Chapter XIII: Part I (1)

The object of this paper is to discover some of the sources of our pleasure in repeated space forms, and the laws which govern this repetition. The repetition of an object, and its regular recurrence subject to certain possible variations, is one of the basal principles of art, and of architecture in particular.

It is necessary at the outset to define our use of the word _repetition_ more exactly, for there are obviously different meanings of the word, which may lead to confusion.

1. The term repetition may be applied to the existence of any two objects similar to each other, whether they are near together or widely sundered. Our pleasure in such a repetition would be merely that of re-seeing and recognizing the two as counterparts of each other. This kind of repetition I call _conceptual_, for it requires only that the memory-picture of the object be held in mind and the two recognized as similar when met again. This is not the kind of repetition which I have in mind, and I shall never use the word in this sense during the discussion.

2. In any one work of art there may be some feature repeated, some motif which is taken up and carried out in different ways throughout the whole, and these features we recognize as having an orderly relation to one another in the unity. This might be termed repetition of _content_, and be applied to the recurrence of some type of decoration over a window or a peculiar arch taken up in various ways throughout a cathedral. I do not use the word in this sense, but limit it still further.

3. By _repetition_ is meant during this discussion the regular recurrence of an object, and an equally regular recurrence of intervals. The repeated object must come at uniform intervals, and this restricts us to the consideration of that repetition alone which consists of recurrence at regular intervals of some object more or less beautiful in itself, and the description of the nature of our æsthetic feeling in experiencing such a series.

Although this discussion is divided into the two divisions of _experiments_ and _analysis_ of architectural examples, and the experiments are described first, the investigation was not carried out separately in this order. The two went along together, the art-analysis suggesting experiments, and the experiments in turn throwing light on the analysis. The two parts of the discussion are kept separate merely for the convenience of the reader, and in the experimental discussion all allusions to the art-illustrations are excluded in order to avoid confusion. In reality the two went hand in hand, but the connection between the experiments and art-analysis will be reserved for the latter half of the paper.

The experiments were begun in the following manner: In a velvet screen about a foot high was cut a window 460 mm. by 35 mm. in size. Behind the window was a metre measure and a rod from which hung small strips of cardboard 10 mm. wide. First two, three, and four strips were hung behind the window, and the subjects were required to arrange them at the intervals where they preferred to see them repeated. The results were uniform in certain particulars and very suggestive. In their arrangements of two, three and four strips, the subjects were guided by considerations of symmetry or proportion. They insisted that although they knew that the strips were repeated, they did not feel the repetition, but the strips seemed like parts of some larger unity to be arranged with reference to the unity of the whole. With the addition of the fifth strip came a difference in their apperception. Instead of the strips seeming parts of a whole including figure they seemed like repeated units.

FAVORITE ARRANGEMENTS

2 _strips_ 3 _strips_ 4 _strips_ 5 _strips_

J. 30 mms. 4 mms. { mid. sp. = 25 any symmetrical
{ ends = 10 arrangement
better than
equality

S. 170 12 { mid. sp. = 15 {mid. sp. = 40
{ ends = 12 {ends = 30

U. 40 20 30 35

R. 30 130 { mid. sp. = 30
{ ends = 10 10

L. 23 40 70 70

W. 40 10 30 30

V. 20 10 { mid. sp. = 100
{ ends = 60 15

It will be seen, from the table, that with two exceptions they preferred five strips equally distant from one another, while with four strips, four subjects had preferred a symmetrical arrangement. These gave as their reason that with five strips the latter appeared more definitely to be repetitions of one another, while the four strips seemed more like parts of a whole which required symmetry in its arrangement. Moreover the two subjects who preferred five strips in symmetrical arrangement instead of at equal distances affirmed that a distinct feeling of repetition came with five strips that had not been felt before, only they did not enjoy this feeling of repetition as well as one of symmetry. After having seen the five strips, some subjects could feel the repetition with four strips, but none with three. The question naturally arose, what is this _feeling_ of repetition which makes one say that four or five repeated objects deserve the name, while three or less are regarded in a different light? The analogy between the apperception of this visual repetition and auditory rhythm seemed so strong as to deserve attention.

In auditory rhythm it is necessary that there be recurrence of more than two elements; they must come at a certain rate and within a certain temporal space to seem connected with each other, and they may be subjectively grouped in different ways. The apperception of both kinds of repetition had so many analogies as to suggest that some of the factors in both experiences were identical.

To focus the problem I took a definite thesis in regard to it. Our apperception of repeated space forms is due to the rhythm of our own motor adjustments which are excited in face of repetition, harmoniously if they accord with certain rhythmic laws in us, inharmoniously if they do not. It was then necessary to find what facts would support such a thesis, to see if in reality such facts could be marshalled, and if the explanation and support they offered was conclusive enough to make it needless to look farther.

It would seem, if our pleasure in repetition depended on temporal motor responses in us, that if the amount of time normally taken to traverse a repeated series were shortened, or if the eyes were fixed and not allowed to move over the field at all, our enjoyment would cease altogether, or at least be seriously diminished. If we found it impossible to enjoy the series except when seen for a certain time, long enough for the eyes to go over it in the rhythm peculiar to each subject, we should then conclude that our enjoyment did depend, to some extent, on such temporal rhythm.

I experimented on this question with nine subjects, and the results brought out different ways of apperceiving repetition, which divided the observers into two rather well-marked types.

The apparatus was of the simplest, consisting of white silk strings hung on a wire against a black background across one side of the room. The strings were attached to the wire by little hooks, which enabled one to change their position easily, while a cloth hid the weights on the ends of the strings, so that nothing but the vertical white lines were visible.

Fifty strings (50 mm. apart) were hung before the subjects, and they were asked to survey the field and give a signal as soon as the experience became pleasant. Then having found the average length of time for each subject to enjoy these simple repetitions, a shorter period was given when they were to shut their eyes at a given signal, and see if in that shortened time they were still able to enjoy the series. Next they fixated the eyes and kept the whole body rigid, to see if pleasure was still possible when all outward motor response was checked, so far as possible.

The results of this experiment were very suggestive. Of nine subjects, all felt pleasure when allowed to move the eyes over the series at random; with eyes fixed, five felt their pleasure much altered in its quality as well as lessened, while with one it was altogether destroyed. With four, however, although there was considerable alteration in the quality of the pleasure, its amount was increased rather than lessened.

B. (1) Average time necessary to enjoy the series: 4.7 seconds.
(2) Three-second exposure. No pleasure, needs more time during
the movement.
(3) Eyes fixed: 4 secs. = Av. time necessary to enjoy it. Lines
bunch toward centre and fade away at sides, giving a kind of
unity, but he feels constraint.

R. (1) Av. time: 4.3. Sees them in pairs.
(2) Two-sec. exposure. Very faint pleasure; feels that only a part
is perceived.
(3) Eyes fixed: 4.3. One pair fixated, the others fade away, making
a kind of figure. Pleasure faint and constrained.

L. (1) Av. time: 2.1.
(2) 1-sec. exposure. Pleasure faint and incomplete. He feels the
pleasure comes from memory of the previous experience.
(3) Eyes fixed: 2.2. Great effort to find any pleasure. It consists
mainly in seeing a few strings, and feeling there are others,
even though they are not distinguished.

V. (1) Av. time: 2.2. Sees them in pairs.
(2) 1.5-sec. exposure. Enjoys the experience in memory after the
eyes are shut again.
(3) Eyes fixed: 1.9. Still sees them in pairs, but cannot see enough
of them, hence they are less pleasant.

W. (1) Av. time: 4.3.
(2) 2-sec. exposure. Not enough time to feel any relation between
the strings, most of the pleasure supplied by the memory.
(3) Eyes fixed: 5.3. Pleasure is very faint, and consists in having
the strings appear to converge to a central point, and fade at
the sides.

J. (1) Av. time: 2.3. Sees them in pairs.
(2) 1.5 exposure. Less pleasant.
(3) Eyes fixed: 2.7. Series seems more like a unity and he enjoys
it more, since no time is spent in exploring the field, but it
is one unified experience.

U. (1) Av. time: 28. Only enjoys it by ignoring all except those in
the centre--does not want so many.
(3) Eyes fixed: 18 secs. Enjoys it when eye lights on one string,
so that the others can fade away equally at the sides, in one
figure.

S. (1) Av. time: 5.
(2) 3-sec. exposure. Less pleasant.
(3) Eyes fixed: 8.8. Pleasure consists in converging of lines toward
central point. It appears like one figure and is more intense
than (1).

H. (1) Av. time: 9. Sees them in pairs.
(2) 1 sec. Just as pleasant as before.
(3) Eyes fixed: 4.6. Pleasure in unity of whole series with centre
of fixation emphasized. Only felt pleasure anyhow when the eyes
had stopped moving, so now it comes all the sooner.

From these introspections it is obvious that there are two distinct ways of apperceiving repetition: One in which the rhythmic element is pronounced, so that when the time necessary for such a rhythm is shortened, or by fixating the eyes the motor response is hindered, the pleasure in the repetition is either altered or destroyed altogether. The other type takes a repeated series in the sense of a unified presentation and wants it all at once in a symmetrical whole. The rhythmic factor is present in both, as is shown by the fact that the quality of the pleasure was changed in every case when the time of exposure was shortened. But in the latter type of subject the pleasure felt in the presentation of the whole at once, and the feeling of symmetry around a middle point, are more intense than a rhythmic apperception. These two kinds of apperception remain fairly constant throughout the experiments, and for convenience' sake we shall call them spatial and temporal types. With the former, the value of the experience consists especially in having a central fixation-point from which the repeated elements fade away equally on the sides, making a symmetrical whole. With the temporal type, the pleasure is felt by means of the rhythmical passage from one element of the series to the other. In passing from point to point the rest of the field still remains in indirect vision, so to the distinctly temporal a distinctly spatial factor is also present. For this reason the temporal type of apperception is the richer of the two, and a description of it comes more nearly to the essence of repetition as such.

Up to this time, the repeated element had always been a single string. This was varied and the strings hung in pairs (50 mm. wide, 100 mm. between pairs). When the strings had hung at equal distances from each other, six out of the nine subjects had seen them in pairs while enjoying them, and had found such grouping more or less essential to enjoyment. In seven cases the pleasure was increased by this grouping. They expressed their preference in various ways: "Easier to keep track of where we are going." "Can go quicker over field, for repetitions are more well-marked." "Single line is too thin to rest on, this gives broader space for repose." All these introspections instanced the necessity of the rhythm being marked and made plain, so that there should be no confusion of point with point. The two who disliked this grouping were of the spatial type, who found no pleasure in traversing the field, hence too little content in it, in this arrangement, at any one time. Grouping of some kind would seem to faciliate the apperception to a certain class of subjects, while with others the amount and quality of the content of the field is of more consequence.

Since accents are such an important factor of auditory rhythm, the next experiment was to see if the apperception of a series of repeated elements would be facilitated by accenting every other one.

Another string was hung in every other pair thus making it more striking, but here came a difference between the feeling of accent in auditory and visual rhythms. The subjects declared the pairs in which a third line was hung were not intensified alone, as when a greater stress is put on a tone in auditory rhythm, but the pairs were changed qualitatively. The group of three became the repeated element, while the pair was only an alternating figure different from the principal unit. This unanimous testimony brought up a variety of questions. 1. Is any purely _intensive_ accent, without involving qualitative changes, possible in visual repetition? 2. What factor makes us choose one object rather than another as the repeated element? 3. What is the value of the alternating figure in such a series? 4. What is the value of the empty space between repeated figures, and does it have as distinct a value as an alternating figure? 5. Are all the recurring objects and spaces felt as separate repetitions; if so, how many can be carried on at once?

These questions were put to the subjects in regard to the series just described with considerable uniformity of answer.

(1) No such thing as purely stress accent seemed possible. The word, signifying greater intensity without change of quality, did not apply. If one attempted to _intensify_ the repeated object in any way, either hanging another string, thickening the strings, or any similar device, it ceased to be the old unit but became a new one, whose repetition was followed for its own sake, while the weaker one retired into the background, and was not _felt_ as the element repeated in the series.

(2) Any regular change of the element which made it more interesting or caught the attention, fixed it as the chosen unit of the series, whose repetition was followed.

(3) Concerning the exact _value_ of the alternating figure in the series, there was great difficulty in introspection. They all "_knew_ the alternate figure was just as truly repeated as the principal one, but could not feel it so." The three-group formed the unit of the repeated series, and although the pair was clearly part of the experience and distinctly perceived, for some reason it was not felt as repeated in the same way as the other. It was merely an alternate, a filling, which was essential to the other, but which had no significance in itself as a repeated thing. Two subjects were able (if they tried) to carry both repetitions along together, _i. e._, not only feel the three-groups as coming at regular distances from each other, but the pairs as forming another interlacing series. This kind of apperception was very fatiguing, however, and they could not enjoy it. For any pleasure to be derived, the pairs must retire into the background, and attention be fastened on the three-group.

(4) If the alternating figure was to be so subordinate, was there any difference between its significance, and that of an empty space? This was everywhere answered in the same way. The alternating, or minor figure, had a very distinct value, and any irregularity in it was even more irritating than in the principal unit itself. When the space was empty they thought nothing of it, the equality of the interspacing was taken for granted; while if they felt an irregularity in it, it destroyed their pleasure in the whole series. But there was no feeling for the empty space until its regularity had been violated, while there was a distinctly pleasant factor in the minor figure, even though different in quality from the principal element.

In the foregoing experiment the differences between the spatial and temporal type of observer were still strongly marked. The former type invariably grouped the elements (usually with the three-group in the centre and a pair on each side) and they took their pleasure in the symmetry of each figure so made, moving from the centre of one to the centre of the next adjacent. In this method of apperception there was no empty space between repetitions, for the whole group of three figures was taken as the repeated unit. The empty or rest-phase was gotten in moving from the centre of one to the next, in which passage the limiting pair was ignored. One spatial subject, finding the proportions of this artificial grouping poor, got no enjoyment at all.

With the temporal type, the experience was quite different. They moved across the field with the three-group as their stopping-points. These principal elements were what they looked for, and their pleasure seemed to consist in expecting and meeting it. What part the _pair_ played, they had difficulty in analyzing. Some said that while the three-groups occupied most of their attention, they gave a lesser degree to the pair, so that the rhythm of the passage across was marked by heavier and lighter beats. Another found the figure in the alternate space only an obstacle, and felt he was hindered in the passage from unit to unit, the only compensation being, that the "hindrance" came at regular distances. Others felt that two repetitions were actually being carried on at once. By this they meant that the two sets of elements were kept distinct, although objectively combined, but the repetition of the pair was subordinate in interest to that of the three-groups.

I tested the same thing (accents or major elements, and the value of the alternating minor elements) by simply doubling every other string of the series 50 mm. apart. In every case the effect was found poor. It was "confusing," "too much work." They all felt adjusted to the repetition of the double string and then encountered the single one, which hindered them, and by trying to keep both elements going at once they were fatigued. Most of them had a distinct feeling that they wanted to swing from one element to the next, and were baffled by the alternate. In this arrangement, even members of the spatial type who had not been able to get any rhythmic feeling before, felt the movement in the series as if they were going across, although they went (in two cases) in groups instead of single elements. They all, however, felt the single string as an obstacle which hindered their enjoyment, whether the double string or a group was taken as element. This suggested the question: What makes the difference between the minor figure being an enrichment to the experience and being a hindrance? They insisted some rest-period was necessary; some really empty space between the repeated units, and when in place of rest they had more to do, it spoilt the pleasure.

Next, two strings were hung at equal distances between the double strings, and the latter put 100 mm. instead of 50 mm. apart. This was liked better in every case, and the reasons given were much alike. The double string was still the repeated unit, while the two strings between did not _feel_ repeated. In spite of the obvious inconsistency of the statement that they did not _feel_ the alternates to be repeated even when they knew that they were so, just as much as the double string, several subjects made the same remark. V. felt the series as a rhythm, where the double strings were all he was interested in, although he knew he should notice if the others were changed. B. could not detect that they were of any importance, except as he imagined them absent. B. could feel either the double strings or the two strings between them as the major unit, only, whichever one he took, the other retired into obscurity. He felt the minor units in a different way as being repeated together with the majors, but very weakly, and not at all unless he previously considered that he ought to do so. L. said his attention was fastened on the double strings, but it was the "effort or ease with which he passed over the alternates which formed the pleasure." Another temporal subject felt the rhythm as the others did, with more emphasis on the double strings. But the major units seemed the _rest-phase_ in his rhythm, _i. e._, he paused here in observation of the series, although his attention was most active; _vice versa_, the minor units required little attention, but were the active or moving parts of the rhythm. Since they all considered the strings in the alternate space merely as steps or lesser beats on the way to the major element which they sought, and as obstacles rather than otherwise, why did they prefer the space with two strings rather than one? This suggested that some factor in the alternate spaces was important other than simply the amount of resistance to overcome in getting past the two lines. In answer to this they could only say that the two strings in the alternate space formed a pleasanter unity by itself, although, as they went across, they did not think of it in terms of unity.

What, then, is the real rest-phase of the rhythm of alternating repeated objects?

In the beginning of the discussion, when the analogy between visual and auditory rhythm was felt so strongly in a certain type of subject, they had expressed themselves as if the object which they called the unit of the repeated series were the active stimulated part of the experience, while the alternate space was the rest-phase, valuable only as a period of repose or blankness before the object was again encountered. But in this case, although they felt they were putting no attention or emphasis on this space, in reality they were keenly alive to what was hung in it, even preferring more "hindrance" in the way of strings than less, which suggested that the alternate space was of more value than they were conscious of. (Some of this increase in pleasure was of course due to the increased actual distance between the double strings, but some also to the extra string.) The introspection on this question as to which part of the rhythm was actually the rest-phase (if there were any such) was difficult for them all. They felt they spent more _time_ on the major element; that was what they looked for and found pleasure in meeting again.

One said, "The unit is what I look for; as soon as I have it the pleasure ends and I want to move on again. The pleasure does not consist in resting on it after it is found, but in knowing I am going to meet it again, and in doing so." As to the alternate spaces, he could only say he was not consciously interested in them, he took them for granted, but knew he should feel it, if they were changed. His feeling for them was wholly negative. The other temporal subjects agreed essentially with this. The alternate figures had to be passed, but passing them was only of importance as it helped or hindered the perceiving of the major elements. All agreed that any change was noticed and felt irritating at once, although they could not understand how it should, since so little attention was paid them normally. One subject felt the alternating strings only as obstacles between the doubles, and demanded an actual, empty rest-period between any repeated units. When asked if it were really the rest-period _between_ elements or _on_ them, he said he felt there was a complete discharge of attention on the major units, and an attempted one on the minor or alternate units, and the attempted ones became confused.

These introspections would point to the fact that alternate minor spaces while affording rest for the attention were periods of activity of some other kind. The fact that no one could say _what_ kind, and yet insisted on the feeling of its being important and distinctive, and moreover repudiated the idea of change in a minor space even more than in a major--this seemed to show that there was a value in the alternate spaces quite aside from attention, but fully as distinct in its own way.

As might be expected, those of my subjects to whom rhythm was not a conscious factor of the experience of repetition could not understand exactly what was meant by the distinction between _rest-phase_ and _emphasis_ of rhythm. In all the preceding cases where the temporal type gave the introspection I have described, the spatial subjects grouped the single lines, in Fig. 2, about the heavier pair as centre, and moved from the centre of one such group to the next. The experience then consisted of a succession of adjacent symmetrical groups, connected by movement from centre to centre. When asked if there was no pleasure in finding equal distances between their centres, _i. e._, any temporal element whatever, they all denied feeling any. They could not detect that they _felt_ the distances between their centres as equal, although they _knew_ them to be. They spent so much attention on the group that all feeling of the distance between its centre and the last was lost before going on to the next.

These two marked types of apperception of an alternating series seem varieties of _emphasis_, rather than of actual experience. It was evident that those in the spatial type must have some recollection of the amount of distance passed over between the various groups to feel the whole series as connected in any way; while those of the temporal type could not be wholly absorbed with the separate lines of the series as they traversed it, but were distinctly conscious of the space relations of those in the side of the field that they had just passed or were coming to.

Next, I tried to see what were the different factors which made up the value of the minor spaces. By varying both their size and filling, and doing the same to the major element, I could judge the relative value of these changes on the two, and their effect on the whole series.

The test was made in the following manner. The series as it stood consisted of a double line alternating with a single one.

With every temporal subject the double line was conceived to be the repeated thing, and the space between considered as an alternate, with a repeated line of its own, to be sure, but not felt in the same way as the other. With the spatial type, the single line was merely the limiting edge of the symmetrical figure, with a double line in the centre. One subject varied back and forth in his method of apperception, and considered the richness and variety of these different apperceptions as one of the chief sources of the pleasure therein.

_Variation of alternating spaces:_ The minor spaces were varied by hanging two strings in one, and one in the other, and subject asked how such a change affected his feeling for them. The change was marked.

The spaces which had before been minor were so no longer. The alternate space in which two strings were hung with the boundary-line of the two double strings became the new element, and the alternate in which only _one_ string was hung continued to be the alternate in the new series. The whole series shifted itself, and settled into a new equilibrium. Some of the subjects were able to feel all the former minor spaces still as such, but only by a definite effort, and not while taking any pleasure in it. The change in the alternates spoilt the whole scheme of the repetition as it already stood, and made a regrouping necessary. I next tried varying alternates by removing a string at intervals.

Since the strings were not removed in any regular fashion, and because the subject could not find any possible consecutive way to group them with the double strings, this variation was partially overlooked, and although confusing the series somewhat, repetition of the double strings could still be felt. Thus a mere _gap_ where the scheme remained the same was not so disturbing as an extra feature inserted, or one noticeably changed. Something could be supplied by the subject, but not altered so easily. In these cases, however, the change was only tolerated because it was ignored. They felt it as a mistake and so overlooked it, but, accepted as a component part of the series, it was impossible to feel it as a repetition or get pleasure from it.

The next variation was in the position of alternate figures. With a three-group as the major element of the repetition and a pair of strings in the alternate space, the size of the two minor spaces was altered, thus making the distance between the three-group and adjacent pair shorter than between that and the next three-group. This immediately threw out the feeling for the old series and made a new one. The new series thus formed varied with the different subjects, although no particular difference was noticed between spatial and temporal types. They all disliked the new arrangement, in whichever of a variety of ways it was apperceived. (It will be noted the actual distance between the three-groups was not varied, but the size of the spaces each side of the minor figure, _i. e._, the minor figure was shifted from its central position.) One typical spatial subject took it in either of three ways: (1) He grouped the three-group and pair nearest together, into the repeated element of the new series; (2) he ignored the pair and regarded it as a repetition of three-groups; or (3) ignored the difference in the division of the alternates, and regarded them as alike. The artificiality of the latter methods of taking the series is evident. What pleasure survived after such a strain was very slight, and was moreover not of the series as given, but as imagined differently, which was not a valid judgment. Most of the subjects grouped both figures into one, and, finding the unity thus made ugly and unsymmetrical, derived no pleasure from it. One tried to keep both elements in separate series and have them go along together, equally distant from those of their own kind, although not from each other. This was, however, very fatiguing and unsatisfactory. Those who grouped the different figures said they did so because they could not help it, not because they liked it, and said it was impossible to regard the alternate figure as such, if varied from its central position. If they were all varied together, they were grouped, with the major unit, into a new one. If varied irregularly the series was spoiled--no rhythm whatever remained. It became a heap.

Next, I tried varying the size of the alternate spaces, keeping the filling in its central position.

Here also it was universally regrouped. They found it more difficult to feel the rhythm of the three-groups as separate elements than when the minor spaces had remained uniform in size, but different in the position of the filling. The alternate space, then, which had at first seemed the unimportant part of the rhythm and for which no subject could assign any conscious value whatever, was evidently a potent factor of the experience, and when varied either in size or filling (especially the former) it not only changed the feeling-tone, but shifted the entire scheme of the rhythm, or broke it up altogether.

_Variation of major units:_ Was variation more allowable in the major than in the minor unit of a series? This was tested first in the same manner as for accents. In a series of which a double string was the major element, a third string was hung with every such double, thus changing the unit in both size and content.

The series immediately readjusted itself with the three-group as element for most of the subjects, although one was still able to feel them all as one unit, varied by the added string. Varying only the _size_ of the major unit gave the same result.

The pairs, instead of remaining the same size, were made alternately larger and smaller, and a new repetition was made, _i. e._, with the larger pair as major element and the smaller one as minor. They all agreed, however, that less change was made in these cases than when the _minor_ spaces had been changed in size. In the latter case either a regrouping was made, changing the whole character of the series, or it was spoiled altogether. With change of _major_ units alone, however, although a new element was made, it was still possible to take it in the old way without much difficulty or change in feeling-tone.

It was then necessary to see how change of content would affect the major unit, the size remaining constant. A group of two sets of double strings 10 ccm. apart was taken as the repeated element, and these groups placed at 10 ccm. from each other.

Within one element was hung one string, and within the next two, thus varying the content while the size remained constant. In every case the answer was the same. It was not so pleasant as when the filling was the same, but the group still remained the unit of the repetition, and the series essentially the same.

Several variations were made in this element. Instead of hanging strings regularly (1 in one, and 2 in the next) they were hung irregularly, _i. e._, an extra one here and there at intervals in no special order. As long as the boundary-lines of each group remained at the same distance from each other, and from the next group, thus keeping the unit at uniform size, although the pleasure-tone varied, the balance of the series was not changed. No regrouping or shifting of the equilibrium resulted.

It would seem from the preceding experiments that in any series variation of the _major unit_ was tolerated more than of the _alternate;_ while in _either case_ variation in _content_ had less influence than variation in _size_.

_Symmetry:_ In the previous experiment, three subjects had insisted on symmetry as a necessary attribute both of the unit and its alternate. U. (spatial type) described his experience as "a succession of symmetrical experiences or states of equilibrium; when they are not so, they must be regrouped, or pleasure is impossible." R. (temporal type) insisted especially on the necessity of the alternate figure being symmetrical as regards the major units, _i. e._, halfway between them; and also on symmetry as regards itself. One temporal subject said there was some pleasure in merely going from one unit to the next, even though no repose was possible on each because of its asymmetry. This suggested experiments on the importance of symmetry in repeated series. Is it necessary that the separate elements of a series be symmetrical? Must both major and minor element be symmetrical? Does this necessity vary according to the temporal or spatial type of the subject, _i. e._, is it more necessary to the spatial type, whose pleasure depends more on repose in the unit, than to the temporal type, whose enjoyment rests mainly in the rhythm of movement from one unit to the next? Or is it a common demand? This experiment was begun in the following simple way. The strings were hung in two group-forms; one with three and the other with four.

This was a symmetrical grouping and uniformly pleasant. The series was then changed by removing the second string in the four-group, thereby making it unsymmetrical.

This change made the repetition less pleasant in every case, but did not spoil it. Instead of the four-groups becoming more prominent they seemed less so, and the three-group on account of its "compactness" became in most cases the major element, thereby shifting the balance of the repetition, but not detracting very much from the pleasure. Next the three-group was changed by moving the middle string to the left. By this means the group which had been minor in Fig. 11, became unsymmetrical, while the four-group was regular.

This change was preferred to that in Fig. 12, although different reasons were given. One said it was because this change in arrangement made the elements more distinct, hence easier to keep apart, while in Fig. 12 they were made more alike. Moreover, one element seemed as important as the other. He did not class them as major or minor, so he could not compare the relative values of symmetry in principal and alternate units, for in this series he did not feel the distinction. The other answers to this question were rather incoherent, but the series did not seem to suffer much change, either pleasantly or otherwise. Since lack of symmetry in _the element_ was at least tolerated in the examples already given, would it be allowable so to place the units that the two adjacent to any one unit should lie unsymmetrically on either side, that is, may the elements lie unsymmetrically with regard to one another? Suppose a four-group to be repeated at regular intervals, and a three-group likewise; if the two series were combined, must they occur halfway between each other? That is, must they be symmetrically placed as regards the intervening space, or could they be put to one side?

The subject was asked not to group them (as in previous similar arrangements), but to keep them as separate repetitions if possible, and to see if this equal distance was necessary to keep them apart. The result was the same in all cases. The subjects could not help grouping them, and found it impossible to keep them distinct unless so much effort was put into it that no pleasure was left. They said they "_knew_ each unit was as equally distant from the next unit in its _own_ series, as if it did not come at unequal distances from the units in the other, but they could not feel it so, and were obliged to group the two together." For this reason the experiments did not satisfactorily illustrate the point in question. It was necessary to have a series of elements whose unity was more strongly marked, and whose different parts would still remain one _whole_ even after variations, instead of shifting into each other. It was suggested by these imperfect experiments that symmetry was _not_ so important a factor in the different units of a series as the subjects had previously supposed; but that, on the other hand, the different units must be placed at equal distances from each other, if they are to be kept distinct either as two series or as one. Moreover, that _two_ series could not be kept distinctly in mind as separate, _anyway_, without fatigue, the tendency being always to group them into one series with a new repeated element, composed of a combination of the other two. It was necessary, however, to test this more completely. By a simple device the former series was changed radically, so that the difficulties mentioned were overcome. The strings of both the three and four groups were twisted together at the bottom, thus binding them closely into separate unities. By remaining attached at the bottom, whatever variations might occur elsewhere in the figures, they could not lose their individuality and become merged in each other as before. They remained distinct groups without effort on the part of the subject.

With this I began as in the previous experiment. The subject was asked to look at the series of repetitions, enjoy them as much as possible, telling what was the pleasant factor in the experience, and how he apperceived the series. The subjects separated into types as before; the spatial type immediately grouping the elements into a larger unity and enjoying the groups more for their own sake than for their repetition, while the temporal type went from one to the next in the series, enjoying the _rhythm_ more than the elements as such. (It may be remarked here that the subjects were perfectly naïve as to their apperception. They did not know they were separated into types, nor were they urged to be consistent. Even the experimenter did not know of the distinctness with which these types separated themselves, and consistently held to their own method of apperception, until looking over the records afterwards.)

With the temporal type the four-group was the major group. Some expressed its prominence in terms of _time_, _i. e._, they spent more time on it, and less on the three-group. One felt it as emphasized, because he moved from one four-group to the next like it, and at each step moved back and forth from left to right, to see the alternate three-groups on each side, always _resting_ on the four-groups.

It is noticeable with these subjects, in whom the rhythmic element was more strongly developed, that although they admitted that the language of "temporal rhythm" did not adequately cover their experience (because the element did not disappear after perception as in auditory rhythm, but remained in the visual field), still they could not express themselves in other terms. L., the most extreme of this type, insisted that the experience of repetition would be exactly as pleasant if he saw the elements pass one by one behind a moving window, with never more than one in the field at once. In other words, their temporal relations were all he felt.

The others did not go so far as this, and agreed to the significance of the whole field, even while especially interested in passing from one to the next. B. partook of the characteristics of both types, and by combining the apperceptions of both bridged the chasm between them.

With the four spatial subjects, the apperception showed its usual divergence. Three grouped the elements, either with the three-group in the centre on account of its being more compact and graceful, or the four-group because it was heavier. One of them could group it either way, distinguishing between the prominence in an element due to _interest_ and due to _beauty_, _i. e._, he found the four-group more noticeable and interesting on account of its size, while the three-group was more beautiful as a unity, on account of its proportion and grace. Therefore according as one factor or the other predominated, one or the other figure was taken as the more prominent element, and placed in the centre of the group. Sometimes they separated into two series running along together, but this was not usual.

Having got these varied introspections, with yet a certain likeness running through them, the balance of the four-group and of the three-group were varied in turns, to see how the change in symmetry of elements would affect the series; and the relative value of symmetry for the major and minor units of a series.

First, the four-group was altered, by moving the second string further to the left, while the three-group remained symmetrical.

In three cases this arrangement was preferred to the regular one previous, and each time for the same reason. The four-group was made more noticeable by being unsymmetrical, and hence more easily distinguished from the other. The two were easier kept apart, and the alternation between the two was made more clear-cut and obvious. With others the change was unpleasant for the reason that it affected them in an exactly opposite manner. The four-group _lost_ its individuality, and, by separation into two unsymmetrical parts, could not be distinguished so well from the three-groups as formerly, hence the effect was spoiled.

A distinction was made between the relative _importance_ and _interest_ attached to the units, when symmetrical and when unsymmetrical. Every one agreed that making the four-group unsymmetrical gave it more prominence of a certain kind. With the first three subjects mentioned, this prominence was enough to accent the rhythm still more than before, and differentiate the two units more strongly. But with the other there was a feeling that while it gained prominence and was more _noticeable_, it lost coherence and interest, thence it could not be kept as the principal unit, but the attention passed over to the three-group which maintained its unity.

It would seem, then, that the mere fact of one unit in a series alternating with another, and being more noticeable, taking up a larger space, being more complicated, etc., did not insure its being the chief unit in the series. One subject voiced essentially the feeling of all, in his comment on the series: "There is a constant struggle between the prominence which the four-group gains from size and eccentricity, and the insignificance which it deserves on account of its looseness and lack of unity; it cannot hold its own as one individual thing, and because the three-group still does, it becomes in one way more prominent, while the four-group remains so in another." Another subject felt he gave more _time_ to the four-group than before, because being separated it would not bind together again without effort. At the same time the three-group gained in interest because it was easy to find and did not vary. Another subject felt that the _time_ spent on a unit had nothing to do with its rhythm; it was all a matter of interest and attention. Often he looked a longer time at one unit, choosing another for the chief element in his series, because it interested him more.

All this introspection brought out two things clearly:

(1) The apperception of a series of alternating units, whether of the spatial or temporal type, is not fixed, but any variation of its unit is liable to shift the emphasis. Thus, as in the present case, when a symmetrical major unit is made unsymmetrical, it may not remain the principal unit, but becomes the minor one, because the attention shifts to the other which was before relatively unimportant.

(2) Whether either element shall be the principal one or not, does not depend wholly on its objective prominence, but on the amount of beauty or interest which it holds for the observer. Neither size, complexity, nor eccentricity can force a certain unit to be taken as the major in a series, unless it thereby presents an interest which makes the observer choose it.

The next change was to vary the three-group in a similar way, by pushing the middle string to the left, thereby making it unsymmetrical.

The responses were as follows: Five said it did more violence to the series to have the alternate varied than the major unit; it was more confusing. Three preferred it, giving as their reason that it made the elements more different from each other than before, hence more easily distinguished. The preponderance of evidence was, therefore, that, although any variation from symmetry in a unit was likely to be detrimental to the repetition, it was more likely to be tolerable in the major unit than in the alternate space. In either case it was demanded that the two units be distinctly different, and it depended on the individual subject, whether in this experiment the variation of one unit or the other brought out this distinction more obviously. Aside from this consideration, however, it appeared that the alternate spaces as such required equilibrium more than the principal unit. Also, variation of symmetry in the major unit, while it made it more prominent in the way of _eccentricity_, also made the symmetrical minor unit more prominent in the way of _interest_. As one subject expressed it, "Since the others vary, the attention requires something which does _not_ vary, and forces prominence on the minor unit, because it remains symmetrical"; and "The minor unit is too small to merit such prominence as it gets by lack of symmetry. It is distorted, and has not enough content to bear it."

These introspections from temporal and spatial subject alike, all point to the fact of a certain _value_ attached to the alternating units in a series. (1) The units must not be too much alike in _interest_, or they rival each other. (2) They must not have more prominence given them as regards the whole than they have interest to sustain. (3) There must be a congruity between the two elements so that one shall not be noticeable in one way, and one in another, thus carrying the attention in two different directions.

One more thing was suggested by this experiment: (4) The subjects who had invariably _grouped_ their different elements in other series found it very difficult to do so in this, or wholly impossible. None of them did so when taking the series naturally, but moved on from one to the next just as the rhythmic type did. They felt "forced to move on," "no place to rest," while one in whom the rhythmic feeling was weakest was much fatigued by this movement, and insisted on having something stable to rest upon if he was to gain any pleasure at all.

Next the series was varied by making both units unsymmetrical; first with the balance tipping the same, and second in opposite ways.

Those who preferred this gave essentially the same reason. They agreed that the unity of both elements was broken up by this change, and they did not stand out distinctly from each other; but all felt a certain _congruity_ in having both major and minor units follow the same scheme in composition. They were not distinctly an alternating series, but harmonized better as lines. The two spatial subjects, who disliked this arrangement more than the other, gave the same reason: the unity of the elements was spoiled, they did not "hang together." Their dislike was similar in kind to that of the others, only the congruity which made up for it with the former failed to satisfy these. With the symmetry broken and the balance tipping in different ways, the feeling was not strong in either direction. They still criticised it in the same terms of congruity and distinctness, with no especial change on account of this modification.

These experiments all pointed to the fact that (1) a certain amount of congruity and equality was necessary between elements of a series (although it did not establish what were the essential features of such a harmony). (2) It is more pleasant, as a rule, to have the elements symmetrical, although symmetry was not a necessity for an agreeable series. (3) Provided the change in the symmetry of the units was not enough to shift the whole order of the series, changing the major to minor units (and _vice versa_), any varying of the symmetry of a minor unit was more disturbing to the repetition than of the major, while varying their symmetrical position, as regards the unit on either side, was absolutely destructive to the order.

The next experiment dealt with a different side of the question. Since the unit of a repeated series may be a group with repetitions inside itself, does the repetition of lines or figures _inside_ the group differ from the repetition of the groups as a whole? If so, how? That is, in the enjoyment of a series of groups with repeated lines in the group, in what respect does our apperception of the repetition differ in the two cases? Or does it in reality differ at all?

To test this, the strings were arranged in the following way. 10 groups of five strings were hung 100 mm. wide and 100 mm. apart. Each unit had, then, five repetitions within it.