from offending us, are very satisfactory. The reason is obvious. In
both cases the statues are not the æsthetic end in themselves, but are
there for a purpose, namely, that of a support. They are not ends but
means to something else, and as soon as we feel _that_ in regard to any
work which would otherwise be of individual significance, it ceases to
be individual, or to demand a peculiar expression different from all
others, but may be duplicated without offence. Therefore, since the
support of the superstructure obviously is dependent on the maidens
in the one case and on the giants in the other, and since instead of
existing simply for their own value they are there to hold up the roof,
their artistic significance changes at once from _ends_ to _means_,
and variation is not required. Moreover, it will be found in the
majority of cases that we demand this invariability in actual supports.
Although we find but these two cases where caryatids are actually
identical, we find also that in most cases the caryatids do not really
uphold the weight, but a pillar or pier behind them supplies the real
architectural support, and, that although they have a place in front of
the pillar and give an apparent assistance in bearing the weight of the
roof, yet the eye is not deceived. We see that the work is really done
by the pillar behind them, so they that resume their place as artistic
ends demanding variation, and not as means to something else. The
following examples were found:
_Milan. Arca di S. Pietro Martire._ Pillars uphold the arch while four
statues of women stand just in front. The pillars bear the weight
although the statues add strength to the whole. The statues are varied.
_Dijon. House of Caryatids._ Piers behind the caryatids give real
supports to the roof, while the figures added for decoration are all
varied.
_Dresden. Zwinger._ Conventionalized figures ending at the waist are
put on the outside of unvarying piers which bear the actual weight of
the superstructure. The figures are all varied, but they cannot be
conceived as really bearing the strain, since they have no foundation,
but are merely added to the pier as a decoration.
_Rouen. Tomb of Duc de Brezé._ Four caryatids, all different, under
four jutting projections of the arch. These projections are built
securely into the rest of the structure and do not depend in the
slightest on the figures for support. The figures are not integral
parts of the whole architecturally, for the arch would stand exactly as
well if they walked away, which indeed they are apparently in the act
of doing.
_Toulouse. Hotel de la Borde._ Two caryatids under jutting projections
of a window. The projections are securely built into the lintel and
no weight rests on the caryatids nor even appears to. They are there
solely as decorations and are different.
_Paris. Hotel de Ville._ Two caryatids under jutting projection of
a window, again. Here is a very slight variation of the two female
figures. The position of each is reversed to accent the symmetry of
the whole. Very little weight is actually borne by them, but more than
in the former cases, and we find proportionately less variation in the
figures. They approach identity, but there is variation in detail.
These were the main instances found of the point in question, and are a
type of the other minor ones found in support of pulpits, choir-stalls,
and windows. It will be seen that in no case but the two classic ones
given at the beginning are the human figures architecturally necessary
to the structures, and in these cases they do not vary. In the other
cases they are more or less playful, and the effect of the whole would
be very unsteady did the superstructure actually depend upon them for
support; but since piers rise invariably behind them and bear the
weight, they fall into the sphere of decoration and from that point of
view they must and do vary.
We have, then, considered variation of units in a repeated series,
where they may vary and where they must, and we find the real value
of repetition to appear in inverse proportion to the individual
significance of the separate units; the more interesting or expressive
the unit is in itself with individual significance, the less do
we want it repeated; and so repetition of the human form must be
conventionalized to the type (or to the same unvarying features), with
enough individual differences still remaining to meet the demands both
of the series and the individual. What apparent exceptions we have
found to this rule have been shown to be meeting, in reality, another
artistic demand.
ENDS OF SERIES AND ARRANGEMENT OF REPETITIONS WITHIN THE UNIT
The next question to consider is the _ends_ necessary for a repeated
series. Do they end with a heavier or with a lighter unit than the rest
of the series, or with a unit of the same size? It will be remembered
in the experiments touching this point that the subjects, without
exception, preferred the series ending with heavier units. We should
then expect, in examples of repeated groups of posts, pillars, etc.,
alternating with wider or more prominent ones of the same kinds, that
the series would end with the heavier or more prominent one. Examples
of railings or balustrades alternating with heavier supports are so
common, and the supports come so invariably on the end, that repeated
examples seem almost unnecessary. But another question arose in
connection with this: Does not the apperception of a group of lines
equidistant from each other consist in going back and forth over them
from edge to edge, with no rest on one point more than on another;
while in a group of lines arranged at equal distances each side of the
centre but not from each other, to emphasize bilateral symmetry, does
not the attention rest on the centre, and move from the centre of one
group to the next?
Moreover, we found that a wider space or embankment of some sort was
necessary, to finish off a series of groups in which the separate lines
were equidistant from each other, than to finish the groups whose lines
were symmetrically arranged. This suggests that the activity which
goes back and forth in the former case, being less coördinated and
not bound to a middle point, needs more at the end to stop it than is
needed in the latter case, when the attention is more upon the centre
of each figure. It would seem, then, that the former arrangement would
be appropriate for railings and balustrades, where the effect is of
continuity either running wholly around the structure and into itself
again or where a continuity of parts is desired and a connected series.
The other arrangement divides the series into discrete parts. If the
attention is stopped at every central point, the effect is less of
continuity and more of separate unities bound together externally by
their equal distances. We should, then, expect such series of units
much less in continuous balustrades, but if they occurred at all, that
they would be in connection with separate unities that did not want
continuity or place in a series emphasized at the expense of their
individuality. All this we might expect from the experiments alone,
although whether such a refinement would have got into architecture
seems questionable. Moreover, the question whether a symmetrical
group of units needs a less heavy end to finish it than a group of
the equidistant type is even more difficult to illustrate. Although
the two types may be given under some conditions in experiments, in
actual architecture they never appear so, for the two types never
appear in the same buildings allowing them to be compared. Besides, few
photographs are taken exactly in front, and no two at just the same
angle. Any accurate measurement of such end piers and any comparison
of them is out of the question in the present methods of research.
One other question may be considered here. Does a series ever occur in
which three units are repeated regularly, instead of one or two? In
experiments we discovered that the subject found it impossible to feel
repetitions of three in a series, and the only way that such a series
was tolerable was when the three could be grouped somehow into one or
two units. Therefore we should not expect to find such repetitions
frequently, if at all.
To sum up: Do series always end with a heavier unit? Are units equally
distant from each other more adapted to continuous or run-on railings,
while units with symmetrical arrangements within themselves are found
more often where separateness of objects enclosed is more aimed at than
their connection? Is a less heavy end found after symmetrical series
than after the other kind? Are repetitions of three units used at all,
and if so in what way?
Obviously the only illustrations of these questions will be found
in the arrangement of posts and pillars in balustrades of whatever
description. In these cases alone do we find repeated series, with
repetitions within the unit, as well as of the unit as a whole. The
following examples have been taken by looking over about one thousand
photographs and by recording every instance that occurred.
100 _Examples_
A. 73 Continuous Railings: Balustrades across façades; around roofs; up
flights of stairs; around towers and baptisteries.
I. 57 Rhythmic Units:
a. 31 Even numbers of units in group. Support arches 5.
b. 26 Odd number of units in group.
11 Support even number of arches.
6 More than eight units in group.
1 Two sections of railing. Odd number in ends, decoration
in centre section to emphasize symmetry.
4 No grouping. Too many to count.
4 Other reasons not assignable.
II. 16 Symmetrical units: Slabs with carved reliefs or plain; Carved
scroll or diamond designs alternating with posts; Heraldic
designs on shields;
Conventional decorations in stone or wrought iron.
B. 27 Detached enclosures: Separate windows and doors.
I. 4 Symmetrical units:
II. 23 Rhythmic unit-groups.
a. 10 Odd number of units in group.
b. 11 Even number of units in group.
4 Support odd number of arches.
4 Although before separate windows make a continuous row
across the side of the building.
2 Three sections of railing. Odd number in ends, even in
centre section to emphasize symmetry.
1 No reason assignable.
c. Indefinite number in group. Iron bars in railings, and slender
pillars on façade.
C. 8 Do not end on the heaviest unit.
D. No cases of regular repetition of three units.
Having 100 illustrations of repetitions of groups, with units repeated
equidistantly between them, and of elements distinctly symmetrical,
several new factors came to light. In all the one thousand photographs
looked over, not a single instance was found of unit-groups with the
units within, arranged at other than equal distances. There were many
variations in the number of units in the groups; but the number being
given, the units were arranged at equal distances from each other
wherever the effect desired was of detached sections or of continued
series. There are obvious structural reasons for this. Any repetition
of groups for a balustrade or protective railing, which is the almost
exclusive use of this variety of repetition, would be weakened by wider
apertures on either side of the centre. A reasonably enclosed space
is necessary to make the railing of value, therefore the specifically
symmetrical unit as opposed to the rhythmic unit was found always
in carvings, scrolls, bas-reliefs, etc., alternating with vertical
supports. We should expect, then, in general, that in railings where
an aspect of continuity of progress along some border or a tendency
to go around an enclosure was sought, the units would be rhythmic
in character, impelling one to motion and to carrying the eye and
general organism out of repose into movement. We should expect, on
the contrary, that symmetrical units would be found where repose or
partial distinctness of the separate elements enclosed was desired, and
where the attention was not to be carried away in so marked a degree.
Seventy-three of the one hundred illustrations were of balustrades
where the rhythmic factor was presumably aimed at.
The Rathaus at Braunschweig had a symmetrical design alternately
occurring, but with four in a section, so that the section as a whole
was not symmetrical and the attention was driven on, and in the other
cases some other effect than rhythm was obviously aimed at. The genius
of the structures was heavy and massive and the balustrade made in
keeping with them, since an effect of motion or rhythm would have
clashed with the spirit of the whole.
These examples have all been of the balustrades around enclosures,
balconies, etc. Since the rhythmic unit has been found more fitting for
them, we should expect, conversely, that in front of separate unities,
such as windows, doors, etc., the symmetrical unit would be more in
evidence. At first sight, the facts do not seem to bear us out in
this. Of twenty-seven examples of separate windows, doors, and gates
enclosed by railings, only four had distinctly symmetrical designs.
(Casa Palladio, Bergamo Chapel, Petit Trianon.) These are wrought-iron
designs in the centre with repeated rods on each side, or a row of six
pillars with the central two larger and more decorated. Twenty-three,
however, remain to be accounted for, and the solution of the difficulty
is observed at once in the distinction between _odd and even_ numbers.
As was previously suggested there are obvious difficulties in having
posts in a balustrade at any but equal distances, since the gaps
left by unequal distances from the centre would destroy their reason
for being. This difficulty can easily be overcome in wrought iron by
extra central decoration, although it is not always done by any means;
but in stone balustrades, unless there is carved open-work, or solid
reliefs, there is no other choice than repeated posts, either divided
into sections or continuous, and no variation is possible except to
have an even or odd number of them. We should then expect that there
would be an odd number in separate detached enclosures, bringing a post
in the centre to emphasize the balance, while in a continuous series
each group would have an even number, thus giving no centre to fixate
upon, but driving the attention on without repose at any one point more
than another. It might seem doubtful that any such refinement should
have been actually expressed in architecture, but examination of these
examples shows this treatment to be very general. Of the twenty-three
examples of separate enclosed details, eleven have an odd number of
posts. Of the ten that remain, _four_ are examples of windows along the
side of a building, with separate detachments of balustrade in front
of each. By having an even number of group-units the continuity of
the row is maintained in spite of a separation of the sections. _Two_
of the ten are sections of balustrade over the central doorway of a
building. These balustrades are divided into three sections, of which
the centre is widest and the ends only half as wide. Thus, although
there are six posts in the central section, the balustrade as a whole
is distinctly divided into a bilateral symmetrical arrangement. _Three_
of the others have an even number of pillars, but they support an odd
number of arches; and the arch, not the pillar, is taken as the unit
of the repeated series. (Arches will be discussed later.) The _one_
example unaccounted for represents a number of possible cases, where
for some reason, following out a general scheme of building, or what
not, the odd number is not insisted upon for separate clusters. But the
fact that only one out of twenty-three is thus unexplained shows an
unmistakeable tendency in the other direction.
A distinction between odd and even numbers cannot be felt above eight
repetitions without actual counting, and often not even then.
The two final exceptions are of a gate and a decoration over a door
(Fontainebleau, Piacenza) where there are nine or more units in the
group. It is impossible to feel the system of this arrangement, and
the result is proportionately confusing. A reservation must be made
here concerning iron railings. There is no discrimination between odd
and even in the number of iron rods in a section of railing and no
tendency to symmetrical designs rather than rhythmic before detached
enclosures. This is because from the nature of the case, there is no
distinction possible between odd and even in the number of slender iron
rods necessary to enclose a space with any security. There must of
necessity be so many of them that the difference cannot be perceived,
and so slight is the importance of each rod that the effect is more
of a variegated surface than of actual beats of a rhythm. As soon as
iron is wrought into large enough shapes, each repeated detail is of
the same importance as in stone, but the slender rods commonly used
in iron railings, although their repetition is rhythmic like all the
others, give too slight a motor impulse to carry the attention past the
heavy limits of whatever they enclose. They are found in front of many
windows, but on account of the lightness of their rhythm compared with
the solidity of limiting piers, no confusion results.
Having thus concluded that the odd numbers of units in groups is
more adapted for separate enclosures, is the opposite true? In the
continuous balustrade, previously discussed, are the units of groups
made up of an even number of elements? Of the fifty-seven examples
cited of continuous railings, thirty-one have an even number of posts
in their groups. These conform to the rule: but what will explain the
twenty-six remaining? It will be noticed that _six_ of these have too
many in a group for the eye to perceive any difference between odd
and even, since they range from nine to thirteen. When so many units
are in a group, the effect is always of the run-on type, whether the
actual number turns out to be odd or even on subsequent count. _One_
has a balustrade with only two sections on a side, each side of the
centre door. Seven are in each section, and since the appearance of
a symmetrical whole is the desired effect, an odd number is more in
keeping than an even; in fact, this example, Monte Berico, might
better come under the other head of separate enclosures, although it
partakes of the character of both. Another balustrade with three in a
section (Blois Château) is so heavy and massive in all its parts that
fixity and solidity is more in keeping with it than rhythm. _Eleven_ of
them, that is, the larger proportion of all those with an odd number
of pillars in a section, support arches, and the arch is taken as the
unit instead of the separate pillar; and we find an even number of
arch-units in each section, which is what we should have expected. It
is a noticeable fact, which was previously suggested in connection
with separate enclosures, that when a row of pillars supports a plain
lintel, the _pillar_ is taken as the unit of repetition. (When the
row is on the front of a building, temple, etc., the _opening_ may be
the unit, if the _purpose_ of the central door or the fact of _going
through_ is in the mind: but when the series stands for itself, the
_pillar_ is the unit.) When pillars support arches, the _arch_ is the
unit, unless it is very narrow as in the Moorish style, when the pillar
is often so high and the arch so narrow in comparison that its value is
weakened.
Of the thirty-one balustrades with an even number of parts in a
section, four sets of pillars bear arches, and make an odd number of
them. This would seem to make an exception to the rule were they not
so narrow in two cases that the pillar was still the unit, and in the
other two the motif of the arch was built around the intervening piers,
so that they did not seem divided into sections at all, but continuous.
We have thus surveyed the whole field of repetitions of rhythmic and
symmetrical units, and their difference in treatment according to
the end they serve, and the results bear out our expectations. The
symmetrical unit, as exemplified chiefly by an odd number of units in
groups, is more used for detached enclosures; and the rhythmic type,
with even numbers, is used more especially for continuous ones. In
the former case the motor tendency is toward the central balance,
while in the latter it is driven on out of itself through the series.
When pillars support arches, the arch is the unit; when they support
lintels, the pillars themselves remain the unit. Any number of units
over eight loses its value of odd or even, since the difference can no
longer be perceived and becomes rhythmic whether odd or even.
It must not be supposed that these rules are inevitably carried out or
that the effect is necessarily poor if they are not. It shows a general
æsthetic demand, however, which in individual cases may be modified by
other demands, or altered in parts to make a more unified whole. When,
however, the series is taken for itself, and judged entirely on its own
merits, these conclusions will be found generally valid.
We have still to consider whether series always end with a heavy unit.
All the series examined _do_ end in this way; in fact we feel the
necessity of this so clearly that one illustration would be as good as
a hundred. But there is a difference in the use of the end unit, which
is noticeable in any two series of symmetrical and rhythmic units. Of
the sixteen examples of continuous series whose units were distinctly
symmetrical instead of rhythmic, eight of them, although ending on
supports, do not end on the principal unit of the series. This can be
best shown by one or two examples. The Orvieto Cathedral has on the
façade a balustrade of rectangular reliefs alternating with supports.
The reliefs are undoubtedly the more interesting and important element
of the series, yet the series ends with the less important element, the
support or post, and we feel that it must do so. The Palazzo Contarini
has a balustrade on its façade in which carved wheel-like designs
alternate with supports which come at the ends. Why, in these cases,
do we feel it as inevitable that the heavier and more important unit
should _not_ come at the end, as with rhythmic units we feel that they
should? The answer to this is partly structural and partly æsthetic.
We must feel, first of all, that the series is properly supported,
that it will not fall away at the ends or down in the middle, and for
this reason support of some kind must come at the end to hold it up
and give a feeling of solidity and stability. But why are not these
supports made the more interesting and important unit so that they
might still bear up the superstructure and end the series as well? Here
the æsthetic demand appears. As soon as the object is regarded as an
æsthetic unity and care put upon it to make it beautiful for its own
sake, it must not be thought of as the _end_ of any series. It must
be cut off from the rest of the world by supports or framed in some
way, and while it still may have a place in a series, provided it is
sufficiently conventionalized and not too important in itself, it must
not be thought of as either ending or beginning, as depending on a
series to give it importance, or lending support to anything else. It
simply exists, cut off from the world, even though in the balustrade
not an integral part of it, and one ought to be able to remove it
without affecting the stability of the structure.
The question whether series of symmetrical units have less heavy ends
to finish them than series of rhythmic units cannot be settled by
these methods of analysis. While it seems certain that the rhythmic
series drives the attention on by its greater motor activity, and hence
would need more of an end to stop it, so many other factors enter in
of more importance, such exact measurements would be necessary (quite
impossible with the photographs of the scale here used), the refinement
would be so great, since the stone of which most of the examples are
made, by its own weight supplies a check to rhythmic activity, all
these considerations make it impossible to illustrate this conclusion
and it must remain an experimental result alone.
There remains one question: Is regular repetition of three units ever
found? They may be in combination of some kind so that they fall into a
rhythm of twos, but are they ever found repeated as three separate and
distinct units? The answer to this is without exception. Of the five
thousand photographs analyzed, not one instance of this kind of series
was found. In many cloisters the pillars are of different design, and
often one design is repeated through an otherwise varying series, but
their repetition is either without scheme of any kind, or in some
combination that falls into a rhythm of twos. No three-rhythm has been
used in art, any more than it has been found possible in experiments.
ARCHES
It has been noticed in the preceding discussion that when a series
of pillars supports arches, the arch, not the pillar, is taken as
the unit. If this is so, it would seem that the arch by binding two
pillars together with a curve awakens a more vigorous response than the
vertical line of the pillars, and this greater expenditure of activity
makes it to be taken as the element of repetition. It suggested that
the arch (like the rhythmic unit) tends to drive attention on out of
one unit to the next in the series. The outward thrust of the arch
arouses an outward-tending activity, and for this reason a row of
_arches_ would need, to give a finished, stable effect, a wider and
heavier embankment at the end than a series of lintels. The experiments
on this point were inconclusive owing to the difficulty of obtaining a
series of arches and of lintels which should be comparable in size.
For this reason the validity of this suggestion must depend upon the
actual treatment of arches in architecture. It would seem that the
arch would, like the rhythmic unit, be more appropriate for continuous
series than for detached short rows; or if the series were short, the
ends should be treated in some way, by reduction in size, change in
width of pillar, pier, or decoration, so that the outward-activity
might be counteracted by some inward thrust or some accentuation of
the centre. Thus the unity or balance of the series as a whole would
prevent the arches from seeming to "run away" which they might appear
to do without such treatment. We shall, then, look through photographs
of buildings where arches are used, to find if their treatment carries
out the supposition.
It may be seen at once that such a treatment of arches differs from
the arrangement necessary to make plain lintels effective. The pillars
on the front of Greek temples were indeed slightly farther apart at
the middle entrance, and the centre was moreover further accented by
the point of the pediment. But on the sides the rows of from thirteen
to sixteen columns had equal interspace and no noticeably heavier
columns or embankment of any kind at the ends, for none was necessary.
The series appeared ended whenever it stopped, and did not carry the
attention over, nor demand some finish to "hold it down," as does the
arch. The pillars, to be sure, completely surrounded the temple, and so
were, in name, continuous. But on a building with square corners, the
other sides do not carry the series on to the eye (with variations in
foreshortening of the ends) as in a circular structure, and the effect
of continuity is not immediate.
Many examples might be given of buildings with pillars and lintels
on the façade, which have no visible modifications of central or end
columns to give balance or symmetry to the whole, and yet which are
perfectly satisfactory as repeated series and do not demand either
such treatment or further continuation, but are complete and finished:
London, Trafalgar Square; Rome, Pantheon; Vienna, St. Karl, Barrome
Kirche; Berlin, Schillerplatz, etc. These have the centre accented by
the superstructure, but there is no discernible modification of the
series itself.
Examples might be multiplied, but there are sufficient to illustrate
the essential stability of repeated vertical units and to contract them
with the outward-tending, run-on effect of arches which need various
kinds of treatments to finish a series.
165 _Arch Series._
A. 45 Go completely around exteriors: Colosseum, arenas, baptisteries,
towers, cloisters, courts, basilicas, tombs.
59 _Series that end:_
B. I. 30 Central arch largest: triumphal arches, doors and windows on
façades of churches.
II. 1 Central arch smallest: doors on Peterborough Cathedral.
III. 4 End arches larger: windows or decorative arches on the walls
of buildings.
IV. 6 End arches smaller: windows, decorative arches, or arches
halfway around a court.
V. 6 Arches go obliquely into higher central point and back:
decorative arches running into the pointed roof on
Romanesque façades.
VI. 6 Central arch accented by decoration: windows and gates.
VII. 6 End arches in different planes: doors on façades of
buildings or in gates.
C. 20 Arches go around interiors: up naves and across the apse of
churches, halls, and loggias.
D. 27 Around the outside of porches, apses, etc.; diminish in size
at ends; are carried on in the transepts; motif is carried on,
although whole arch is not; end arches are closed, or centres
decorated.
7 _Good_
E. 14 Other arrangements: Roman aqueducts (endless); interlacing
arches; filled with statues; finished by gables or turrets;
bridges (land on each side a sufficient embankment); arches
included in large ones.
7 _Poor_
Series not sufficiently finished at the ends; only two arches
in series; three arches, with first arch different from the
others.
Of one hundred and sixty-five examples of such series examined, only
seven do not conform to the principles we have considered, and these
are proportionately unsatisfactory. Forty-five illustrate buildings
where the arches go completely around the outside of a structure,
so that the series instead of requiring an end simply runs into
itself again. It will be noticed further, that unlike series of
columns around rectangular Greek temples, these are around circular
structures where the series does not change its direction suddenly
but by degrees. With the exception of courts and cloisters where the
observer stands within and sees the whole series, these are all around
domes, baptisteries, etc., where the end arches in the field at any
one point of view are seen in perspective gradually fading off and
yet leading attention on around the building. There may indeed be
arches which go across square-cornered buildings or even around them,
but in these cases some other device is necessary to make each side
a finished series in itself. The mere fact of its continuance around
a corner where it cannot be seen from the same point of view is not
enough. (These various arrangements of arches on a flat façade will be
taken up later.) Rows of arches are often used around towers square
as well as round, but towers from their very shape and size allow the
observer to see different sides from nearly the same point of view,
so the series is not broken up into sections on different sides of
the tower as it is in a larger building. Twenty more examples are of
arches in interiors and are all of arches down a nave, with either a
regular arch or an arch motif carried across the apse. It might be
supposed that an arrangement of arches in an interior would be more
difficult than on an exterior surface, since the genius of an arch
is its outward thrust and its tendency to run on. Without careful
treatment it would spoil the interior by trying to overstep its bounds;
by making certain walls look wider than others; the arched sections
utterly discrete in general character from the plain or otherwise
decorated section. In point of fact, the use of the arch-series in
interiors is quite conventionalized, and all the illustrations are of
loggias, or of churches where the arch goes down the nave and in a
more or less modified form across the apse. In the Sistine Chapel the
arched windows go down the side walls and across the end in a vaulted
double-arch. In some cases a series of Roman arches down the nave has
a more or less pointed arch across the apse, but in every case the
continuity has been kept in some way so that the series is unbroken.
Moreover the columns in the cathedral naves are often so high and the
arches so proportionally narrow that the pillar instead of the arch is
taken as the unit. This is somewhat true in St. Mark, Venice, also in
St. Sophia, Constantinople, where the large arches are divided into
sections of seven smaller ones, each one of which is so narrow that the
pillar is felt as the repeated unit instead of the arch; or if the arch
be taken, the narrow span prevents it from too great outward thrust.
Thirty of the arch-series are on façades of buildings or in structures
by themselves, as gates and triumphal arches, where the central arch
is larger than the other, thereby emphasizing the middle point and
drawing attention to it away from the ends. This centralizing a series
or balancing it as a whole may be accomplished in various ways. Two
examples make the central arch larger instead of smaller. Six make the
end arches smaller while four make them larger. It will be readily
seen that just which one of these variations is chosen for the series
depends on the function of the series. The central arch is wider, with
only one exception, when the series is of arched doors and the central
door is the main entrance; while the end arches are more apt to be
varied when the series is purely decorative and serves no function.
The central balance may be further gained by differences of level.
In the decorations of many façades, especially the early Romanesque,
rows of arches go obliquely into the point of the roof and by this
strong pointing toward the centre create an inward tendency. Six of
the illustrations have the central arch accented by decoration; seven
have heavier piers around the central and end arches; six have the end
arches brought out into a nearer plane which effectually finishes the
series. All these examples illustrate the necessary disposition of
arches on a flat wall or façade where the series in the field of vision
must end suddenly, that is, cannot gradually fade away around a corner.
The variety and yet invariability of these devices shows the need felt
for some finish at the end, some balance of the whole with the central
accent, which need, apparently, is not felt for pillars and lintels.
When the arch-series is on a circular structure, such as apses,
porches, and the like, even when it does not entirely surround it, as
an arena or spire, the regular diminishing of the series on either
side, owing to the curve, supplies the finish necessary, and the size
and arrangement of the arches need not vary otherwise. Twelve of the
examples illustrate such a use of the arch, and although in some cases,
Morano Cathedral, Nomantala Church, the arches are continued into the
transepts gradually tapering in size, or are modified in size growing
narrower from the centre, as in the Bergamo Church, such a treatment
is not necessary for finished effect. The difference in proportion
resulting from a curved series, or even on arches carried around a
square corner (as in porches on Goslar and Braunschweig Rathäuser),
where the series is open enough to clearly see its continuity as it
runs into the main building, will suffice to make a series finished
without modifications of the arch-units.
There are many instances of long rows of very narrow arches on
cathedral façades which are too narrow to give outward tendency, or
else they have statues within them which really take the attention
and form a series of vertical units in place of the arches. There
is also the common device of interlacing arches, where a supporting
pillar of another arch stands in the centre of every arch, thereby
always driving the attention backward and restraining it. Perhaps the
natural outward tendency of the arch-series and the necessity for its
limitation can be seen by violations of the principle. Seven of the
examples do not conform to any application of this rule and the results
are not satisfactory so far as the mere series itself is concerned.
Over the right and left doors of the Piacenza Cathedral are sections
of nine arches which end abruptly and do not even meet each other.
The Fredericksborg Schloss at Copenhagen has a row of fifteen arches
enclosing a court. These run into wings on each side, to be sure, but
all seen at once as they are and without central or end modification
they are too sharply cut off and inclined to overstep their limits. The
Loggia dei Lanzi at Florence, with its three wide arches and narrow
pillars, the William Tell Chapel in Switzerland, with only two arches,
illustrate forcibly the tendency of an arch to move outward, to appear
too wide for the superstructure and too "active" unless bound down in
some way. Four arches on the right and left of the façade of Marmonte
Church, but not across the centre, have the same unfinished effect. The
roman arch on one side of the St. Lo Cathedral façade with two gothic
arches on the other defy every principle of repetition and symmetry as
well.
From this survey of one hundred and sixty-five of arch-series we find
through a variety of means a uniformity of purpose in their treatment;
that all point to a common demand, however differently expressed,
according to the function of the series. The series must be prevented
from "running away." It must either run completely around a structure
into itself, or be balanced as a whole so that the attention which
naturally runs off the ends is driven towards the centre. This may be
accomplished by enlarging, decreasing, decorating, or pointing toward
centre of the arch by means of the obliquity of both halves of the
series. It may also be brought by enlarging, decreasing, changing the
plane of the end arches or altering the size of the limiting piers. The
essential value of the arch may be altered by narrowing it, by filling
it with something more important than itself, thereby making it only an
attendant series upon its content, by interlacing it, or by any device
that transforms or revises its outward tendency.
165 _Examples of Arch-Series._
45 Go around outside a circular structure.
32 Go around interior and apses.
30 Central arch largest.
2 Central arch smallest.
4 Ends largest.
6 Ends smallest.
6 Central arch accented by decoration.
6 Central arch accented by upward incline of two halves.
6 Ends in different planes.
7 Different width of piers around centre and ends.
5 Very narrow arches.
9 Other reasons.
7 Unaccounted for.
The question discussed in the experiments, as to whether narrower
interspacing was required between units decorated toward the centre,
and units blank, or covered entirely with non-centrally accented
decoration, could not be taken up in the latter analysis. To settle
such a point, illustrations would have to be found of blank and
decorated units of the same shape and size, in the same structure, and
their relative interspacing compared. But no such examples were found,
where the spacing was not regulated by some obvious structural reason
other than pure pleasure in the repetition. This must stand, therefore,
solely as an experimental result.
The use made of difference in plane or end, to facilitate two series
being taken along together, whereas they would be fatiguing if the
same in those respects, has been touched upon in the discussion of
statues and bas-reliefs, and other series of more complicated units.
Where the unit and alternate are both rich and significant, and would
tire the observer by following each other at the distances they are
obliged to be in a series, a slight difference in plane relieves the
situation, and is used largely in monuments, fountains, pulpits, and
such structures.
Many other questions have come up in the investigation which might be
discussed in the same manner as the preceding, but can only be hinted
at in conclusion:
Just what factors make an element and its alternate congruous? What
is the exact relation of lines, which makes the scroll decoration in
a balustrade alternate satisfactorily with an upright support, while
the alternation of the arches in the Colosseum with the Greek pillars
between them is incongruous?
In what does the pleasure in repeated series differ, when the observer
is not certain just what is the repeated element? May there be a bare
rhythmic pleasure, when the series is too far away to distinguish
what the elements are, or when they run together, so that no definite
demarcation is felt between them? Do such series excite a pleasure of
repetition without content as to elements, and does it differ from mere
variation and contrast?
The series of unsymmetrical units was found in the experiments to have
a peculiarly unstable run-on effect similar to that of rhythmic units
and of arches. Are they used in the same kind of cases as the others
were, when a particularly active effect is desired?
Must a space be wholly enclosed, to be taken as a unit?
In a series of projections along a wall, the _projections_ are taken as
the unit, even when they almost meet at the top of the alternate space.
When they actually do meet at the top, the enclosed space becomes the
unit instead.
These questions and others similar might be experimented upon, and
examples of their treatment analyzed, as in the previous questions
discussed.
[Illustration: PLATE V.]
FOOTNOTES:
[Footnote 86: Stratton: Eye-Movements and Æsthetics of Visual Forms,
Philosophische Studien, vol. 20, p. 350, 1902.]
[Footnote 87: MacDougall: Structure of Simple Rhythm Forms, Harvard
Psych. Studies, vol. 1, p. 321, 1903.]
[Footnote 88: MacDougall: Structure of Simple Rhythm Forms, _ibid._ p.
322.]
[Footnote 89: MacDougall: Structure of Simple Rhythm Forms, _ibid._ p.
322.]
[Footnote 90: MacDougall: Structure of Simple Rhythm Forms, p. 325.]
[Footnote 91: Bolton: American Journal of Psychology, p. 223, 1894.]
[Footnote 92: Külpe: Outlines of Psychology, p. 395.]
[Footnote 93: MacDougall: Structure of Simple Rhythm Forms, p. 348.]
[Footnote 94: MacDougall: Structure of Simple Rhythm Forms, p. 349.]
[Footnote 95: Stetson: Rhythm and Rhyme, Harvard Psychological Studies,
vol. 1, p. 455, 1903.]
[Footnote 96: Stetson: Rhythm and Rhyme, Harvard Psychological Studies,
vol. 1, p. 455, 1903.]
[Footnote 97: MacDougall: Structure of Simple Rhythm Forms, p. 377.]
[Footnote 98: Perrot and Chipiez: Art in Ancient Egypt, p. 100.]
[Footnote 99: Perrot and Chipiez: Art in Assyria and Chaldea, p. 126.]
[Footnote 100: Perrot and Chipiez: Art in Persia.]
THE FEELING-VALUE OF UNMUSICAL TONE-INTERVALS
BY L. E. EMERSON
Modern theories of melody start always with the presupposition that the
scale must be composed of tones having the simple mathematical relation
to one another of 2, 3, 4, 5, 6 (and by Meyer 7) and their multiples
in order to give pleasant combinations of successive tones. But the
question arises whether other tone-combinations which given together
appear disharmonious may not, by their mere acoustical difference,
similarity, and contrast, awake definite feelings of pleasure. And
if such feeling-tones exist independently from harmony it is evident
that they would enter into every melody in addition to the strictly
musical feelings of harmony and that they deserve consideration as a
factor of music. It would not even appear impossible that if every
successive tone-distance has its particular natural feeling-character,
the distances of successive harmonious tones might be only through
secondary factors as habit and training preëminent among the various
possibilities of combinations. A tone-consciousness, which under the
guidance of experiences of harmony has been trained in our musical
tone-relations, must give instinctive preference to such successions
as our melodies offer. But if we artificially inhibit the conscious
relation to our musical system by introducing a continuous tone-series,
or at least one of steps much smaller than musical intervals, do
we destroy the possibility of pleasure, and if not, do we find the
pleasure in the musical interval stronger than that in other instances?
That even the musical subject introduced into the realm of smallest
tone-steps can easily forget and inhibit his normal standards is well
known; the whole acoustical perspective seems changed by the new
intervals, and the subject begins at once to build up a new temporary
system of relations. The experiments in Wundt's laboratory have shown
that in such cases the theoretical judgment of distances is indeed
quite different from the standardized one; the octave may appear
equal to the higher fifth. I wanted to study in a similar way the
feeling-value in such a state of musical disorientation, when all
imaginative representations of our musical intervals are inhibited.
The instrument I used was an Appun Tonmesser giving reed-tones from 128
to 512 vibrations in intervals of 4 vibrations between adjacent tones.
The intervals with which I experimented varied from 4 to 88 vibrations
in steps of 4. The observers were all experimental psychologists, and
varied in musical discrimination from a very low to a very high degree
of natural ability and skill.
The observer reported his pleasure in the progression given, in the
traditional grades of 1 to 7, where 1 represents the greatest degree
of pleasure, 2 means very pleasant, 3 pleasant, 4 indifferent, 5
unpleasant, 6 very unpleasant, and 7 most unpleasant of all.
The immediate problem was: What is the relation between the width of
interval used and the pleasure got by hearing the motive _a-b-a_ and
_b-a-b_, where _a_ is always the lower tone. The method of procedure
was to take a fixed tone (460 vibrations in the first case) and get
a series of observations on successive progressions _b-a-b_ where
_a_ differed from _b_ by 4, 8, 12 ... 56 vibrations. The greatest
difference thus is approximately a musical whole tone. Then a series of
observations was taken on _a-b-a_ where _a_ similarly differed from _b_
by 4, 8, 12 ... 52 vibrations. The progressions were given in irregular
order, that there might be no chance of the observer getting into a
fixed habit of replying. The intimate relation between the pleasure
in successive musical tones and the pleasure in musical harmonies
suggested naturally the question whether the feeling-value of these
unmusical progressions was not somehow dependent upon the affective
character of the simultaneous presentation of the same tones. Therefore
after a progression had been given once and judgment recorded, the
two tones used were given as a "harmony," that is simultaneously,
and a judgment taken as to its agreeableness. This was immediately
followed by the same progression, thus giving opportunity to observe
the relation between the feeling-tone of the interval as it appeared in
successive and in simultaneous presentation.
The results of this part of the investigation are graphically
represented in the following plates. Tables I and II indicate the
feeling-value of _a-b-a_ where _a_, the lower tone, is 460 vibrations,
and _b_ is from 4 to 56 vibrations in addition, and the feeling-value
of _b-a-b_ where _b_, the higher tone, is 460 vibrations and _a_ is
from 4 to 56 vibrations less.
[Illustration: PLATE VI.]
The base-lines from which the vertical lines to the curves are drawn
represent the feeling-tone 4, the indifference-point. Above comes 3,
2, 1 and below 5, 6, 7; each square represents a unit. The horizontal
abscissæ represent the width of the interval; the arrows indicate the
musical intervals. The observers are given by initials. The first
evident fact for both average curves of Plate V is that the maximum
pleasure does not coincide with a musical interval, but comes with an
interval four or eight vibrations less than either the half or the full
tone of the musical scale. While in both cases the first elevation
of the curve comes before the semi-tone, _b-a-b_ shows a decrease of
pleasure as the whole step is approached while _a-b-a_ rises again. The
order _a-b-a_ is liked better than _b-a-b_.
Plate VI gives the "harmony" curve for the same tone-combinations, and
it is clear at the first glance that the curves for the simultaneous
tones do not correspond to those for the successive ones; in many
respects they are directly the opposite. The hypothesis that the
pleasure in such an amusical "melody" results from the resolution
of the corresponding "harmony" is thus untenable; both are highly
independent of each other. Yet, here too we notice the insignificance
of the musical interval, while the strong pleasure in the tones
different by 4 vibrations only refers probably to the complete fusion
of the tones; there arises a direct enjoyment from the four waves of
sound in every second, given by the beats. The pleasure-curve of these
simultaneous tones indicates of course that the inhibition of the
musical dispositions and expressions holds over from the successive to
the simultaneous series. The pleasure is thus clearly different from
that in real harmony.
Plate VII finally gives the "melody" curve for _aba_ and _bab_ with
changes from four to four vibrations when the interval started with is
larger than a full musical step. In _aba_ the _a_ is 384 vibrations
and _b_ varies from 436 to 516, the variations lying thus between the
musical Second and the musical Fourth. It is evident that here again no
feeling-preference is given to the musical intervals.
The question arises whether such small tone-intervals of amusical
character allow the construction of more complex combinations of
æsthetic value. Can we have amusical micromelodies with their own
completeness and feeling of end? The following experiments represent a
first step into this field. We used three tones only, _a, b, c_ in 26
different combinations, and each of the 26 variations with intervals of
4, 8 and 12 vibrations between _a-b_ and _b-c_. Each of the resulting
78 "melodies" was given repeatedly to six subjects in a time-order
which allowed one second for each tone. The subject had to judge on
the pleasantness of the whole progression and had further to judge
whether it produced a feeling of end or not.
The combinations followed in the experiments in this order: _abc_,
_cbabc_, _abcb_, _cba_, _abcba_, _cbab_, _bcba_, _cbabcb_, _ababc_,
_babc_, _abcbab_, _babcba_, _cbcba_, _bcbabc_, _abca_, _acba_, _acb_,
_cbac_, _abcab_, _cabc_, _cbacb_, _acbab_, _cab_, _bca_, _cabcb_,
_bac_. The lowest tone was varied between 200 and 444 vibrations; _b_
and _c_ were thus always still less distant than the next musical
tone. The chief results may be shortly characterized as follows.
There are hardly any judgments of indifference, the combinations are
always decidedly pleasing or unpleasing. Of course a certain training
in the apperception of such small-interval melodies preceded the
real experiments and produced an attitude of adjustment to amusical
relation. If we are in the midst of musical tone-relations and go
over directly to such miniature intervals, we are seeking for the
fulfilment of the habitual expectation and feel dissatisfied, or in
the best case the procession is an indifferent chance combination.
But as soon as a certain training with small intervals has inhibited
the strictly musical expectations, a new setting of judgments with
new standards comes in and a new source of pleasantness is opened.
Of course even then no extreme feelings are to be expected; while
the indifference-judgment 4 is lacking, the strong pleasure and
displeasure, the judgments 1 and 7 are completely lacking too; three
fourths of the judgments are 3 and 5. The pleasantness is decidedly
more frequent than the unpleasantness, and this relation increases
with the interval. The differences of four vibrations were especially
with the higher tones hardly distinct for some of the subjects. Among
288 judgments in each group there were 150 pleasant and 138 unpleasant
when the distances between _a-b_ and _b-c_ were four vibrations, 208
pleasant and 80 unpleasant when the distances were 8 vibrations, and
226 pleasant and 64 unpleasant when the distances were 12 vibrations.
The order of pleasantness expressed by the fraction of judgments of
pleasantness and unpleasantness is the following: the largest number of
pleasant feelings belonged to the figures _cbab_ and _bac_, immediately
followed by _abcb;_ the further order downwards in affective value was:
_cab_, _cbac_, _babc_, _abca_, _cbcba_, _ababc_, _abc_, _cabc_, _acba_,
_cbabcb_, _bcba_, _acb_, _abcba_, _cba_, _cbabc_, _abcab_, _babcba_,
_cbacb_, _acbab_, _bcbabc_, _abcbab_, and _cabcb_ as least pleasant.
[Illustration: PLATE VII.]
As to the feeling of end or æsthetic completeness the results are
similar and yet independent. In a few cases the answer was "doubtful,"
but in the overwhelming majority a definite reply was given; and
while the judgment of completeness was by far more frequent in the
pleasant combinations than in the unpleasant ones, yet often the
unpleasant processions appeared as complete and the pleasant ones
as incomplete. Here again the feeling of completeness grows with
the interval, being smallest for the figures with distances of four
vibrations. But most characteristic seems the fact that the feeling
of end is in no way as in music dependent upon the return to the
starting-point. The combinations which involved such return to the
"tonica" show in no way a preponderance of judgments of completeness.
If we order the results according to the number of this æsthetic factor
the figures _acba_, _cbac_, and _cabc_ stand very low, giving in the
majority of cases the suggestion of not-completeness in spite of their
return to the beginning, while the figures of the type _abcb_, _cbab_,
or _cba_, or even the complex _babcba_, suggest in a majority of
judgments the feeling of an end. The feeling of an end comes, according
to the subjective reports of the observers, with an "internal unity of
meaning" of the phrase given. This unity of meaning is here evidently
quite independent from any simple mathematical relation.
The music-like quality of the figures was emphasized frequently in
the subjective records. "I just enjoyed the progressions as music."
"The elements are the same as in music." A melody of 384, 392, 400
was called a "very mournful strain"; 444, 452, 460 "Wagnerian motive;
Tristan and Isolde"; and the same tones in another order "Very
pleasant; expressed a pathetic resignation," or "Sounds like a little
piece of music"; and so in most varied forms.
The basis of these experiments is of course by far too slender to
build on them a theory, yet our results suggest at least a greater
interest in the æsthetics of those tone-combinations which are
excluded from our regular music. This interest is reënforced by the
self-observations of all participants. They felt strongly that after
all our musical pleasure in melody does not belong intrinsically to
the tone-perception, but is learned and acquired like the grammar of
our mother tongue. Such grammar too controls completely our internal
demands for expression, and yet the learning of a different language
can bring a new adjustment and a new set of psychophysical dispositions
for linguistic demands. That whole apparently natural demand for the
tone-combinations which give fusion and consonance can be inhibited
during the listening to amusical combinations as soon as a short
training in miniature intervals changes the acoustical perspective.
The development of instrumental music demanded evidently the selection
of distinctly separated tones and of intervals which give harmonious
combinations. The external conditions of resonant chambers may have
reënforced this selective process of historical music. It is certainly
different with oriental nations, which produce music not in resounding
chambers but in the free air and who are singers and not players, using
instruments mostly for producing a mere body of tone as a background
against which the melodies move; their intervals appear to our musical
ear at first bizarre, and yet there too we are readjusted to the
new dispositions for satisfaction with unsuspected quickness. We
have no right to identify æsthetic pleasure in successive tones with
the pleasure in our conventional music with the simple mathematical
relations which alone give the pleasure of fusion; but being accustomed
to this system of harmonies and being trained to expect it also in the
resolved form of the melody, we need indeed an inhibition of habits and
a certain new training till the more modest pleasure in amusical tone
progressions comes to its natural right.
ASSOCIATION, APPERCEPTION ATTENTION
CERTAINTY AND ATTENTION
BY FRANCES H. ROUSMANIERE
The results of the experiments on the feeling of certainty which I
have conducted fall into two divisions--those on the nature of the
feeling itself, and those on the effect of voluntarily attending to
certain aspects of a total experience upon certainty in the judgments
as to the constitution of that experience. The problems of the first
division are: Are there different kinds of certainty? In any one kind
of certainty are there degrees, and if so, are these of a limited or an
unlimited number? Can certainty be analyzed into elements? The problems
of the second division are: Can it be said that in the report of any
experience the judgments made with the highest degree of certainty will
be confined to an attended-to group, and if not, will there be more
there than elsewhere? In such a report will the direction of voluntary
attention toward certain aspects materially alter the distribution
of the judgments of the highest order of certainty over the various
aspects of any given field?
These two divisions are so distinct in problem and result as to make
it seem best to describe them as independent experiments. As some
interesting results on the relation of error to the different grades of
certainty and to the effect of attention developed in connection with
this second division of the experiment, those results are given also.
In general the same subjects took part throughout the experiments.
One, an instructor in Harvard University, whom I shall call K, was
not subject for the second division of the experiment. Two others, E
and H, both graduate students in Harvard University, could not serve
as subjects in an important part of the first division. Of those
remaining, B was a student in Radcliffe College, F an instructor in
Harvard University, and A, C, and D graduate students in Harvard
University. These last five were my subjects for all parts of the
experiment.
I. THE NATURE OF THE FEELING OF CERTAINTY
The general method here was, of course, the method of introspection.
Situations were created about which the subject might be expected
to make judgments with different sorts or different degrees of
certainty, if such should be possible. He was then questioned as to
his experience. The method has the fault of all introspective methods,
viz., its results can in no case be verified. The results here are none
the less suggestive, and, for the second problem, at any rate, definite
enough to be convincing.
Most of the experiments were conducted in connection with visual
fields. In working at the first problem which we have now to consider,
however, the certainty connected with the dermal sensations and that
connected with the simple reasoning process of addition were also
examined. The apparatus used consisted of three sets of cards. On
one set were pasted geometrical shapes cut from colored paper, and
black and white letters or figures. Each of these cards was shown to
a subject for a second and a half, or two seconds. After the exposure
he told what he judged to be on the card, giving all that he could
about the nature of his feeling of confidence (or certainty) for each
judgment. On the second set of cards square pieces of tin, smooth
rubber, rough rubber, cotton, felt, undressed kid, leather, eiderdown,
flannel, coarse and fine sandpaper, and pricked paper were stuck, six
on each card. The experimenter passed these cards so that these bits
of material rubbed against the forefinger of the subject, while a
curtain kept the card and the hand hidden from the subject's sight.
Here, again, the subject judged of what had been on the card, just as
he had done after seeing each of the first set of cards. Small sample
cards, each having pasted upon it a piece of one of the substances
used, were also behind the curtain, and the subject was allowed to feel
of these as much as he wished while giving his report. Such sample
cards were required because of the underdevelopment of the association
of names of any kind with the dermal sensations. A single card with
three groups of figures for addition upon it made up the third part
of the apparatus. Here the subject was asked first to add the columns
rapidly and to introspect as to his certainty of the correctness of the
different results; then to go over the addition again, and yet a third
time, and to compare his feelings of certainty in the different cases.
The introspection was developed partly through the help of questions
put by the experimenter, but in asking these questions great care was
taken to prevent their influencing the judgment of the subject. Some
observations made by the subjects during the second division of the
experiment (also conducted in connection with visual fields) are, also,
introduced here. Apart from this, the experiments on the feeling of
certainty connected with this sense of sight were greater in number
than the other experiments; and it is those that have given us most of
the data for answering the second and third problems.
The subjects did not agree in their answers to the first problem. Some
found not only that the certainty connected with their belief in the
results of their addition seemed to be of a distinct type from that
connected immediately with the sense of sight, but also that there
were different sorts of certainty connected immediately with the sense
of sight itself. Others found but one kind of a feeling of certainty.
All agreed, however, that so far as the kind or kinds of certainty
associated with them was concerned there was no difference between
the sense of sight and the dermal senses, so that it would seem to be
true that any distinctions which are to be found within the feeling
of certainty will not be distinctions springing from the difference
in the sense-organs. Within the sense of sight, however, subjects B,
E, and F divided their feelings of certainty into two classes,--an
absolute feeling of certainty which they felt could not be shaken,
and a feeling of confidence which they would act upon but which they
felt might be shaken by questioning, and which seemed different by
more than degree from the feeling of certainty proper. Subjects A,
C, K and H found no such marked distinction between their feeling of
greatest certainty and all lesser feelings of conviction. Subject D
at one time felt that the distinction into two such distinct classes,
the definitely certain and the more wavering, fitted his experience,
and at another time said that it seemed to him that each degree of
conviction stood for an unique feeling of certainty and that any two
of them were as different from each other as any other two. A second
division of the feelings of certainty into two classes is to be found
with subjects A, F and H. This developed in connection with the
visual experiments again. The distinction here may be called one into
psychological and logical certainty. The latter rests on reasoning
either from the probable character of the field, or from a feeling
as to its general character, to the nature of some detail. We shall
notice the characteristics of these two classes later. One subject, A,
further distinguished as different the feelings of certainty connected
with the two methods of logical certainty just given. The others made
no such distinctions. In the experiment with the columns for addition
only six subjects, A, B, C, D, F, and K took part. Of these the two
who had made the distinction into psychological and logical certainty
with the visual experiments (subjects A and F) again made the same
distinction. Subject F, however, who had had occasion to do a good deal
of important work with statistics, found practically no element of
logical certainty in connection with his addition, though it seemed to
him that what confidence he felt in his result should be distinguished
from the psychological certainty he had had as to the character of
the visual fields. Subject B felt no certainty in her results except
as she could so hold the process together as to have what seemed to
her a simultaneous experience. When she had to judge of the results
of a set of successive experiences that could not be so unified, she
characterized her state of consciousness not as holding a feeling
of certainty or of uncertainty, but as simply lacking any feeling
of certainty. The other three subjects found no difference between
the feelings of certainty and uncertainty associated with visual
experiences and those associated with the process of addition. As a
whole, it seems then that we must answer our first problem by saying
that the case seems to be different with different individuals. With
some the highest grade of certainty associated with a sense-experience
is sharply distinct from the other grades, and with some again there
appear at least the two general classes of psychological and logical
certainty. On the other hand, there seem to be people for whom the
feeling of certainty has no such sharp distinctions of kind within it.
The results as to the second problem may be more briefly and more
distinctly given. No subject found any evidence that the number of the
grades of certainty which he could distinguish would be limited by
anything except his keenness in introspection, although in the simple
tests given for the experiment, four was the greatest number of grades
distinguished at any one time. Two of the subjects (B and F), who set
the highest grade of certainty apart from the judgments made with
lesser confidence, said that there might be degrees within that higher
grade as well as among the "uncertainties." There was no evidence that
logical certainty differed from psychological in respect of the grades
to be found within it, and some evidence that they were alike in that
respect, although logical certainty was less carefully examined. It
would seem, then, that our second problem is to be answered thus: There
are degrees present in some if not in all kinds of certainty, and there
is no evidence that the number of these degrees is limited.
It was not generally found possible to analyze the feeling of certainty
into a sum of elements, although certain characteristics seemed to be
persistent in it. Here again there is marked individual variation. The
general test used for the difference in degrees of confidence was the
question "On which judgment would you risk more?" This satisfied every
one as a true criterion for such distinctions, but subjects H and C
said that for them the feeling of certainty had a much more distinct
relation with the past than with the future. Perhaps for that reason,
subject H proposed the test "Which judgment could I be converted from
most easily and simply?" The distinctness of an image had something to
do with the feeling of certainty for subject C. Beyond this, he could
not characterize his feeling. Neither was he sure that the degree of
certainty varied exactly with the degree of distinctness. Subject D
found that all objects about which he made judgments of which he was
certain were present to his mind in the form of distinct images; but
did not feel that that covered all that was to be said of the feeling
of certainty. The number of images present, as visual and auditory,
seemed to increase the degree of certainty for him. Subject F could
give no characterization of his feeling of psychological certainty. His
feeling of logical certainty seemed to spring largely from a feeling of
consistency between the present experience and his past experiences.
With subjects A, B, and K the vividness of an image was a strong
determining factor in the degree of certainty felt in any judgment, but
again was not the whole story. Something they could not characterize
was also present for A and B, and, as well, a feeling of more or less
perfect congruence between an image and the general character of a
field. (This introspection developed in connection with the visual
experiments.) Among these eight subjects we have but one (K) who is
satisfied with reducing certainty to a set of elements.
To my mind the most valuable thing to be gained from this division
of the experiment is the suggestion that there are definite types
of certainty, and that people may be classified by these. There are
obviously marked individual variations as to the characteristics of
this feeling. I should expect from my work this year that two pretty
distinct types could be discovered. For one of these, certainty in a
judgment as to an experience would rest very largely upon the vividness
of an image; for the other, upon the congruence of an image with other
previously accepted images, that is, the absence of conflicting images
when the experience judged about is imagined part of a wide setting
of past experiences. I should not expect either element of certainty
to appear absolutely, without the other form. For many people one
element would predominate in certain fields, as in judgments regarding
sense-experiences, the other in the more logical fields. For some,
again, perhaps, the two would be nearly coördinate in every experience
of certainty. But for some subjects, as, I think, for subject K here,
the vividness of the image would always be the determining factor,
while for others, as for subject H, congruence with wider experience
would be much more important. This classification of subjects according
to their types of certainty might develop into a much more complicated
affair. The experiments described here have gone no farther than
to suggest lines along which it may perhaps run. There may be other
elements equally important with these two. A set of experiments
consisting of attempts to raise uncertainty to certainty would bring
out the essentials of certainty from a new point of view, and would,
perhaps, test this theory that individuals may be classified according
to the types of their certainty, in the most satisfactory manner.
II. THE EFFECT OF VOLUNTARILY ATTENDING TO CERTAIN ASPECTS OF A TOTAL
EXPERIENCE UPON CERTAINTY IN THE JUDGMENTS AS TO THE CONSTITUTION
OF THAT TOTAL EXPERIENCE.
As has been said, judgments as to the elements of visual fields were
tested for this part of the experiment. The apparatus used was the
following: The subject was seated before a low table which was shut
from his view by curtains and boards. He looked down upon the table
through an opening into which a camera-shutter had been fitted. This
shutter was set for a two seconds' exposure and opened by means of a
bulb which the subject held in his hand. Just before each exposure,
the experimenter placed a card on the table below the camera-shutter.
The set of twenty cards so used were alike in that the background for
all was gray and the objects pasted upon the cards black letters and
numerals and simple geometrical figures of chosen shapes and colors.
No color was repeated on any one card. The cards were different in the
choice and arrangement and in the number of objects used. The number of
letters and numerals on any one card varied from two to five, the total
number of objects from eight to twelve. A white card on which were
pasted dark gray samples of each of the eleven shapes used, together
with a card of the background of those shown in the experiment on which
were pasted torn scraps of the eleven colored papers used, was always
in sight at the subject's side. A camera-shutter, experiment cards and
sample cards thus made up the apparatus.
The presence of the sample cards needs explanation. They stood for
the attempt to place the colors and shapes on the same footing as the
letters and numerals. Their presence, in the first place, and, as well,
the limitation of the number of letters and numerals used, did away
somewhat with the advantage that letters and numerals naturally have
for ease of naming. In the second place, the use of a new color for the
sample shapes and the absence of definite shape in the sample colors
helped to keep the colors and shapes more distinct. With the help of
these cards it seemed that we could properly hold we had a a visual
field of three very nearly coördinate sets of elements.
The experiment as a whole, as conducted, had four phases which, except
for one particular, were exactly alike. The subject's attention was
directed toward a certain aspect of the field by (1) asking him before
each exposure (or less often if that appeared unnecessary) to attend
to that aspect, as, for instance, to the colors present, and (2)
taking care that any questions asked should tend to strengthen rather
than counteract the effect of that voluntary attention. At a given
signal the subject pressed the bulb which opened the shutter. On the
closing of the shutter he reported what he had seen. This report the
experimenter recorded almost in the subject's own words, and later
tabulated in the manner described presently. So far as giving the
objects present was concerned, the report was given almost invariably
without any suggestion by the experimenter as to the possibilities of
the field. To help the subject distinguish the amount of confidence
which he had in the judgments that such or such objects were present,
however, the experimenter frequently asked such questions as, "Would
you risk more on the fact that there was a square in the field than
on the fact there was something blue there?" In giving his report the
subject pointed to the sample cards or spoke, as he might wish. He was
also allowed to be as leisurely or as rapid in giving it as he chose.
A half-minute interval elapsed between the end of each report and
the signal that the shutter be opened again. No persistent effort to
distract the subject's attention was made then, though conversation on
other topics was frequently carried on. The point in which the phases
of the experiment differed was in the aspect of the field to which
attention was called. In the first, this was the shapes, in the second,
the colors, in the third, the letters and numerals, and in the fourth,
the number of objects in the field. Fixing the attention upon the
number of objects in the field served to distribute it equally over all
the groups represented there. The general method of calling attention
to the different aspects and of learning the effect of such attention
was, as has just been said, the same for all phases.
As a preliminary to making up the tables here given, from which we are
to answer our problems, the experimenter first tabulated the reports
of the subjects in such a way as to show how many judgments (correct
and incorrect) of each of the four grades of certainty adopted for
this division of the experiment were made by each subject on each card
for each group on the card (shape, color, or letter or numeral). From
these tabulations the tables that follow were in turn compiled.
The number of grades of certainty adopted for this division of the
experiment is obviously decidedly arbitrary. Grades of certainty there
surely are. The introspection of the subjects develops that clearly,
as has been stated. But there is no reason in the conditions of the
case for holding to the number four, as is done here. In giving the
results for which the experiment was undertaken, I shall, indeed,
confine myself to studying the range of the judgments made with as high
a grade of confidence as the subject believed he should ever have. This
is called certainty (1) or certainty proper. But for the tributary
discussion on the relation of certainty and error, the consideration
of three other grades used in the report and early tabulation, is also
introduced. This lowest grade (4) might better be named "as complete
uncertainty as will admit of one's making any judgment." The other two
are intermediate. It was at first intended to give the results with
regard to the effect of voluntary attention upon the place of these
grades of certainty, also, but such a discussion has been omitted
because it promised to add very little more than complexity to the
report. Besides this, the classification into these lower grades is
too purely approximate to make the distinction there of great value.
For judgments of the order certainty (1) we have the test, "Are you
as certain of this as you can imagine being in an experiment of this
sort?" but no such test for the other grades could be found. Yet,
though he tended to omit judgments of the lower grades of certainty,
each subject seemed to find four grades a convenient number to use in
giving his report.
The number of experiment cards used varied with the subjects. E had so
clear a memory of the cards that after as many as ten had been shown,
he found difficulty in distinguishing his memory of the one which he
had just seen from that of others seen earlier. Ten cards only were
used in his case. A, B, D, and F showed signs of fatigue after fifteen
cards which made the value of any later results questionable. C and K
showed no such signs of fatigue. The same set of cards was, of course,
shown any one subject for all four phases of the experiment. Those
omitted were the last ten or the last five of the complete set as the
case might be.
TABLE I
% of cards where % of cards where % of cards where % of cards where
certainty (1) certainty (1) certainty (1) certainty (1) is
appears in the appears elsewhere in attended-to stronger outside
attended-to than in the group only. than within the
group. attended-to attended-to
group. group.
A 91% 49% 49% 13.3%
B 97 91 83 28
C 95 67 30 16.6
D 93.3 69 24.5 11.2
E 96.6 83.3 13.3 26.6
F 88.8 30 53.3 8.3
H 91.6 70 26.6 10
Table I answers the first part of our first problem promptly. Every
subject gave judgments of the order certainty (1) about groups other
than that attended to, in the case of a very considerable percentage of
the cards. True, again in the case of a considerable (though generally
smaller) percentage of those cards, each subject confined his judgments
to the group attended to. The fact of individual variation stands out
again here; and, moreover, the conclusions drawn should be qualified
slightly because of the fact that it was often possible for the
subjects to give all the letters and numerals on the cards, and still
have, as it were, some attention left over for the other, supposedly
non-attended-to groups. Such reaching beyond the properly attended-to
group never seemed to be possible with either shapes or colors. Aside
from this, however, it is clear that judgments of the highest grade of
certainty were by no means limited to the group attended to.
This same table answers, also, the second part of the problem. Each
subject found certainty of the highest grade sometimes stronger outside
than within the group which held his attention. It is, of course,
practically impossible to make absolutely certain that each subject's
attention was invariably held to the group toward which it was turned,
yet the percentage where certainty was stronger outside than within
such groups seems large enough, in some cases, at least, as with
subjects A, B, and H, to warrant our answering this second part of the
problem in the negative. I should feel, however, that this was answered
less definitely than was the first part of the problem. We may say,
then, that the judgments made with the highest degree of certainty
about a visual field will not be confined to the group attended to, and
that we have strong evidence pointing toward the belief that we cannot
expect there will invariably be more of such judgments within the group
attended to than outside it.
TABLE II
# 1: % of judgments of certainty
(1) given to each group in phase
I (or when shapes were attended to).
# 2: % of judgments of certainty
(1) given to each group in phase
II (or when colors were attended to).
# 3: % of judgments of certainty
(1) given to each group in phase
III (or when letters and numerals
were attended to).
# 4: % of judgments of certainty
(1) given to each group in phase
IV (or when the attention was
equally distributed over all the
groups).
1 2 3 4
Subject Shapes (a) 94% 38% 18% 31%
A Colors (b) 5 61 20 59
Letters and (c)
Numerals 0 0 61 9
Subject (a) 48 39 21 33
B (b) 43 60 29 38
(c) 8 0 51 28
Subject (a) 88 15 26 34
C (b) 8 77 28 8
(c) 5 7 47 58
Subject (a) 60 13 11 40
D (b) 19 67 2 37
(c) 19 19 86 23
Subject (a) 51 15 0 37
E (b) 22 56 8 29
(c) 26 28 91 34
Subject (a) 66 12 0 50
F (b) 14 77 0 27
(c) 19 10 100 23
Subject (a) 43 21 7 24
H (b) 29 52 4 19
(c) 27 26 88 57
The most interesting part of this division of the experiment is brought
out in Table II in answer to the problem, "Will the place of voluntary
attention materially alter the distribution of judgments of the
highest order of certainty among the given groups?" In every case the
percentage is affected, in most cases, greatly affected. Take the case
of subject A, for instance. Although, when his attention is equally
distributed over the field 59% of the judgments we consider were of
colors, yet when his attention was fixed on shapes and on letters and
numerals this fell to 5% and 20% respectively. When it was fixed on
colors, it rose, indeed, only to 61%. When, however, subject A fixed
his attention upon the letters and numerals, 61% of the judgments
were confined to the group attended to,--the same percentage as when
colors were the attended-to group,--although, when his attention was
distributed over the whole field, the percentage of these judgments
about the group of letters and numerals was 9% only. When shapes were
attended to, the 31% of the fourth phase of the experiment rose to
94%,--almost all of the judgments of the highest grade of certainty
that were given were judgments about shapes. A similar study of the
results given in the table can be made for the other subjects. The
degree of change varies with the subject and with the group, but
always there is some change, and often a very marked one. In this
experiment the place of voluntary attention clearly did alter, and
alter materially, the proportion of judgments of the highest order of
certainty made about any given group.
That, indeed, would seem to me to be the answer of this experiment to
the question as to the effect of voluntary attention upon certainty
in one's judgments. Every subject showed a tendency to have more
certainty in those judgments which were made about that aspect of the
field toward which his attention was directed. Yet, on the other hand,
this was a tendency only, one not strong enough to make it possible to
predict beforehand exactly how great a proportion of the judgments in
which he had the highest degree of confidence would be limited to that
field, or even to be sure in every case that the greater proportion of
those judgments would be so limited. The place of voluntary attention
has an influence upon the subject-matter of the judgments made with
certainty about a visual field just seen, but an influence of varying
and uncertain strength.
TABLE III
1 = % of mistakes in judgments of certainty (1).
2 = % of mistakes in judgments of certainty (2).
3 = % of mistakes in judgments of certainty (3).
4 = % of mistakes in judgments of certainty (4).
x = no judgments of that kind given.
1 2 3 4
Subject A (in giving shapes) (a) 7% 10% 0% 100%
(in giving colors) (b) 2 14 23 0
(in giving letters
and numerals) (c) 0 0 x x
Subject B (a) 2 10 10 0
(b) 3 6 20 25
(c) 4 50 0 x
Subject C (a) 1 8 10 0
(b) 4 14 14 0
(c) 1 0 16 0
Subject D (a) 3 4 0 16
(b) 1 6 0 0
(c) 5 0 0 0
Subject E (a) 2 10 25 50
(b) 1 33 40 0
(c) 0 0 0 0
Subject F (a) 1 25 7 25
(b) 4 15 29 26
(c) 3 0 0 x
Subject H (a) 3 6 5 0
(b) 6 2 15 15
(c) 4 0 0 20
TABLE IV
Label 1: General % of mistakes
in judgments
of certainty (1).
Label 2: % of mistakes in judgments
of certainty (1) about
attended-to groups.
Label 3: General % of mistakes
in judgments
not of certainty (1).
Label 4: % of mistakes in
judgments not of
certainty (1) about
attended-to groups.
1 2 3 4
Subject A 4% 1% 17% 27%
Subject B 3 2 10 7
Subject C 2 3 9 24
Subject D 3 4 4 0
Subject E 1 2 22 34
Subject F 3 1 21 23
Subject H 4 6 6 10
The results given in Tables III and IV were compiled from the same
records as those of the two Tables just discussed. They give the
relation of error to certainty and to attention, as that relation was
developed in this experiment. No experiments were conducted with these
relations of error primarily in view, but the results developed in
connection with the problem of the effect of attention upon certainty
in one's judgments.
Both Tables show again marked individual variation. They suggest to me,
in the first place, a further line of investigation in the same field
and for the same purpose as those investigations which L. William Stern
outlines in an article[101] entitled _Aussagestudium_. This further
line is the testing subjects to learn the probable relative correctness
of the judgments made with different degrees of confidence. Although a
comparison of the first and third columns in Table IV makes it clear
that the proportion of mistakes for the highest grade of confidence is
lower than for the other grades taken together, there is a very marked
difference among the subjects to be noticed. The difference in the two
percentages is, for instance, very slight in the cases of D and H, and
very great in the case of E. It is interesting to notice with regard
to E that while he has the lowest percentage of mistakes for certainty
(1), he has the highest percentage for the group of certainties (2),
(3), and (4). In the more detailed percentages given in Table III we
see further that in certain fields and sometimes in all fields (as
with subject C) judgments made with the lowest grade of confidence
were invariably correct. Such Tables might be of help in a case where
the evidence of eye-witnesses conflicted. We might perhaps learn that
witness N made a large proportion of mistakes where he was absolutely
certain, whereas witness M was seldom wrong in judgments in which he
had a low degree of confidence. Even when the probity of both was
unquestioned, we should not then assume that N was more probably right
because he had so much more confidence in his judgments than M had in
his. A much longer and more comprehensive set of experiments would be
necessary before we could feel that we had at hand a table from which
to work in this way.
The question of the effect of voluntary attention upon error, for
answering which Table IV was compiled, brings out again the marked
individual variation among these seven subjects which has shown itself
in practically all parts of the experiment. Some effect seems to
have been produced always, but this was sometimes to give a larger
percentage of mistakes in the attended-to groups and sometimes a
smaller. With A, B, and F the percentage of mistakes in certainty (1)
was lower for the groups attended to than for the total number of
judgments of that order. Only with subject B, however, is this true
of the group of lower grades of certainties also. On the other hand,
with subjects C, D, E, and H the percentage is greater for certainty
(1) in the groups attended to than for certainty (1) in the collection
of all the judgments of certainty (1) taken together. Here, too, in
the case of subject D, the results with regard to the lower grades of
certainty reverse those for certainty (1). Thus all four possibilities
as to the kind of influence of voluntary attention upon certainty
appear. We cannot say that the place of voluntary attention will tend
to affect the percentage of error in any given way. We can only say
that apparently it made some difference with each subject. It might be
found by further experimenting that the character of this difference
is associated with some other characteristic of either attention or
the feeling of certainty, as, for instance, with the ease with which
attention is held to the chosen field or with the type of the subject's
certainty.
Like all experiments, these open up further questions quite as much
as they answer those toward which they are aimed. To repeat something
of what has already been said, I feel that what it has established is
(1) that introspection develops distinct grades of certainty in the
case of every individual, (2) that the particular characteristics of
the feeling of certainty vary markedly among individuals; (3) that the
feelings of certainty associated with the different senses are not, as
feelings of certainty, to be distinguished from each other; (4) that
the judgments of the highest degree of certainty which are made about
the constitution of any visual field just seen will not be confined to
the group in that field toward which the attention is directed; and
(5) that such fixing of the attention will, nevertheless, materially
alter the subject-matter of such judgments of greatest certainty. The
rather vague statement that the percentage of error is not surely less
with the judgments of a group because attention is fixed on that group
may perhaps be added as a sixth conclusion. The most interesting and
promising of the problems which the experiments seem to me to raise
are: (1) the problem, are there such definite types of the feeling
of certainty that people may be classified according to their types,
and, if so, what are the types and what their relation to other
psychological characteristics of the individual? (2) the problem, what
will be the result of careful and trained introspection as to the
relation of so-called logical and psychological certainty and in what
fields do these appear for different individuals? (3) the problem,
how can a test for grading the probable percentage of error in the
judgments of different grades of certainty made by any one person be
constructed? and (4) the problem, how are such facts as those given
in Table IV to be connected with the effort required for attention,
the type of certainty of each subject, etc.? Other problems could, of
course, be suggested, but these, I feel, mark the steps that naturally
follow the experiments described here.
[Illustration: PLATE VIII.]
FOOTNOTE:
[Footnote 101: Stern: Beiträge zur Psychologie der Aussage, vol. 1, p.
46, 1904.]
INHIBITION AND REËNFORCEMENT
BY LOUIS A. TURLEY
Experiments made by Ranschburg[102] on the significance of similars
in the process of learning and remembering determined that when
duplicates occur within a series of stimuli, one either totally or
very greatly inhibits the perception of the other according as they
are contiguous or are separated by other stimuli. Dr. Yerkes,[103]
in testing the effect of auditory on visual and tactual stimuli in
frogs, found that if the auditory stimulus preceded another stimulus
by various time-intervals, it had an alternating reënforcing and
inhibitory effect. A similar result was obtained by Hofbauer[104] in
a similar experiment on human subjects. The question now arises,--if
the time-interval were increased between a stimulus and its duplicate
in a series would the inhibitory effect gradually approach zero where
all effect of the preceding stimulus ceased, to which Ranschburg's
experiments point, or would the inhibitory effect be alternated with
one of reënforcement as the experiments of Dr. Yerkes and Hofbauer
would indicate? This problem--the effect of a stimulus on its duplicate
in a succeeding series of stimuli--is the problem I undertook to solve.
For this purpose, it was necessary to introduce exactly determinable
time-intervals between the stimulus and its duplicate. Therefore I
used--as Miss Kleinknecht[105] did for other purposes--a stroboscopic
arrangement instead of simultaneous presentation which Ranschburg used.
My apparatus was Professor Münsterberg's Stereoscope without Prisms or
Lenses, a description and photograph of which was published in the
article by that title in Psychological Review, vol. 1; or rather, I
used Professor Münsterberg's attachment to Kohl's centrifugal machine,
since my apparatus was not identical, except in principle, with the
"Stereoscope." The "attachment" consists of two black discs about
thirty inches in diameter, mounted about eight inches apart on the
disc-shaft of the centrifugal machine. The back disc is of wood. The
outer three inches of its face is furnished with thirty-six equidistant
strips of black tin, one end of each of which is bent so as to grip a
groove in the rim of the disc, and the other end of each is gripped
by tiny thumb-screws so that the strips lie along radii of the face
of the disc. The front disc, slightly smaller than the back disc, is
of pasteboard. Between the two discs a stationary black screen with
a short narrow slit was placed so that the slit revealed only the
strip on the horizontal radius of the back disc. Behind this screen an
eight-candle-power electric light was placed to illuminate the back
disc,--as the experiment was carried on in a darkened room. By moving
this light I was enabled to vary the intensity of illumination to
offset the skill of the observer.
For my purpose, a small white figure--one of the ten characters of
the Arabic notation--was stuck on about the middle of each of the tin
strips on the back disc; and radial slits, one millimetre wide and an
inch long, were cut from one sixth of the circumference of the front
disc so as to come opposite six of the strips on the back disc. Similar
radial slits were cut at various intervals from the remaining five
sixths of the circumference of the front disc. These were covered by
small pieces of cardboard fastened to niagara clips, thus making them
readily removeable. By this means any desired figure could be exposed
in the same revolution with the series exposed by the six slits above
mentioned.
The thirty-six strips were divided into six series of six each,
indicated by chalk-marks on the disc. Each of the series was often
changed in whole or in part by shifting and interchanging the strips.
The figure on which the effect of a preceding stimulus was tested
occupied the fourth place in the series, since this is the place where
the greatest number of errors occur, as is shown by the experiments
of Ranschburg and previous investigators in the Harvard Laboratory.
In my experiment, 4, 5, 6, 7, 8, and 9 occupied the fourth place
in the 1st, 2d, 3d, 4th, 5th, and 6th series respectively, and the
effect of a preceding stimulus was tried on each of these figures
for each time-interval. The preceding stimulus in each case was a
duplicate of the fourth member of a series, and was a member of some
other series. Thus the fourth member of each series was at all times
fixed and constant while the preceding stimulus occupied successive
progressive positions round the disc. The other members of each series
were chosen at random, care being taken that the fourth figure was not
duplicated within its series, since it would then have taken part in
inhibition within the series.
[Illustration: PLATE IX.]
By adjusting the front disc, I exposed any one of the series desired,
and by removing the cardboard blind from one of the suggestion slits, I
gave a stimulus at the desired time-interval in advance of the fourth
member of the series. The first interval I used was 1.11 sec. as Miss
Kleinknecht had tried intervals up to 1 sec. My second interval was
1.39 sec., the third 1.8 sec., and then every .277 sec. up to 4.3 sec.
In performing the experiment I exposed alternately a series without
and a series with a preceding stimulus--taking from the observer three
reports of each--until the six series had been seen. I then repeated
this, exposing with a preceding stimulus those series that had been
exposed without preceding stimulus, and without preceding stimulus
those series that had been exposed with a preceding stimulus in the
first instance. In this way I equalized and minimized the effects of
novelty and memory.
At 1.11 sec. there was considerable inhibition in five out of six
cases. In the sixth case there was slight reënforcement at this
interval. With an interval of 1.39 sec., with one exception,--not the
exception above mentioned,--there was a stronger inhibition than at
1.11 sec. Inhibition in all cases began to decrease from 1.39 sec.
until it ceased at about 1.8 sec. The preceding stimulus then had a
reënforcing effect which reached a maximum in four cases at 2.08 sec.,
one at 2.36 sec., and one at 2.64 sec. Then, in all cases, there was
a decrease of the reënforcing effect which in three cases amounted to
inhibition. In the other three cases, the preceding stimulus had no
inhibitory effect for an interval greater than 1.8 sec. For one of
these, Fig. 5, the preceding stimulus had a reënforcing effect for
all the intervals beyond 1.8 sec. The second trough in the wave or
interval of maximum inhibition was at either 2.64 sec. or 2.92 sec.,
except for the person for whom there was constant reënforcement beyond
1.8 sec., in which case the first interval of least reënforcement or
second trough was at 3.19 sec. This was the second interval of greatest
enhancement, or second crest, for four of the others. Then followed a
third point of no effect or inhibition, which was 3.75 sec. or 4.03
sec. For the person for whom the preceding stimulus had least enhancing
effect at 3.19 sec., the second interval of greatest reënforcement
coincided with the interval of greatest inhibition for the majority
of the other observers. For four of the six observers, the third
interval of greatest reënforcement was 4.3 sec. In this, the observer
agreed for whom the last interval of greatest reënforcement was 3.75
sec. Thus while, for this observer, the first two points of greatest
reënforcement were separated by an interval of 1.11 sec., the second
and third points were separated by an interval of only .55 sec. This
same thing occurred in the records of two other observers, for one at
this point, and for the other at another point. Of the two dissenters
from the opinion of the majority that the third crest was at 4.3 sec.,
one was an erratic observer; and for the other, there was a slight
reënforcement at 4.03 sec. and no effect at all at 4.3 sec.
Fig. 1 represents the average of the records of the six observers.
The curve is based on the difference between the number of times the
fourth members of the series were seen with and without preceding
stimulus. The base-line represents the number of times the figure was
seen without preceding stimulus, taken each day as the normal for that
day. Figures above the base-line represent the greater, and those below
the line, the less number of times the figure was seen with preceding
stimulus, or reënforcement and inhibition, respectively. The first two
points are the average of fifty-four observations; each point beyond
the second is the average of 108 observations. Figs. 2, 3, 4, and 5
represent individual records constructed as Fig. 1, each point being
the average of eighteen observations.
The curve in Fig. 1 is somewhat misleading in showing points of maximum
reënforcement at 3.19 sec., 3.75 sec., and 4.3 sec. In no individual
case was this true. The reason for the crest at 3.75 sec., or at least
for its height, is that in two cases reënforcement was considerable
at this interval, and there was little inhibition to offset this in
the general average. At 3.19 sec., which was the second interval of
greatest reënforcement, for four out of the six observers, owing to
practice, the reënforcement was not great (Fig. 4), but in no case was
there inhibition at this point. Thus for the lack of strong positive
effect at 3.19 sec. and the lack of strong negative effect at 3.75
sec., the two crests are the same height, while the first represents
the maximum effect for four and the second for two observers.
From these results, taking everything into consideration, my
conclusions are:
(1) If a stimulus precedes at various time-intervals its duplicate
in a series of stimuli, it will alternately inhibit and reënforce the
perceiving of the duplicate stimulus.
(2) Within 4.5 sec. there are at least three points each of maximum
inhibition and maximum reënforcement.
(3) The points of maximum inhibition and likewise those of maximum
reënforcement are separated by intervals of from .55 sec. to 1.2
sec.--more often by one of the two extremes than by any mean.
(4) Up to 4.5 sec., as the time-interval increases, the maximum
inhibition generally decreases, while the maximum enhancement
correspondingly increases.
What the limit of this periodic effect is, I cannot as yet say, as up
to the present I have not used time-intervals beyond 4.3 sec. But from
the intensity of the effect at this interval, I do not expect the limit
to be within several seconds.
FOOTNOTES:
[Footnote 102: Ranschburg: Ueber die Bedeutung der Ähnlichkeit beim
Erlernen, Behalten und bei der Reproduction, Journal der Psychologie
und Neurologie, Bd. 5, p. 94.]
[Footnote 103: Dr. R. M. Yerkes: The Sense of Hearing in Frogs, Journal
of Comparative Neurology and Psychology, vol. 15, no. 4, 1905; also
this vol. Harvard Psychological Studies.]
[Footnote 104: L. Hofbauer: Interferenz zwischen verschiedenen Impulsen
im Central-nervensystem, Pflügers Archives, Bd. 68, p. 564, 1897.]
[Footnote 105: Kleinknecht: This volume.]
THE INTERFERENCE OF OPTICAL STIMULI
BY H. KLEINKNECHT
The purpose of this investigation is the determination of the location,
extent, nature, and cause of the interference of optical stimuli.
Ranschburg[106] studied the phenomena carefully in using optical
stimuli which were spread over the retinal field, for instance, a
series of letters or figures one beside the other. But if we are
to experiment on the inhibitory influence of a certain qualitative
impression, we must try to eliminate the local difference; the letters
or figures ought to be seen at the same spot.
This became possible by a stroboscopic arrangement, consisting of two
parallel circular discs one foot apart on the same axis, whose motion
was controlled by an electric current.