420 



SCIENCE. 



[Vol. VIII., No. 196 



a class of aesthetic impressions depending pre- 

 eminently on the sensations furnished by the great 

 aesthetic educators of the race, — the eye and the 

 ear. It is to the explanation of these simple forms 

 of beauty that M. J. L. Soret devoted an address 

 delivered before the Swiss society of natural 

 science.^ The field is by no means anew one, but 

 perhaps so convenient a statement of the problem 

 has not before been available. 



The arts depending upon the eye are those in 

 which form is the predominant element, — sculp- 

 ture, architecture, etc. , — and those in which color 

 plays the important role. If we look for the phy- 

 siological basis of beauty of form, we find one 

 great principle in symmetry, especially in sym- 

 metry about a vertical axis. If we stand in this 

 jDlane of the vertical axis, and look at the sym- 

 metrical object, the impression on the retina of 

 the right eye will closely correspond to that on the 

 retina of the left eye. The recognition of simi- 

 larity, so essential and useful as a logical habit of 

 mind, seems at the same time to furnish the emo- 

 tional element of aesthetic pleasure. The fact 

 that we recognize and enjoy symmetry when not 

 standing opposite the centre of the object is the 

 result of our education : we recognize that the two 

 retinal impressions would be alike if we assumed 

 that position. 



It may be well to introduce here a distinction 

 between intellectual and aesthetic pleasure, in 

 which M. Soret has great confidence. It is this : 

 the pleasure caused by the solution of a problem 

 is due to a conscious reasoned analysis ; an 

 aesthetic pleasure is caused by an unconscious 

 intuited analysis. The one is laboriously and 

 slowly wrought out : the other is readily and sud- 

 denly revealed. This distinction is best illustrated, 

 as will be seen, in the analysis of tone : the 

 analysis of form is so simple that we can readily 

 perform it consciously. 



Proceeding with this analysis, we find a second 

 principle in the repetition of design. It leads to 

 the mathematical conception of a periodic func- 

 tion. We see it represented in friezes, in a series 

 of columns, in ornaments, etc., even in those 

 belonging to the most primitive periods of art. 

 As before, there is the recognition of. similarity ; 

 and, as before, this similarity may be greatly di- 

 versified, so long as the artistic education of the 

 beholder enables him to recognize the fundamental 

 regularity. A third character of beauty of form 

 is continuity of lines and surface : a straight 

 line is an important artistic element. This is again 

 a repetition of design, for the several parts of a 

 straight line are again straight. 



W^hat, then, is the origin of this intuition that 

 1 Revue scientifique, Sept. 2, 1886. 



gives rise to aesthetic pleasure ? It is the recogni- 

 tion of equality, — the simplest conception fur- 

 nished by the senses. The ear recognizes when 

 two sounds are of the same pitch, as well as when 

 two intervals of time are alike : equalities of space 

 are appreciated by sight as well as by touch. This 

 recognition of equality, of the identity or the rep- 

 etition of two sensations, reveals an order in the 

 objective world, and the intuition of this regu- 

 larity gives pleasure. The degree of pleasure de- 

 pends on the universality and importance of the 

 regularity thus revealed, and on the vividness and 

 the variety of the sense-impressions. And what 

 we mean by ugliness is not the lack of regularity 

 which we see in a stone, for example : that is 

 aesthetically indifferent. But that is ugly in 

 which we recognize a law, but see that law vio- 

 lated. An unsuccessful attempt at symmetry is 

 ugly. A piece of goods in which the pattern to 

 be repeated shows irregularities in size and execu- 

 tion belongs in the same category. 



Passing now to sounds, we have simply to trans- 

 late the language of sj)ace into that of time. The 

 repetition of design finds its parallel in rhythm, 

 and both are capable of endless complications. 

 When we consider that poetry, music, dancing, 

 even ordinary speech, that the organic functions 

 such as the pulse, respiration, sleep, locomotion, 

 and many of the acquired habits of mind and 

 body, are all subject to a periodicity, the impor- 

 tance of rhythm is strongly impressed. Again : 

 the continuity of the straight line is paralleled by 

 that of the musical note. But here and in the 

 consideration of melody we touch upon a fact un- 

 paralleled in the world of sight (though there is a 

 slight analogy with color), and which owes its 

 complete discovery to the genius of Helmholtz. 

 The musical notes are not simple in their character, 

 but each is accompanied by a certain series of 

 overtones or harmonics which bear a definite rela- 

 tion to the fundamental note ; and it is a wonder- 

 ful fact that it is just this series of harmonics 

 that give rise to the octave and the musical scale ; 

 and the relative importance and distinctness of 

 the notes composing this series of harmonics is 

 exactly mii-rored in the historic development of 

 the scale from the earliest times to the present. 



Long before it was known that sound was a 

 periodic motion of vibrating air particles, in times 

 when the counting of these minute vibrations 

 would have been regarded as a miracle, the intui- 

 tional instinct of the untutored ear had already 

 selected that pair of notes the vibration rates of 

 which had the simplest ratio of one to two, as the 

 basis of aesthetic sounds. It had performed un- 

 consciously but correctly that analysis for the 

 conscious discovery of which we required aU the 



