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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 twofold 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

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