Chapter XX: Section II: showed that the shorter filled distances are (16)

4 9 5 9 1 3 6 _9_a 25 33
2 8 5 6 4 5 5 _10_b No increase in length.
2 5 2 5 2 5 5 _11_a
1 5 2 5 5 10 2 _12_b 32 34

The evidence of an increased intensity on the rhyme is not so positive in the case of rhymes in the third foot. Among the rhymes in the second foot there is but one exception. The rhymes in the second and third feet were never given very satisfactorily by several of the subjects. The rhymes within the verse determine a climax in the foot in which they occur, and all the verses follow this well-defined type. It is interesting to note, in studying the phonographic record, that in verses in which the accentuation of the rhythm is not very definite, the accentuation is perceived when the record is repeated at the normal speed. If the record is repeated more slowly, and especially at such a distance that the rhyming consonants cannot be distinguished, then the accentuation seems to disappear. It is probable that after a verse or stanza type has been established the voice may deviate from the type, and the accentuation will be supplied by the hearer.

TABLE XI.

INTENSITIES OF IAMBIC TETRAMETERS WITH RHYMES IN THE THIRD FOOT
(SHOWING INCREASE IN INTENSITY OF THE RHYME SYLLABLE).

' ' ' '
\/ -- \/ -- \/ -- \/ --
Ha. 13 18 10 16 _7_ _9_a 6 12
9 10 4 11 7 _14_a 4 7
-- 12 5 10 7 9b 6 9
2 12 5 12 3 _14_b 4 6

2 12 4 13 7 8a 4 9
6 8 4 14 4 _15_a 2 9
2 13 -- 12 8 8b -- --
5 9 6 10 -- 3b 4 6

Am. 10 10 4 12 6 _14_a 5 5
4 12 6 9 7 8a 4 4
5 12 8 9 7 _10_b 3 4
3 7 5 8 5 7b 2 4

10 13 5 10 4 _10_a 4 6
1 9 4 9 3 5a 3 5
2 8 3 5 -- _8_b 1 5
1 7 2 7 5 _8_b 2 3

G. 6 13 6 13 7 _12_a 1 10
6 10 6 6 _7_ _7_a 1 8
4 9 7 7 _6_ 9b 1 7
7 12 4 10 2 7b 1 7

10 12 4 11 6 _10_a -- 8
5 12 5 11 6 _10_a -- 8
3 9 6 9 _7_ _9_b 3 8
2 8 5 9 5 5b 1 6

D. 10 12 10 10 7 9a 7 11
5 8 6 9 7 7? 6 6
5 12 7 9 6 _10_b -- 8
6 9 7 10 7 7b 5 5

10 15 5 11 6 9a -- 9
5 9 4 8 6 6a? 6 7
7 11 7 11 _11_ _13_b 8 10
8 11 8 10 7 9b 6 8

INTENSITIES OF IAMBIC TETRAMETERS WITH RHYMES IN THE SECOND FOOT.

' ' ' '
_ - _ - _ - _ -
Hu. 5 6 6 6a 5 7 5 6
5 6 5 4a 5 4 5 6?
5 6 6 7b 5 6 4 7
5 6 4 4b 5 7 4 7
5 7 7 7a 6 7 6 6
5 7 5 5a 5 6 5 6?
5 7 _6_ 8b 6 7 6 7
6 7 6 5b 6 7 6 7
Mc. 5 7 6 _10a_ 5 4 3 5
1 6 6 _8a_ - 6 1 4
1 6 6 _10b_ 1 4 - 4
- 7 6 5b 3 3 - 3
Ha. 16 14 _8_ _10a_ 6 10 5 9
5 10 7 8a 5 9 5 7
2 8 4 _11b_ 4 7 2 8
2 8 4 6b 1 9 4 8
7 12 7 _10a_ - 10 6 10
3 10 5 8a 5 8 6 10
2 8 3 _11b_ 3 7 3 10
- 7 5 9b 4 8 6 12
Am. 4 9 _9_ _10a_ 4 7 4 5
4 8 _9_ _7a_ 5 7 4 6
1 8 5 _10b_ 4 6 3 6
- 10 _10_ 7b_ 3 5 2 7
15 15 _10_ 13a_ 9 11 - 11
5 12 7 9a 4 10 4 9
5 8 _8_ _9b_ 4 7 - 6
7 8 5 _9b_ 2 4 - 3
G. 2 6 _6_ _8a_ 1 7 2 3
- 10 _7_ _12a_ 1 9 4 8
4 9 _6_ _9b_ 8 8 2 7
- - - -b - - - -
4 9 _5_ _11_a - 7 4 6
- 8 6 7a 2 7 4 5
- 9 _7_ _6_b - 7 3 6
- 7 3 5 - 5 - 3
D. - - - - - - - -
7 11 _11_ _9_a 7 11 6 10
11 15 11 11a 8 11 9 14
6 10 _10_ 8b 7 8 7 11
12 13 10 10a 7 1? 8 11
6 10 9 8a 5 8 5 9
9 12 12 13b 8 10 7 9
7 11 _10_ 7b 4 8 4 8

The values surrounded by '_'s (Transcriber's Note: Original
italics) show the increase in intensity. Rhymes are indicated
by 'a' and 'b.'

IV. SUGGESTIONS FOR A MOTOR THEORY OF RHYTHM.

If the basis of rhythm is to be found in muscular sensations, rather than in the supposed activity of some special 'mental' function, the nature of the movement cycle involved is of the greatest interest.

In every case where a rhythm comes to peripheral expression, there are two opposing sets of muscles involved. If a rhythmic movement be attempted with but a single set of muscles at work, it is very unsatisfactory and soon ends in the tonic contraction of the muscle set. One may assume that in all cases of rhythm perception there is a cycle of movement sensations involved, and that the simplest possible case of a peripheral rhythmic movement is the type of any rhythm. In tapping a rhythm with the finger, the flexors which bring the finger down become the positive muscle set, and the opposing extensor muscles which raise the finger for the next blow become the negative muscle set.

In Fig. 9 the upper curve represents the actual movement of the finger tip, and the heavy lines _a_, _a'_, _a''_ represent the pressure-tension-sound sensation which we call the 'beat,' and which is the limiting sensation of the rhythm, and the regulating factor in the movement cycle of the rhythm. The movement is divided into two phases; _B_, the phase of relaxation, during which the finger is raised, and _A_, the phase of contraction, during which the finger delivers the blow which produces the beat.

The curves below represent the changes in the two opposing sets of muscles whose interaction brings about the movement cycle. The contraction of the flexors, the positive muscle set, is represented by the curve above the base line. It is obvious that during the contraction phase, the contraction in the positive muscle set is at its height; it continues at a maximum during the limiting sensation and then dies away during the relaxation phase. The sensations from this positive muscle set have the principal place in consciousness during the rhythm experience. The curve below the base line represents the contraction of the extensors, the negative muscle set. The contraction of the negative muscles reaches its climax very soon after the maximum contraction of the positive muscles, in the contraction phase. The sharp tension between the two opposing sets of muscles at the limiting sensation may be made very apparent if the finger beats the rhythm entirely in the air; in that case the limiting sensation consists entirely of the feeling of a sudden increase of tension between the positive and negative muscle sets. During the relaxation phase the contraction of the negative muscles continues, but the tension between the two sets grows less and less, for the positive muscles are rapidly relaxing. At the highest point in the movement either muscle set is exerting but very little strain; the condition is represented in the figure by the approach of either curve to the base-line; the amount of tension between the two sets is figured by the distance of the two curves from each other.

Assuming such a movement cycle, in which the tension between the two opposing sets never comes to zero until the close of the series, it is not difficult to arrange many of the facts of rhythmic perception under the motor theory.

1. The feeling of rhythm is more definite as we proceed in a verse, or a series of simple sound sensations. At first the cycle is not perfectly adjusted and complete automatism established.

2. If an observer is listening to a series, and an unusually long pause is introduced between two beats, there is always a feeling of suspense or tension during the 'lag.' As long as the tensions are maintained there is a rhythmic continuity; the feeling of tension is the strain of opposition between the opposing muscle sets.

3. The continuity of the rhythmic series, whereby all the beats of a period seem to belong to a single whole, is due to the continuity of the muscle sensations involved and the continuous feeling of slight tension between the positive and negative muscle sets; nowhere within the period does the feeling of strain die out.

4. But at the close of the period we have a pause which is demonstrably not a function of any of the intervals of the period. During this pause the tension between the two sets 'dies out,' and we have a feeling of finality. This gradual dying out of the tension is clearly seen in the constant appearance of the cone-shaped final syllable at the end of each nonsense verse.

5. The period composed of a number of unit groups (the verse, in nonsense syllables) has a general form which suggests strongly that it has the unity of a single coördinated movement. There is no more reason for assuming a transcendental mental activity in the case of a rhythmic period than in the case of a single act which appears in consciousness as a unity. Undoubtedly the breathing is correlated with the rhythmic movements and may be a factor in determining the verse period. Meumann's principal accent, about which a number of subordinate accents are grouped, is characteristic not only of poetry but of the simplest rhythms. At some point in the period there is a definite climax, a chief accent; the movement 'rises' to that point and then falls off. This is strikingly seen in nonsense verses spoken with a heavy accent within the verse. The accent does not stand out from a dead level, but the verse culminates at that point.

Unfortunately very little is known of the mechanism of so simple a coördinated muscular activity as that necessary for a simple rhythm. Sherrington[17] and Hering[18]have pointed out the primary character of the grouping of the muscles in opposing sets and the reciprocal nature of almost all muscular activity, but in a review of the work of coördinated movements Hering denies any simultaneous stimulation of the two sets and considers the question of the innervation mechanism of opposing muscle-sets entirely unsettled.

[17] Sherrington, C.S.: _Proceedings Royal Soc._, 1897, p. 415.

[18] Hering, H.E.: _Archiv f. d. ges. Physiol._ (Pflüger's),
1897, Bd. 68, S. 222; _ibid._, 1898, Bd. 70, S. 559.

That the connection between the positive and negative set of muscles in a rhythmic movement is very close, and that the reaction is of the circular type, is evident from the automatic character of all rhythmic movements, and it is evident that the limiting sensation is the primary cue in the reaction. Anything further is mere hypothesis. Robert Müller's[19] thorough criticism of the Mosso ergograph throws great doubt on the present methods of investigation and invalidates conclusions from the various curves of voluntary movements which have been obtained.

[19] Müller, R.: _Phil. Stud._, 1901, Bd. 17, S. 1.

The curve of contraction and relaxation of a simple muscle is well known and is not affected by Müller's criticism. Its chief characteristic, with or without opposing tension, is the inequality of the intervals of the contraction and relaxation phases. As one might expect, since a single set of muscles dominates in a rhythmic movement, the typical rhythmic curve has the general character of the curve of the simple muscle. The average values of the phases of curves of simple rhythmic movement obtained by A. Cleghorn[20] from a large number of observations with at least three subjects, are as follows: phase of contraction, .44 second; phase of relaxation, .54 second. It is very significant for a motor theory of rhythm that this general form of the curve of rhythmic movement may easily be altered in all sorts of fashions by unusual stimuli to the two muscle sets.

[20] Cleghorn, A.: _Am. Journal of Physiol._, 1898, I., p. 336.

While it is well recognized that a rhythm does not consist necessarily of sound sensations, the 'rhythmization' of a series of sound sensations in the ordinary perceived rhythms is a matter of great interest. Ewald found strong reasons for believing that the ear is peculiarly connected with the motor apparatus. The experiments of Hofbauer[21] and Cleghorn[22]show that any strong stimulus to either eye or ear modifies decidedly the reactions of coördinated muscles. How shall we assume that the automatic movement cycle necessary to rhythmic perception is set up when one listens to a series of sounds?

[21] Hofbauer: _Archiv f. d. ges. Physiol._ (Pflüger's), 1897,
Bd. 68, S. 553.

[22] Cleghorn, A.: _op. cit._

It must be assumed that any chance sound sets up a contraction in a set of muscles, however large or small. If but a single sound occurs, the phase of contraction in that muscle set is followed by a longer phase of relaxation, and the musculature is passive as before; it may be that the stretching of the antagonistic set of muscles weakly stimulates them, and they then contract during the relaxation phase and assist in restoring the original condition.

But if a second sound occurs toward the end of the relaxation phase, before the tension is quite exhausted, the movement will be repeated; the negative set of muscles will be more definitely stimulated, for the activity will not have been exhausted when the second sound occurs. If the sound continues to recur at regular intervals, the movement cycle thus established will rapidly become coördinated. The positive set in its vigorous contraction furnishes a limiting sensation which becomes a cue for its own relaxation and for the reciprocal contraction of the negative muscle set. The contraction of the negative muscle set and the resulting changes in tension may become in turn a cue for the positive set. The reaction is now of the circular type and the process has become self-regulative, though constantly reinforced by the recurring sound (which has become a part of the limiting sensation of the rhythmic movement cycle).

But it is very probable that the second sound may not be timed so as to come at the close of the relaxation phase in the set of muscles roused; moreover, in almost all rhythms there are secondary sounds occurring between the main beats. What happens when a sound occurs out of place, early in the phase of relaxation, or just before or just after the climax in the contraction phase? Does it make it impossible to establish the coördination, or destroy it if already established?

Hofbauer demonstrated that a stimulus which appears in close proximity to the limiting sensation, _either before or after_, always increases the force of the reaction, so that such a slight displacement could not affect the rhythm, which would quickly readjust itself. The possibility of a stimulus occurring in the relaxation phase is of much more importance for a motor theory of the initiation of a rhythmic movement. Cleghorn made the stimulus occur at the beginning of the relaxation phase. Instead of prolonging or reinstating the contraction phase, he found that the stimulus _intensified the relaxation process and shortened its period_. "The stimulated relaxation is not only quicker than the normal, but also more complete; the end of the normal relaxation is slow; ... relaxation under the influence of the stimulus, on the contrary, shows nothing of this, but is a sudden sharp drop directly to the base line and sometimes below it." A comparison of the normal phases with the same phases, when the stimulus occurs within the relaxation phase, follows:

Normal: Contraction-phase, .44 sec.; relaxation-phase, .54 sec.;
total, .98 sec.
With stim.: Contraction-phase, .47 sec.: relaxation-phase, .30 sec.;
total, .77 sec.

It will be noticed that the total time of the movement cycle is reduced. One may then assume that a sound which occurs too early to become a factor in the limiting sensation, functions as a stimulus to the relaxation process and shortens the interval between the limiting sensations. Thus the movement cycle would be modified, but not destroyed. It is impossible to say just how the relaxation process is affected, and Cleghorn's own conclusions are open to criticism in the light of Müller's comments on the method. The simplest assumption would be that the stimulus acted on the negative set of muscles.

E.W. Scripture[23] objects to such a 'tonus theory,' because some subjects regularly react _before_ the signal. But in no case in the published records to which he refers is the error more than.05 sec. either before or after the signal. The investigation of Hofbauer shows conclusively that in such cases the effect of the external stimulus simply fuses with the limiting sensation. Scripture overlooks the automatic character of the rhythmic movement.

[23] Scripture, E.W.: 'The New Psychology,' London, 1897, p. 182.

There is a striking difference between rhythmic movement from unit group to unit group within a period, and movement from period to period (_i.e._, from verse to verse of nonsense syllables). Each foot is simply the repetition of the movement cycle; all the tensions are maintained, and each foot is an integral part of a larger act. At the close of the period (verse) the active tensions die out, either because of the introduction of some unusual stimulus which causes the positive muscle set to strike a heavy blow, and abruptly upset the balanced tensions, or because a pause of indefinite length ensues in which the tensions die out. This is the process which we call 'finality.'

In the stanza there is evidently a different type of unity from that in the single verse. When we hear the first verse of the stanza, we do not know what the verse whole is, until the finality factor or the verse pause is reached, at its close. Then the verse has a certain definite cumulative effect, a synthetic effect which results from the echoes of the various movements and the total effect on the organism. One may call it the tetrameter feeling. The verse pause may vary within large limits, but after a few verses there is a definite scheme, or 'Gestaltqualität,' which represents the verse unity. It is some sort of a memory image, which functions as a cue to the motor process. This motor image, set of strains, or whatever it be, is more than a mere standard by which we judge the present verse. The memory image fuses in some way with the living motor process. _The preceding verse affects the character of the following verse._ An irregularity, easily noted in the first verse, is obscure in the second, and not detected in the third verse, when the verses are identical.

The experiments of Hofbauer and Cleghorn, and many facts about the unit groups themselves, make it evident that the function of stimuli, during the movement cycle, varies with the position of the stimulus in that cycle. This offers a possible explanation of the striking peculiarities of the unit groups. The iamb [\/ _'] and the trochee [_' \/] should be quite alike for a general synthesizing process; but not only is the experiential character of the two quite unlike, but the ratio between their intervals is entirely different.

A number of measurements by different observers show that in the iambic foot the unaccented syllable is proportionately much shorter than the unaccented syllable in the trochaic foot. It is very easy to beat a simple up-and-down accompaniment to a series of simple feet of nonsense syllables; in the accompaniment the bottom of the down stroke, the limiting sensation of the movement cycle, coincides with the accented syllable of the foot. It is not an unwarranted assumption that such a fundamental accompaniment represents the fundamental movement cycle of that rhythm.

During the present investigation several observers were asked to determine at just what point in the fundamental movement the unaccented syllable occurred, when the subject gave a series of nonsense syllables. In the fundamental accompaniment the excursion of the hand and arm was at least.4 meter. Four subjects were thus tested, and the results were uniform in the case of all the simple types of unit groups.

In the case of the iamb the unaccented syllable occurs at the top of the movement, at the very beginning of the contraction phase (A, in Fig. 5).

In the case of the trochee the unaccented syllable occurs in the first third of the relaxation phase (B).

It is interesting to note that the unaccented element of the trochee comes at the earlier part of the relaxation phase, where it must intensify the relaxation process, and tend to shorten the total length of the cycle. This may be the reason for its peculiar buoyant, vigorous and non-final character. On the other hand the unaccented element of the iamb occurs at a point where it may initiate and intensify the contraction, which gives the limiting sensation; it is, therefore, more closely bound to the limiting sensation, and has the character of intensifying the beat. There is a similar contrast in the cases of the dactyl and anapæst. The accented syllable of the dactyl is longest, and the second unaccented syllable, the last in the group, is shortest. The accented syllable of the anapæst is much longer in proportion than that of the dactyl, and the unaccented syllables are very short, and hence, very close to the accented syllable, as compared with the dactyl.

In the case of the dactyl the first unaccented syllable in the movement cycle occurs at the beginning of the relaxation phase (B), in the same zone as the unaccented of the trochee. The second unaccented syllable of the dactyl appears at the beginning of the next contraction phase (A), in the zone of the unaccented syllable of the iamb. The group seems a sort of combination of the iamb and trochee, and has an element in every possible zone of the movement cycle. Like the trochee the dactyl is a non-final foot.

The unaccented syllables of the anapæst both occur at the beginning of the contraction phase (A). They are both within the zone of the unaccented syllable of the iamb. The group seems an iamb with a duplicated unaccented syllable. It is possible to form a unit group in nonsense syllables where the unaccented syllable of the iamb shall be represented not by two syllables, as in the anapæst, but by even three.

The anapæst and dactyl, if they correspond to this construction, should show a decided difference as to the possibility of prolonging the foot pause. The prolongation of the foot pause would make the dactyl but a modified trochee.

It is significant that in poetry no other types of unit groups are often recognized. The amphibrach, laid out on this scheme, would coincide with the dactyl, as there are but three possible zones for foot elements: the zone of the limiting sensation (always occupied by the accented syllable), the zone of the contraction phase (occupied by the unaccented syllables of the iamb and anapæst), and the zone of the relaxation phase (occupied by the unaccented syllable of the trochee and the middle syllable of the dactyl).

The simple sound series is fairly regular, because of its cyclic and automatic character. It is not a matter of time estimation, and the 'Taktgleichheit' is not observed with accuracy. The primary requisite for the unit groups is that they shall be _alike_, not that they shall be _equal_. The normal cycle with a heavy accent is longer than the normal cycle with a lighter accent, for the simple reason that it takes muscles longer to relax from the tenser condition. Time is not mysteriously 'lost'; the objective difference is not noticed, simply because there are no striking differences in the cycles to lead one to a time judgment. Ebhardt's notion that the motor reaction interferes with the time judgment, and that a small amount of time is needed in the rhythmic series in which to make time judgments, is a mere myth.

An unusual irregularity, like a 'lag,' is noted because of the sense of strain and because other events supervene in the interval. But such lags may be large without destroying the rhythm; indeed cæsural and verse pauses are essential to a rhythm, and in no sense rhythm-destroying. An unbroken series of unit groups is an abstraction to which most forms of apparatus have helped us. Between the extreme views of Bolton[24] and Sidney Lanier,[25]who make regularity an essential of the rhythm of verse, and Meumann, on the other hand, who makes the meaning predominate over the rhythm, the choice would fall with Meumann, if one must choose. Bolton comes to the matter after an investigation in which regularity was a characteristic of all the series. Lanier's constructions are in musical terms, and for that very reason open to question. He points out many subtle and interesting relationships, but that verse can be formulated in terms of music is a theory which stands or falls by experimental tests.

[24] Bolton, T.L.: _loc. cit._

[25] Lanier, S.: 'The Science of English Verse.'

TABLE XII.

I saw a ship a sailing
50 16 20 13 9 18 32 23- 132
A sailing on the sea
10 16 45 22 8 15 49 -68
And it was full of pretty things
8 6 20 6 6 27 37 12 8 7 20 12 41 -34
For baby and for me
14 9 27 37 18 20 14 8 46 --

Totals of the feet: --/66/60/187
26/45/45/117
14/59/49/47/75
23/64/60/46--

Who killed Cock Robin
19 34 23 24 17-77
I said the sparrow
45 21 19 3 47 29 --
With my bow and arrow
22 36 25 49 11 38 12 23 33-42
I killed Cock Robin
33 12 33 21 22 5 21 16-95

(The first stanza was measured in the Harvard Laboratory. The
last is modified from Scripture's measurements of the
gramophone record (1899). As the scansion of the last is in
doubt with Scripture, no totals of feet are given.)

In the cases given in the above table there is an irregularity quite impossible to music.

In the movement cycle of the simple sounds there is a perfect uniformity of the movements of the positive and negative sets of muscles from unit group to unit group. But in verse, the movements of the motor apparatus are very complicated. Certain combinations require more time for execution; but if this variation in the details of the movement does not break the series of motor cues, or so delay the movements as to produce a feeling of strain, the unit groups are felt to be alike. We have no means of judging their temporal _equality_, even if we cared to judge of it. It is a mistake, however, to say that time relations ('quantity') play no part in modern verse, for the phases of the movement cycle have certain duration relations which can be varied only within limits.

Extreme caution is necessary in drawing conclusions as to the nature of verse from work with scanned nonsense syllables or with mechanical clicks. It is safe to say that verse is rhythmic, and, if rhythm depends on a certain regularity of movements, that verse will show such movements. It will of course use the widest variation possible in the matter of accents, lags, dynamic forms, and lengths of sonant and element depending on emphasis. The character of the verse as it appears on the page may not be the character of the verse as it is actually read. The verses may be arbitrarily united or divided. But in any simple, rhythmic series, like verse, it seems inevitable that there shall be a pause at the end of the real verse, unless some such device as rhyme is used for the larger phrasing.

There is a variety of repetitions in poetry. There may be a vague, haunting recurrence of a word or phrase, without a definite or symmetrical place in the structure.

Repetition at once attracts attention and tends to become a structural element because of its vividness in the total effect. There are two ways in which it may enter into the rhythmic structure. It may become a well-defined refrain, usually of more than one word, repeated at intervals and giving a sense of recognition and possibly of completeness, or it may be so correlated that the verses are bound together and occur in groups or pairs. Rhyme is a highly specialized form of such recurrence.

The introduction of rhyme into verse must affect the verse in two directions.

It makes one element in the time values, viz., the verse pause, much more flexible and favors 'run on' form of verses; it is an important factor in building larger unities; it correlates verses, and contributes definite 'Gestaltqualitäten' which make possible the recognition of structure and the control of the larger movements which determine this structure. Thus it gives plasticity and variety to the verse.

On the other hand, it limits the verse form in several directions. The general dynamic relations and the individual accents must conform to the types possible with rhyme. The expressional changes of pitch, which constitute the 'melody,' or the 'inflections' of the sentences, play an important part. The dynamic and melodic phases of spoken verse which have important relations to the rhyme are not determined by the mere words. The verses may scan faultlessly, the lines may read smoothly and be without harsh and difficult combinations, and yet the total rhythmic effect may be indifferent or unpleasant. When a critic dilates on his infallible detection of an indefinable somewhat, independent of material aspects of the verse and traceable to a mystic charm of 'thought,' it may very well be that the unanalyzed thing lies in just such dynamic and melodic conditions of rhythm and rhyme.

The most primitive characteristic of music is the _ensemble_. Savage music is often little else than time-keeping. When the social consciousness would express itself in speech or movement in unison, some sort of automatic regulation is necessary. This is the beginning of music. The free reading of verse easily passes over into singing or chanting. When this happens, the thing most noticeable in the new form is its regulated, automatic and somewhat rigid character. It is stereotyped throughout. Not only are the intervals and accents fixed, but the pitch and quality changes are now definite, sustained and recurrent. The whole sum of the motor processes of utterance has become coördinated and regulated. Along with this precision of all the movements comes a tendency to beat a new rhythm. This accompanying rhythm is simpler and broader in character; it is a kind of long swell on which the speech movements ripple. This second rhythm may express itself in a new movement of hand, head, foot or body; when it has become more conscious, as in patting time to a dance or chant, it develops complicated forms, and a third rhythm may appear beside it, to mark the main stresses of the two processes. The negro patting time for a dance beats the third fundamental rhythm with his foot, while his hands pat an elaborate second rhythm to the primary rhythm of the dancers.

The essential character of musical rhythm, as contrasted with the rhythm of both simple sounds and of verse, is just this coördination of a number of rhythms which move side by side. This is the reason for the immense complexity and variety of musical rhythms. The processes check each other and furnish a basis for a precision and elaborateness of rhythmical movement in the individual parts which is quite impossible in a simple rhythm.

Even when the concomitant rhythms are not expressed, as in an unaccompanied solo, an accompaniment of some sort is present in the motor apparatus, and contributes its effect to the consciousness. This regulation of the movement by the coincidence of several rhythms is the cause of the striking regularity of the temporal relations. At some points in the musical series the several movement cycles may appear in the same phase, and at these points the same irregularities as in verse are possible, as in the case of pauses at the ends of periods and the irregularities of phrasing. It is evident in cases of expressional variations of tempo that a single broad rhythm is dominating and serving as a cue for the other more elaborate rhythmic processes, instead of being regulated by them.

* * * * *

STUDIES IN SYMMETRY.[1]

BY ETHEL D. PUFFER.

[1] SOURCES OF ILLUSTRATIONS.

Fig. 1 was copied from Reiss u. Stübel, 'Todtenfeld v. Ancou,'
Berlin, 1880-1887.

Figs. 2, 3, 4, 5, 6, 7, 8 and 11 were copied from the
publications of the American Bureau of Ethnology by the kind
permission of the Direction.

Fig. 9. was copied from A.C. Haddon, 'The Decorative Art of
British New Guinea,' Cunningham Memoir, N., Royal Irish
Academy, 1894.

Fig. 10 was copied from Franz Boas, 'The Decorative Art of the
Indians of the North Pacific Coast,' Bulletin of the Am. Mus.
of Nat. Hist., Vol. IX.

I. THE PROBLEMS OF SYMMETRY.

The problem of æsthetic satisfaction in symmetrical forms is easily linked with the well-known theory of 'sympathetic reproduction.' If there exists an instinctive tendency to imitate visual forms by motor impulses, the impulses suggested by the symmetrical form would seem to be especially in harmony with the system of energies in our bilateral organism, and this harmony may be the basis of our pleasure. But we should then expect that all space arrangements which deviate from complete symmetry, and thus suggest motor impulses which do not correspond to the natural bilateral type would fail to give æsthetic pleasure. Such, however, is not the case. Non-symmetrical arrangements of space are often extremely pleasing.

This contradiction disappears if we are able to show that the apparently non-symmetrical arrangement contains a hidden symmetry, and that all the elements of that arrangement contribute to bring about just that bilateral type of motor impulses which is characteristic of geometrical symmetry. The question whether or not this is the fact makes the leading problem of this paper, and the answer to it must throw light on the value of the theory itself.

An exhaustive treatment of our question would thus divide itself into two parts; the first dealing with real (or geometrical) symmetry, the second with apparent asymmetry; the first seeking to show that there is a real æsthetic pleasure in geometrical symmetry, and that this pleasure is indeed based on the harmony of the motor impulses suggested by symmetry, with the natural motor impulses of the human organism; the second seeking to show in what manner æsthetically pleasing but asymmetrical arrangements conform to the same principles. Within these two groups of problems two general types of investigation are seen to be required; experiment, and the analysis of æsthetic objects.

The main question, as stated above, is of course whether the theory can explain our pleasure in arrangements which are completely or partly symmetrical. It is, however, an indispensible preliminary to this question, to decide whether the pleasure in symmetrical arrangements of space is indeed immediate and original. If it were shown to be a satisfaction of expectation, bred partly from the observation of symmetrical forms in nature, partly from the greater convenience of symmetrical objects in daily use, the whole question of a psychophysical explanation would have no point. If no original æsthetic pleasure is felt, the problem would be transformed to a demand for the explanation of the various ways in which practical satisfaction is given by symmetrical objects and arrangements. The logical order, then, for our investigation would be: First, the appearance of symmetry in the productions of primitive life, as a (debatable) æsthetic phenomenon emerging from pre-æsthetic conditions; secondly, the experimental study of real symmetry; thirdly, the analysis of geometrical symmetry in art, especially in painting and architecture, by means of which the results of the preceding studies could be checked and confirmed. Having once established a theory of the æsthetic significance of real symmetry, we should next have to examine asymmetrical, beautiful objects with reference to the relation of their parts to a middle line; to isolate the elements which suggest motor impulses; to find out how far it is possible to establish a system of substitution of these psychological factors and how far such substitution takes place in works of art--_i.e._, to what extent a substitutional symmetry or balance is found in pleasing arrangements. These investigations, again, would fall into the two groups of experiment and analysis. The products of civilized art are too complicated to admit of the complete analysis and isolation of elements necessary to establish such a system of substitution of psychological factors as we seek. From suggestions, however, obtained from pleasing asymmetrical arrangements, first, isolated elements may be treated experimentally, and secondly, the results checked and confirmed by works of art.

With regard to the study of objects without a natural or suggested middle line, as for instance sculpture, many types of architecture, landscapes, gardens, room-arrangements, etc., we may fitly consider it as a corollary to the study of asymmetrical objects with artificial limits which do suggest a middle. If we find, by the study of them, that a system of substitution of psychological factors does obtain, the whole field can be covered by the theory already propounded, and its application extended to the minutest details. The hypothesis, having been so far confirmed, may be then easily applied to the field of asymmetrical objects without a natural middle line.

The set of problems here suggested to the student of symmetry will not be fully followed out in this paper. The experimental treatment of geometrical symmetry, the analysis of the completely symmetrical products of civilized art, and the analysis of all forms of asymmetry except asymmetry in pictures will be omitted. If, however, the fact of an original æsthetic feeling for symmetry is established by the study of primitive art, and the theory of the balance of motor impulses through the substitution of factors is established by the experimental treatment of isolated elements, and further confirmed by the analysis of pictures, the general argument may be taken as sufficiently supported. This paper, then, will contain three sections: an introductory one on symmetry in primitive art, and two main sections, one on experiments in substitutional symmetry, and one on substitutional symmetry or balance in pictures.

II. SYMMETRY IN PRIMITIVE ART.

The question which this section will attempt to answer is this: Is there in primitive art an original and immediate æsthetic feeling for symmetry? This question depends on two others which must precede it: To what extent does symmetry actually appear in primitive art? and, How far must its presence be accounted for by other than æsthetic demands?

For the purpose of this inquiry the word _primitive_ may be taken broadly as applying to the products of savage and half-savage peoples of to-day, as well as to those of prehistoric races. The expression _primitive art_, also, requires a word of explanation. The primitive man seldom makes purely ornamental objects, but, on the other hand, most of his articles of daily use have an ornamental character. We have to consider primitive art, therefore, as represented in the form and ornamentation of all these objects, constituting practically an household inventory, with the addition of certain drawings and paintings which do not appear to serve a definite practical end. These last, however, constitute only a small proportion of the material.

The method of the following outline treatment will be to deduct from the object under consideration those symmetrical elements which seem to be directly traceable to non-æsthetic influences; such elements as are not thus to be accounted for must be taken as evidence of a direct pleasure in, and desire for symmetry on the part of primitive man. These possible non-æsthetic influences may be provisionally suggested to be the technical conditions of construction, the greater convenience and hence desirability of symmetrical objects for practical use, and the symmetrical character of natural forms which were imitated.

The first great group of objects is given in primitive architecture. Here is found almost complete unanimity of design, the conical, hemispherical or beehive form being well-nigh universal. The hut of the Hottentots, a cattle-herding, half-nomadic people, is a good type of this. A circle of flexible staves is stuck into the ground, bent together and fastened at the top, and covered with skins. But this is the form of shelter constructed with the greatest ease, suitable to the demands of elastic materials, boughs, twigs, reeds, etc., and giving the greatest amount of space with the least material. There are, indeed, a few examples of the rectangular form of dwelling among various primitive races, but these seem to be more or less open to explanation by the theory advanced by Mr. V. Mendeleff, of the U.S. Bureau of Ethnology. "In his opinion the rectangular form of architecture which succeeds the type under discussion, must have resulted from the circular form by the bringing together within a limited area of many houses.... This partition would naturally be built straight as a two-fold measure of economy."[2] This opinion is confirmed by Mr. Cushing's observations among the Zuñi villages, where the pueblos have circular forms on the outskirts. Thus the shape of the typical primitive dwelling is seen to be fully accounted for as the product of practical considerations alone. It may therefore be dismissed as offering no especial points of interest for this inquiry.

[2] Cushing, F.H.: 'Pueblo Pottery and Zuñi Culture-growth,'
Rep. of Bur. of Ethnol., 1882-3, p. 473.

Next in the order of primitive development are the arts of binding and weaving. The stone axe or arrow-head, for example, was bound to a wooden staff, and had to be lashed with perfect evenness,[3] and when in time the material and method of fastening changed, the geometrical forms of this careful binding continued to be engraved at the juncture of blade and handle of various implements. It should be noted, however, that these binding-patterns, in spite of their superfluous character, remained symmetrical.

[3] Haddon, A.C.: 'Evolution in Art,' London, 1895, pp. 84 ff.

On the great topic of symmetry in weaving, monographs could be written. Here it is sufficient to recall[4] that the absolutely necessary technique of weaving in all its various forms of interlacing, plaiting, netting, embroidering, etc., implies order, uniformity, and symmetry. The chance introduction of a thread or withe of a different color, brings out at once an ordered pattern in the result; the crowding together or pressing apart of elements, a different alternation of the woof, a change in the order of intersection, all introduce changes by the natural necessities of construction which have the effect of purpose. So far, then, as the simple weaving is concerned, the æsthetic demand for symmetry may be discounted. While it may be operative, the forms can be explained by the necessities of construction, and we have no right to assume an æsthetic motive.

[4] Holmes, W.H.: 'Textile Art in its Relation to the
Development of Form and Ornament,' Rep. of Bur. of Ethnol.,
1884-5, p. 195.

The treatment of human and animal forms in weaving is, however, indicative of a direct pleasure in symmetry. The human form appears almost exclusively (much schematized) _en face_. When in profile, as for instance in Mexican and South American work, it is doubled--that is, two figures are seen face to face. Animal figures, on the other hand, are much used as row-ornaments in profile.[5] It would seem that only the linear conception of the row or band with its suggestions of movement in one direction, justified the use of profile (_e.g._, in Peruvian woven stuffs), since it is almost always seen under those conditions, indicating that a limited rectangular space is felt as satisfactorily filled only by a symmetrical figure.[6] Moreover, and still more confirmatory of this theory, even these row-pattern profiles are immensely distorted toward symmetry, and every 'degradation' of form, to use Professor Haddon's term, is in the direction of symmetry. (See Fig. 1.)

[5] Reiss, W., und Stubel, A.: 'Todtenfeld von Ancon,' Berlin,
1880-7, Bd. II.

[6] Hein, W.: 'Die Verwendung der Menschen-Gestalt in
Flechtwerken,' Mitteil. d. Anthrop. Gesellsch. in Wien, Bd.
XXI.

The shape of primitive pottery is conditioned by the following influences: The shapes of utensils preceding clay, such as skins, gourds, shells, etc., which have been imitated, the forms of basket models, and the conditions of construction (formation by the hands). For all these reasons, most of these shapes are circular. The only (in the strict sense) symmetrical shapes found are of unmistakably animal origin, and it is interesting to notice the gradual return of these to the eurhythmic form; puma, bird, frog, etc., gradually changing into head, tail and leg excrescences, and then handles and nodes (rectangular panels), upon a round bowl or jar L, as shown in the figures. In fact, in ancient American pottery,[7] at least, all the symmetrical ornamentations can be traced to the opposition of head and tail, and the sides between them, of these animal forms. But beyond this there is no degradation of the broad outline of the design. The head and tail, and sides, become respectively handles and nodes--but the symmetry becomes only more and more emphasized. And as in the case of textiles, the ornaments of the rectangular spaces given by the nodes are strikingly symmetrical. Many of these are from animal motives, and nearly always heads are turned back over the body, tails exaggerated, or either or both doubled, to get a symmetrical effect. Although much of the symmetrical ornament, again, is manifestly from textile models, its symmetrical character is so carefully preserved against the suggestions of the circular form that a direct pleasure in its symmetry may be inferred. (See Figs. 2-7.)

[7] Cushing, F.H.: _op. cit._; Holmes, W.H.: three articles on
pottery, Rep. of Bur. of Ethnol., 1882-83, p. 265, p. 367, and
p. 443.

The subject of drawing can be here only touched upon, but the results of study go to show, in general, two main directions of primitive expression: pictorial representation, aiming at truth of life, and symbolic ornament. The drawings of Australians, Hottentots and Bushmen, and the carvings of the Esquimaux and of the prehistoric men of the reindeer period show remarkable vigor and naturalness; while the ornamentation of such tribes as the South Sea Islanders has a richness and formal beauty that compare favorably with the decoration of civilized contemporaries. But these two types of art do not always keep pace with each other. The petroglyphs of the North American Indians[8] exhibit the greatest irregularity, while their tattooing is extremely regular and symmetrical. The Brazilian savage [9] draws freehand in a very lively and grotesque manner, but his patterns are regular and carefully developed. Again, not all have artistic talents in the same direction. Dr. Schurtz, in his 'Ornamentik der Aino,'[10] says: "There are people who show a decided impulse for the direct imitation of nature, and especially for the representation of events of daily life, as dancing, hunting, fishing, etc. It is, however, remarkable that a real system of ornamentation is scarcely ever developed from pictorial representations of this kind; that, in fact, the people who carry out these copies of everyday scenes with especial preference, are in general less given to covering their utensils with a rich ornamentive decoration."[11] Drawing and ornament, as the products of different tendencies, may therefore be considered separately.

[8] Mallery, Garrick: 'Pictographs of the North American
Indians,' Rep. of Bur. of Ethnol., 1882-3, p. 13.

[9] Von den Steinen, Karl: 'Unter den Naturvôlkern
Zentral-Brasiliens,' Berlin, 1894.

[10] _Internal. Archiv s. Ethnog._, Bd. IX.

[11] Cf. Andrée, Richard: 'Ethnographische Parallelen,' Neue
Folge, Leipzig, 1889, S. 59.

The reason for the divergence of drawing and ornament is doubtless the original motive of ornamentation, which is found in the clan or totem ideas. Either to invoke protection or to mark ownership, the totem symbol appears on all instruments and utensils; it has been shown, indeed, that practically all primitive ornament is based on totemic motives.[12] Now, since a very slight suggestion of the totem given by its recognized symbol is sufficient for the initiated, the extreme of conventionalization and degradation of patterns is allowable, and is observed to take place. The important point to be noted in this connection is, however, that all these changes are toward symmetry. The most striking examples might be indefinitely multiplied, and are to be found in the appended references (see Figs. 8 and 9).

[12] Haddon, _op. cit._; Frazer, J.G.: 'Totemism,' 1887;
Grosse, Ernst: Anfänge der Kunst,' Freiburg i. B. u. Leipzig,
1894.

We may distinguish here, also, between the gradual disintegration and degradation of pattern toward symmetry, as seen in the examples just given, and the deliberate distortion of figures for a special purpose. This is strikingly shown in the decorative art of the Indians of the North Pacific coast. They systematically represent their totem animals--their only decorative motives--as split in symmetrical sections, and opened out flat on the surface which is to be covered[13] (see Fig. 11). Dr. Boas argues that their purpose is to get in all the received symbols, or to show the whole animal, but, however this may be, every variation introduces symmetry even where it is difficult to do so, as in the case, for instance, of bracelets, hat-brims, etc. (Fig. 10). This may in some cases be due to the symmetrical suggestions of the human body in tattooing,[14] but it must be so in comparatively few.

[13] Boas, Franz: 'Decorative Art of the Indians of the North Pacific Coast,' _Bulletin_ of Am. Mus. of Nat. Hist., Vol. IX.

[14] Mallery, G.: _op. cit._; Haddon, A.C.: _op. cit._, p. 257; 'Decorative Art of British New Guinea,' Cunningham Memoir X., Royal Irish Acad., 1894, p. 26.

The primitive picture has for its object not only to impart information, but to excite the very definite pleasure of recognition of a known object. All explorers agree in their accounts of the savage's delight in his own naïve efforts at picture making. All such drawings show in varying degrees the same characteristics; first of all, an entire lack of symmetry. In a really great number of examples, including drawings and picture-writing from all over the world, I have not found one which showed an attempt at symmetrical arrangement. Secondly, great life and movement, particularly in the drawings of animals. Thirdly, an emphasis of the typical characteristics, the logical marks, amounting sometimes to caricature. The primitive man draws to tell a story, as children do. He gives with real power what interests him, and puts in what he knows ought to be there, even if it is not seen, but he is so engrossed by his interest in the imitated object as to neglect entirely its relation to a background.

Now, this very antithesis of ornament and picture is enlightening as to the dawn of æsthetic feeling, and the strongest confirmation of our hypothesis of an original impulse to symmetry in art. In the ornamentation of objects the content or meaning of the design is already supplied by the merest hint of the symbol which is the practical motive of all ornamentation. The savage artist need, therefore, concern himself no more about it, and the form of his design is free to take whatever shape is demanded either by the conditions of technique and the surface to be ornamented, or by the natural æsthetic impulse. We have found that technical conditions account for only a small part of the observed symmetry in pattern, and the inference to a natural tendency to symmetry is clear. Pictorial representation, on the other hand, is enjoyed by the primitive man merely as an imitation, of which he can say, 'This is that animal'--to paraphrase Aristotle's Poetics. He is thus constrained to reproduce the form as it shows meaning, and to ignore it as form, or as his natural motor impulses would make it.