THE SCIENCE OF BEAUTY.
EDINBURGH:
PRINTED BY BALLANTYNE AND COMPANY,
PAUL’S WORK.
THE
SCIENCE OF BEAUTY,
AS DEVELOPED IN NATURE AND
APPLIED IN ART.
BY
D. R. HAY, F.R.S.E.
“The irregular combinations of fanciful invention may delight
awhile, by that novelty of which the common satiety of life
sends us all in quest; the pleasures of sudden wonder are soon
exhausted, and the mind can only repose on the stability of
truth.”
DR JOHNSON.
WILLIAM BLACKWOOD AND SONS,
EDINBURGH AND LONDON.
MDCCCLVI.
TO
JOHN GOODSIR, ESQ., F.R.S S. L. & E.,
PROFESSOR OF ANATOMY IN THE UNIVERSITY OF EDINBURGH,
AS AN EXPRESSION OF GRATITUDE FOR VALUABLE ASSISTANCE,
AS ALSO OF HIGH ESTEEM AND SINCERE REGARD,
THIS VOLUME IS DEDICATED,
BY
THE AUTHOR.
PREFACE.
My theory of beauty in form and colour being now admitted by the best
authorities to be based on truth, I have of late been often asked, by
those who wished to become acquainted with its nature, and the manner of
its being applied in art, which of my publications I would recommend for
their perusal. This question I have always found difficulty in answering;
for although the law upon which my theory is based is characterised by
unity, yet the subjects in which it is applied, and the modes of its
application, are equally characterised by variety, and consequently
occupy several volumes.
Under these circumstances, I consulted a highly respected friend, whose
mathematical talents and good taste are well known, and to whom I have
been greatly indebted for much valuable assistance during the course
of my investigations. The advice I received on this occasion, was to
publish a _résumé_ of my former works, of such a character as not only
to explain the nature of my theory, but to exhibit to the general reader,
by the most simple modes of illustration and description, how it is
developed in nature, and how it may be extensively and with ease applied
in those arts in which beauty forms an essential element.
The following pages, with their illustrations, are the results of an
attempt to accomplish this object.
To those who are already acquainted, through my former works, with
the nature, scope, and tendency of my theory, I have the satisfaction
to intimate that I have been enabled to include in this _résumé_ much
original matter, with reference both to form and colour.
D. R. HAY.
CONTENTS.
PAGE
INTRODUCTION 1
THE SCIENCE OF BEAUTY, EVOLVED FROM THE HARMONIC LAW OF NATURE,
AGREEABLY TO THE PYTHAGOREAN SYSTEM OF NUMERICAL RATIO 15
THE SCIENCE OF BEAUTY, AS APPLIED TO SOUNDS 28
THE SCIENCE OF BEAUTY, AS APPLIED TO FORMS 34
THE SCIENCE OF BEAUTY, AS DEVELOPED IN THE FORM OF THE HUMAN HEAD
AND COUNTENANCE 54
THE SCIENCE OF BEAUTY, AS DEVELOPED IN THE FORM OF THE HUMAN FIGURE 61
THE SCIENCE OF BEAUTY, AS DEVELOPED IN COLOURS 67
THE SCIENCE OF BEAUTY APPLIED TO THE FORMS AND PROPORTIONS OF
ANCIENT GRECIAN VASES AND ORNAMENTS 82
APPENDIX, NO. I. 91
APPENDIX, NO. II. 99
APPENDIX, NO. III. 100
APPENDIX, NO. IV. 100
APPENDIX, NO. V. 104
APPENDIX, NO. VI. 105
ILLUSTRATIONS.
PLATES
[Illustration: I. Three Scales of the Elementary Rectilinear Figures,
viz., the Scalene Triangle, the Isosceles Triangle, and the Rectangle,
comprising twenty-seven varieties of each, according to the harmonic
parts of the Right Angle from ¹⁄₂ to ¹⁄₁₆.
_D. R. Hay delᵗ._ _G. Aikman sc._]
[Illustration: II. Diagram of the Rectilinear Orthography of the
Principal Front of the Parthenon of Athens, in which its Proportions are
determined by harmonic parts of the Right Angle.
_D. R. Hay delᵗ._ _G. Aikman sc._]
[Illustration: III. Diagram of the Rectilinear Orthography of the
Portico of the Temple of Theseus at Athens, in which its Proportions are
determined by harmonic parts of the Right Angle.
_D. R. Hay delᵗ._ _G. Aikman sc._]
[Illustration: IV. Diagram of the Rectilinear Orthography of the East End
of Lincoln Cathedral, in which its Proportions are determined by harmonic
parts of the Right Angle.
_D. R. Hay delᵗ._ _G. Aikman sc._]
[Illustration: V. Four Ellipses described from Foci, determined by
harmonic parts of the Right Angle, shewing in each the Scalene Triangle,
the Isosceles Triangle, and the Rectangle to which it belongs.
_D. R. Hay delᵗ._ _G. Aikman sc._]
[Illustration: VI. The Composite Ellipse of ¹⁄₆ and ¹⁄₈ of the Right
Angle, shewing its greater and lesser Axis, its various Foci, and the
Isosceles Triangle in which they are placed.
_D. R. Hay delᵗ._ _G. Aikman sc._]
[Illustration: VII. The Composite Ellipse of ¹⁄₄₈ and ¹⁄₆₄ of the Right
Angle, shewing how it forms the Entasis of the Columns of the Parthenon
of Athens.
_D. R. Hay delᵗ._ _G. Aikman sc._]
[Illustration: VIII. Sectional Outlines of two Mouldings of the Parthenon
of Athens, full size, shewing the harmonic nature of their Curves, and
the simple manner of their Construction.
_D. R. Hay delᵗ._ _G. Aikman sc._]
[Illustration: IX. Three Diagrams, giving a Vertical, a Front, and a Side
Aspect of the Geometrical Construction of the Human Head and Countenance,
in which the Proportions are determined by harmonic parts of the Right
Angle.
_D. R. Hay delᵗ._ _G. Aikman sc._]
[Illustration: X. Diagram in which the Symmetrical Proportions of the
Human Figure are determined by harmonic parts of the Right Angle.
_D. R. Hay delᵗ._ _G. Aikman sc._]
[Illustration: XI. The Contour of the Human Figure as viewed in Front
and in Profile, its Curves being determined by Ellipses, whose Foci are
determined by harmonic parts of the Right Angle.
_D. R. Hay delᵗ._ _G. Aikman sc._]
[Illustration: XII. Rectilinear Diagram, shewing the Proportions of the
Portland Vase, as determined by harmonic parts of the Right Angle, and
the outline of its form by an Elliptic Curve harmonically described.
_D. R. Hay delᵗ._ _G. Aikman sc._]
[Illustration: XIII. Rectilinear Diagram of the Proportions and
Curvilinear Outline of the form of an ancient Grecian Vase, the
proportions determined by harmonic parts of the Right Angle, and the
melody of the form by Curves of two Ellipses.
_D. R. Hay delᵗ._ _G. Aikman sc._]
[Illustration: XIV. Rectilinear Diagram of the Proportions and
Curvilinear Outline of the form an ancient Grecian Vase, the proportions
determined by harmonic parts of the Right Angle, and the melody of the
form by an Elliptic Curve.
_D. R. Hay delᵗ._ _G. Aikman sc._]
[Illustration: XV. Two Diagrams of Etruscan Vases, the harmony of
Proportions and melody of the Contour determined, respectively, by parts
of the Right Angle and an Elliptic Curve.
_D. R. Hay delᵗ._ _G. Aikman sc._]
[Illustration: XVI. Two Diagrams of Etruscan Vases, whose harmony of
Proportion and melody of Contour are determined as above.
_D. R. Hay delᵗ._ _G. Aikman sc._]
[Illustration: XVII. Diagram shewing the Geometric Construction of an
Ornament belonging to the Parthenon at Athens.
_D. R. Hay delᵗ._ _G. Aikman sc._]
[Illustration: XVIII. Diagram of the Geometrical Construction of the
ancient Grecian Ornament called the Honeysuckle.
_D. R. Hay delᵗ._ _G. Aikman sc._]
[Illustration: XIX. An additional Illustration of the Contour of the
Human Figure, as viewed in Front and in Profile.
_D. R. Hay delᵗ._ _G. Aikman sc._]
[Illustration: XX. Diagram shewing the manner in which the Elliptic
Curves are arranged in order to produce an Outline of the Form of the
Human Figure as viewed in Front.
_D. R. Hay delᵗ._ _G. Aikman sc._]
[Illustration: XXI. Diagram of a variation on the Form of the Portland
Vase.
_D. R. Hay delᵗ._ _G. Aikman sc._]
[Illustration: XXII. Diagram of a second variation on the Form of the
Portland Vase.
_D. R. Hay delᵗ._ _G. Aikman sc._]
[Illustration: XXIII. Diagram of a third variation on the Form of the
Portland Vase.
_D. R. Hay delᵗ._ _G. Aikman sc._]
INTRODUCTION.
Twelve years ago, one of our most eminent philosophers,[1] through the
medium of the _Edinburgh Review_,[2] gave the following account of what
was then the state of the fine arts as connected with science:—“The
disposition to introduce into the intellectual community the principles
of free intercourse, is by no means general; but we are confident that
Art will not sufficiently develop her powers, nor Science attain her
most commanding position, till the practical knowledge of the one is
taken in return for the sound deductions of the other.... It is in the
fine arts, principally, and in the speculations with which they are
associated, that the controlling power of scientific truth has not
exercised its legitimate influence. In discussing the principles of
painting, sculpture, architecture, and landscape gardening, philosophers
have renounced science as a guide, and even as an auxiliary; and a
school has arisen whose speculations will brook no restraint, and whose
decisions stand in opposition to the strongest convictions of our
senses. That the external world, in its gay colours and lovely forms, is
exhibited to the mind only as a tinted mass, neither within nor without
the eye, neither touching it nor distant from it—an ubiquitous chaos,
which experience only can analyse and transform into the realities
which compose it; that the beautiful and sublime in nature and in art
derive their power over the mind from association alone, are among the
philosophical doctrines of the present day, which, if it be safe, it is
scarcely prudent to question. Nor are these opinions the emanations of
poetical or ill-trained minds, which ingenuity has elaborated, and which
fashion sustains. They are conclusions at which most of our distinguished
philosophers have arrived. They have been given to the world with all the
authority of demonstrated truth; and in proportion to the hold which they
have taken of the public mind, have they operated as a check upon the
progress of knowledge.”
Such, then, was the state of art as connected with science twelve years
ago. But although the causes which then placed science and the fine arts
at variance have since been gradually diminishing, yet they are still
far from being removed. In proof of this I may refer to what took place
at the annual distribution of the prizes to the students attending our
Scottish Metropolitan School of Design, in 1854, the pupils in which
amount to upwards of two hundred. The meeting on that occasion included,
besides the pupils, a numerous and highly respectable assemblage of
artists and men of science. The chairman, a Professor in our University,
and editor of one of the most voluminous works on art, science, and
literature ever produced in this country, after extolling the general
progress of the pupils, so far as evinced by the drawings exhibited on
the occasion, drew the attention of the meeting to a discovery made by
the head master of the architectural and ornamental department of the
school, viz.—That the ground-plan of the Parthenon at Athens had been
constructed by the application of the _mysterious_ ovoid or _Vesica
Piscis_ of the middle ages, subdivided by the _mythic_ numbers 3 and 7,
and their intermediate odd number 5. Now, it may be remarked, that the
figure thus referred to is not an ovoid, neither is it in any way of a
mysterious nature, being produced simply by two equal circles cutting
each other in their centres. Neither can it be shewn that the numbers 3
and 7 are in any way more mythic than other numbers. In fact, the terms
_mysterious_ and _mythic_ so applied, can only be regarded as a remnant
of an ancient terminology, calculated to obscure the simplicity of
scientific truth, and when used by those employed to teach—for doubtless
the chairman only gave the description he received—must tend to retard
the connexion of that truth with the arts of design. I shall now give
a specimen of the manner in which a knowledge of the philosophy of the
fine arts is at present inculcated upon the public mind generally. In
the same metropolis there has likewise existed for upwards of ten years
a Philosophical Institution of great importance and utility, whose
members amount to nearly three thousand, embracing a large proportion
of the higher classes of society, both in respect to talent and wealth.
At the close of the session of this Institution, in 1854, a learned and
eloquent philologus, who occasionally lectures upon beauty, was appointed
to deliver the closing address, and touching upon the subject of the
beautiful, he thus concluded—
“In the worship of the beautiful, and in that alone, we are inferior to
the Greeks. Let us therefore be glad to borrow from them; not slavishly,
but with a wise adaptation—not exclusively, but with a cunning selection;
in art, as in religion, let us learn to prove all things, and hold fast
that which is good—not merely one thing which is good, but all good
things—Classicalism, Mediævalism, Modernism—let us have and hold them
all in one wide and lusty embrace. Why should the world of art be
more narrow, more monotonous, than the world of nature? Did God make
all the flowers of one pattern, to please the devotees of the rose or
the lily; and did He make all the hills, with the green folds of their
queenly mantles, all at one slope, to suit the angleometer of the most
mathematical of decorators? I trow not. Let us go and do likewise.”
I here take for granted, that what the lecturer meant by “the worship of
the beautiful,” is the production and appreciation of works of art in
which beauty should be a primary element; and judging from the remains
which we possess of such works as were produced by the ancient Grecians,
our inferiority to them in these respects cannot certainly be denied.
But I must reiterate what I have often before asserted, that it is
not by borrowing from them, however cunning our selection, or however
wise our adaptations, that this inferiority is to be removed, but by
a re-discovery of the science which these ancient artists must have
employed in the production of that symmetrical beauty and chaste elegance
which pervaded all their works for a period of nearly three hundred
years. And I hold, that as in religion, so in art, there is only one
truth, a grain of which is worth any amount of philological eloquence.
I also take for granted, that what is meant by Classicalism in the
above quotation, is the ancient Grecian style of art; by Mediævalism,
the semi-barbaric style of the middle ages; and by Modernism, that
chaotic jumble of all previous styles and fashions of art, which is the
peculiar characteristic of our present school, and which is, doubtless,
the result of a system of education based upon plagiarism and mere
imitation. Therefore a recommendation to embrace with equal fervour “as
good things,” these very opposite artic_isms_ must be a doctrine as
mischievous in art as it would be in religion to recommend as equally
good things the various _isms_ into which it has also been split in
modern times.
Now, “the world of nature” and “the world of art” have not that equality
of scope which this lecturer on beauty ascribes to them, but differ very
decidedly in that particular. Neither will it be difficult to shew why
“the world of art _should_ be more narrow than the world of nature”—that
it should be thereby rendered more monotonous does not follow.
It is well known, that the “world of nature” consists of productions,
including objects of every degree of beauty from the very lowest to the
highest, and calculated to suit not only the tastes arising from various
degrees of intellect, but those arising from the natural instincts of the
lower animals. On the other hand, “the world of art,” being devoted to
the gratification and improvement of intelligent minds only, is therefore
narrowed in its scope by the exclusion from its productions of the lower
degrees of beauty—even mediocrity is inadmissible; and we know that the
science of the ancient Greek artists enabled them to excel the highest
individual productions of nature in the perfection of symmetrical beauty.
Consequently, all objects in nature are not equally well adapted for
artistic study, and it therefore requires, on the part of the artist,
besides true genius, much experience and care to enable him to choose
proper subjects from nature; and it is in the choice of such subjects,
and not in plagiarism from the ancients, that he should select with
knowledge and adapt with wisdom. Hence, all such latitudinarian doctrines
as those I have quoted must act as a check upon the progress of knowledge
in the scientific truth of art. I have observed in some of my works, that
in this country a course had been followed in our search for the true
science of beauty not differing from that by which the alchymists of the
middle ages conducted their investigations; for our ideas of visible
beauty are still undefined, and our attempts to produce it in the various
branches of art are left dependant, in a great measure, upon chance.
Our schools are conducted without reference to any first principles or
definite laws of beauty, and from the drawing of a simple architectural
moulding to the intricate combinations of form in the human figure, the
pupils trust to their hands and eyes alone, servilely and mechanically
copying the works of the ancients, instead of being instructed in the
unerring principles of science, upon which the beauty of those works
normally depends. The instruction they receive is imparted without
reference to the judgment or understanding, and they are thereby led to
imitate effects without investigating causes. Doubtless, men of great
genius sometimes arrive at excellence in the arts of design without a
knowledge of the principles upon which beauty of form is based; but it
should be kept in mind, that true genius includes an intuitive perception
of those principles along with its creative power. It is, therefore, to
the generality of mankind that instruction in the definite laws of beauty
will be of most service, not only in improving the practice of those who
follow the arts professionally, but in enabling all of us to distinguish
the true from the false, and to exercise a sound and discriminating
taste in forming our judgment upon artistic productions. Æsthetic
culture should consequently supersede servile copying, as the basis of
instruction in our schools of art. Many teachers of drawing, however,
still assert, that, by copying the great works of the ancients, the mind
of the pupil will become imbued with ideas similar to theirs—that he
will imbibe their feeling for the beautiful, and thereby become inspired
with their genius, and think as they thought. To study carefully and
to investigate the principles which constitute the excellence of the
works of the ancients, is no doubt of much benefit to the student; but
it would be as unreasonable to suppose that he should become inspired
with artistic genius by merely copying them, as it would be to imagine,
that, in literature, poetic inspiration could be created by making boys
transcribe or repeat the works of the ancient poets. Sir Joshua Reynolds
considered copying as a delusive kind of industry, and has observed, that
“Nature herself is not to be too closely copied,” asserting that “there
are excellences in the art of painting beyond what is commonly called the
imitation of nature,” and that “a mere copier of nature can never produce
any thing great.” Proclus, an eminent philosopher and mathematician of
the later Platonist school (A.D. 485), says, that “he who takes for his
model such forms as nature produces, and confines himself to an exact
imitation of these, will never attain to what is perfectly beautiful. For
the works of nature are full of disproportion, and fall very short of the
true standard of beauty.”
It is remarked by Mr. J. C. Daniel, in the introduction to his
translation of M. Victor Cousin’s “Philosophy of the Beautiful,” that
“the English writers have advocated no theory which allows the beautiful
to be universal and absolute; nor have they professedly founded their
views on original and ultimate principles. Thus the doctrine of the
English school has for the most part been, that beauty is mutable and
special, and the inference that has been drawn from this teaching is,
that all tastes are equally just, provided that each man speaks of what
he feels.” He then observes, that the German, and some of the French
writers, have thought far differently; for with them the beautiful is
“simple, immutable, absolute, though its _forms_ are manifold.”
So far back as the year 1725, the same truths advanced by the modern
German and French writers, and so eloquently illustrated by M. Cousin,
were given to the world by Hutchison in his “Inquiry into the Original
of our Ideas of Beauty and Virtue.” This author says—“We, by absolute
beauty, understand only that beauty which we perceive in objects, without
comparison to any thing external, of which the object is supposed an
imitation or picture, such as the beauty perceived from the works of
nature, artificial forms, figures, theorems. Comparative or relative
beauty is that which we perceive in objects commonly considered as
imitations or resemblances of something else.”
Dr. Reid also, in his “Intellectual Powers of Man,” says—“That taste,
which we may call rational, is that part of our constitution by which we
are made to receive pleasure from the contemplation of what we conceive
to be excellent in its kind, the pleasure being annexed to this judgment,
and regulated by it. This taste may be true or false, according as it is
founded on a true or false judgment. And if it may be true or false, it
must have first principles.”
M. Victor Cousin’s opinion upon this subject is, however, still more
conclusive. He observes—“If the idea of the beautiful is not absolute,
like the idea of the true—if it is nothing more than the expression of
individual sentiment, the rebound of a changing sensation, or the result
of each person’s fancy—then the discussions on the fine arts waver
without support, and will never end. For a theory of the fine arts to
be possible, there must be something absolute in beauty, just as there
must be something absolute in the idea of goodness, to render morals a
possible science.”
The basis of the science of beauty must thus be founded upon fixed
principles, and when these principles are evolved with the same care
which has characterised the labours of investigators in natural science,
and are applied in the fine arts as the natural sciences have been in
the useful arts, a solid foundation will be laid, not only for correct
practice, but also for a just appreciation of productions in every branch
of the arts of design.
We know that the mind receives pleasure through the sense of hearing,
not only from the music of nature, but from the euphony of prosaic
composition, the rhythm of poetic measure, the artistic composition
of successive harmony in simple melody, and the combined harmony of
counterpoint in the more complex works of that art. We know, also,
that the mind is similarly gratified through the sense of seeing, not
only by the visible beauties of nature, but by those of art, whether
in symmetrical or picturesque compositions of forms, or in harmonious
arrangements of gay or sombre colouring.
Now, in respect to the first of these modes of sensation, we know,
that from the time of Pythagoras, the fact has been established, that
in whatever manner nature or art may address the ear, the degree of
obedience paid to the fundamental law of harmony will determine the
presence and degree of that beauty with which a perfect organ can impress
a well-constituted mind; and it is my object in this, as it has been
in former attempts, to prove it consistent with scientific truth, that
that beauty which is addressed to the mind by objects of nature and art,
through the eye, is similarly governed. In short, to shew that, as in
compositions of sounds, there can be no true beauty in the absence of a
strict obedience to this great law of nature, neither can there exist,
in compositions of forms or colours, that principle of unity in variety
which constitutes beauty, unless such compositions are governed by the
same law.
Although in the songs of birds, the gurgling of brooks, the sighing of
the gentle summer winds, and all the other beautiful music of nature,
no analysis might be able to detect the operation of any precise system
of harmony, yet the pleasure thus afforded to the human mind we know to
arise from its responding to every development of an obedience to this
law. When, in like manner, we find even in those compositions of forms
and colours which constitute the wildest and most rugged of Nature’s
scenery, a species of picturesque grandeur and beauty to which the mind
as readily responds as to her more mild and pleasing aspects, or to her
sweetest music, we may rest assured that this beauty is simply another
development of, and response to, the same harmonic law, although the
precise nature of its operation may be too subtle to be easily detected.
The _résumé_ of the various works I have already published upon the
subject, along with the additional illustrations I am about to lay before
my readers, will, I trust, point out a system of harmony, which, in
formative art, as well as in that of colouring, will rise superior to the
idiosyncracies of different artists, and bring back to one common type
the sensations of the eye and the ear, thereby improving that knowledge
of the laws of the universe which it is as much the business of science
to combine with the ornamental as with the useful arts.
In attempting this, however, I beg it may be understood, that I do not
believe any system, based even upon the laws of nature, capable of
forming a royal road to the perfection of art, or of “mapping the mighty
maze of a creative mind.” At the same time, however, I must continue to
reiterate the fact, that the diffusion of a general knowledge of the
science of visible beauty will afford latent artistic genius just such a
vantage ground as that which the general knowledge of philology diffused
throughout this country affords its latent literary genius. Although
_mere learning_ and _true genius_ differ as much in the practice of art
as they do in the practice of literature, yet a precise and systematic
education in the true science of beauty must certainly be as useful in
promoting the practice and appreciation of the one, as a precise and
systematic education in the science of philology is in promoting the
practice and appreciation of the other.
As all beauty is the result of harmony, it will be requisite here to
remark, that harmony is not a simple quality, but, as Aristotle defines
it, “the union of contrary principles having a ratio to each other.”
Harmony thus operates in the production of all that is beautiful in
nature, whether in the combinations, in the motions, or in the affinities
of the elements of matter.
The contrary principles to which Aristotle alludes, are those of
uniformity and variety; for, according to the predominance of the one or
the other of these principles, every kind of beauty is characterised.
Hence the difference between symmetrical and picturesque beauty:—the
first allied to the principle of uniformity, in being based upon precise
laws that may be taught so as to enable men of ordinary capacity to
produce it in their works—the second allied to the principle of variety
often to so great a degree that they yield an obedience to the precise
principles of harmony so subtilely, that they cannot be detected in its
constitution, but are only felt in the response by which true genius
acknowledges their presence. The generality of mankind may be capable
of perceiving this latter kind of beauty, and of feeling its effects
upon the mind, but men of genius, only, can impart it to works of art,
whether addressed to the eye or the ear. Throughout the sounds, forms,
and colours of nature, these two kinds of beauty are found not only in
distinct developments, but in every degree of amalgamation. We find in
the songs of some birds, such as those of the chaffinch, thrush, &c.,
a rhythmical division, resembling in some measure the symmetrically
precise arrangements of parts which characterises all artistic musical
composition; while in the songs of other birds, and in the other numerous
melodies with which nature charms and soothes the mind, there is no
distinct regularity in the division of their parts. In the forms of
nature, too, we find amongst the innumerable flowers with which the
surface of the earth is so profusely decorated, an almost endless variety
of systematic arrangements of beautiful figures, often so perfectly
symmetrical in their combination, that the most careful application
of the angleometer could scarcely detect the slightest deviation from
geometrical precision; while, amongst the masses of foliage by which
the forms of many trees are divided and subdivided into parts, as also
amongst the hills and valleys, the mountains and ravines, which divide
the earth’s surface, we find in every possible variety of aspect the
beauty produced by that irregular species of symmetry which characterises
the picturesque.
In like manner, we find in wild as well as cultivated flowers the
most symmetrical distributions of colours accompanying an equally
precise species of harmony in their various kinds of contrasts, often
as mathematically regular as the geometric diagrams by which writers
upon colour sometimes illustrate their works; while in the general
colouring of the picturesque beauties of nature, there is an endless
variety in its distributions, its blendings, and its modifications. In
the forms and colouring of animals, too, the same endless variety of
regular and irregular symmetry is to be found. But the highest degree of
beauty in nature is the result of an equal balance of uniformity with
variety. Of this the human figure is an example; because, when it is
of those proportions universally acknowledged to be the most perfect,
its uniformity bears to its variety an apparently equal ratio. The
harmony of combination in the normal proportions of its parts, and the
beautifully simple harmony of succession in the normal melody of its
softly undulating outline, are the perfection of symmetrical beauty,
while the innumerable changes upon the contour which arise from the
actions and attitudes occasioned by the various emotions of the mind,
are calculated to produce every species of picturesque beauty, from the
softest and most pleasing to the grandest and most sublime.
Amongst the purely picturesque objects of inanimate nature, I may, as in
a former work, instance an ancient oak tree, for its beauty is enhanced
by want of apparent symmetry. Thus, the more fantastically crooked its
branches, and the greater the dissimilarity and variety it exhibits in
its masses of foliage, the more beautiful it appears to the artist and
the amateur; and, as in the human figure, any attempt to produce variety
in the proportions of its lateral halves would be destructive of its
symmetrical beauty, so in the oak tree any attempt to produce palpable
similarity between any of its opposite sides would equally deteriorate
its picturesque beauty. But picturesque beauty is not the result of the
total absence of symmetry; for, as none of the irregularly constructed
music of nature could be pleasing to the ear unless there existed in
the arrangement of its notes an obedience, however subtle, to the great
harmonic law of Nature, so neither could any object be picturesquely
beautiful, unless the arrangement of its parts yields, although it may be
obscurely, an obedience to the same law.
However symmetrically beautiful any architectural structure may be, when
in a complete and perfect state, it must, as it proceeds towards ruin,
blend the picturesque with the symmetrical; but the type of its beauty
will continue to be the latter, so long as a sufficient portion of it
remains to convey an idea of its original perfection. It is the same with
the human form and countenance; for age does not destroy their original
beauty, but in both only lessens that which is symmetrical, while it
increases that which is picturesque.
In short, as a variety of simultaneously produced sounds, which do not
relate to each other agreeably to this law, can only convey to the mind
a feeling of mere noise; so a variety of forms or colours simultaneously
exposed to the eye under similar circumstances, can only convey to the
mind a feeling of chaotic confusion, or what may be termed _visible_
discord. As, therefore, the two principles of uniformity and variety,
or similarity and dissimilarity, are in operation in every harmonious
combination of the elements of sound, of form, and of colour, we must
first have recourse to numbers in the abstract before we can form a
proper basis for a universal science of beauty.
THE SCIENCE OF BEAUTY EVOLVED FROM THE HARMONIC LAW OF NATURE, AGREEABLY
TO THE PYTHAGOREAN SYSTEM OF NUMERICAL RATIO.
The scientific principles of beauty appear to have been well known to the
ancient Greeks; and it must have been by the practical application of
that knowledge to the arts of Design, that that people continued for a
period of upwards of three hundred years to execute, in every department
of these arts, works surpassing in chaste beauty any that had ever before
appeared, and which have not been equalled during the two thousand years
which have since elapsed.
Æsthetic science, as the science of beauty is now termed, is based
upon that great harmonic law of nature which pervades and governs the
universe. It is in its nature neither absolutely physical nor absolutely
metaphysical, but of an intermediate nature, assimilating in various
degrees, more or less, to one or other of those opposite kinds of
science. It specially embodies the inherent principles which govern
impressions made upon the mind through the senses of hearing and seeing.
Thus, the æsthetic pleasure derived from listening to the beautiful in
musical composition, and from contemplating the beautiful in works of
formative art, is in both cases simply a response in the human mind to
artistic developments of the great harmonic law upon which the science
is based.
Although the eye and the ear are two different senses, and, consequently,
various in their modes of receiving impressions; yet the sensorium is
but one, and the mind by which these impressions are perceived and
appreciated is also characterised by unity. There appears, likewise,
a striking analogy between the natural constitution of the two kinds
of beauty, which is this, that the more physically æsthetic elements
of the highest works of musical composition are melody, harmony, and
tone, whilst those of the highest works of formative art are contour,
proportion, and colour. The melody or theme of a musical composition
and its harmony are respectively analogous,—1st, To the outline of
an artistic work of formative art; and 2d, To the proportion which
exists amongst its parts. To the careful investigator these analogies
become identities in their effect upon the mind, like those of the more
metaphysically æsthetic emotions produced by expression in either of
these arts.
Agreeably to the first analogy, the outline and contour of an object,
suppose that of a building in shade when viewed against a light
background, has a similar effect upon the mind with that of the simple
melody of a musical composition when addressed to the ear unaccompanied
by the combined harmony of counterpoint. Agreeably to the second analogy,
the various parts into which the surface of the supposed elevation is
divided being simultaneously presented to the eye, will, if arranged
agreeably to the same great law, affect the mind like that of an equally
harmonious arrangement of musical notes accompanying the supposed melody.
There is, however, a difference between the construction of these two
organs of sense, viz., that the ear must in a great degree receive its
impressions involuntarily; while the eye, on the other hand, is provided
by nature with the power of either dwelling upon, or instantly shutting
out or withdrawing itself from an object. The impression of a sound,
whether simple or complex, when made upon the ear, is instantaneously
conveyed to the mind; but when the sound ceases, the power of observation
also ceases. But the eye can dwell upon objects presented to it so long
as they are allowed to remain pictured on the retina; and the mind has
thereby the power of leisurely examining and comparing them. Hence the
ear guides more as a mere sense, at once and without reflection; whilst
the eye, receiving its impressions gradually, and part by part, is more
directly under the influence of mental analysis, consequently producing
a more metaphysically æsthetic emotion. Hence, also, the acquired power
of the mind in appreciating impressions made upon it through the organ of
sight under circumstances, such as perspective, &c., which to those who
take a hasty view of the subject appear impossible.
Dealing as this science therefore does, alike with the sources and the
resulting principles of beauty, it is scarcely less dependent on the
accuracy of the senses than on the power of the understanding, inasmuch
as the effect which it produces is as essential a property of objects,
as are its laws inherent in the human mind. It necessarily comprehends a
knowledge of those first principles in art, by which certain combinations
of sounds, forms, and colours produce an effect upon the mind, connected,
in the first instance, with sensation, and in the second with the
reasoning faculty. It is, therefore, not only the basis of all true
practice in art, but of all sound judgment on questions of artistic
criticism, and necessarily includes those laws whereon a correct taste
must be based. Doubtless many eloquent and ingenious treatises have been
written upon beauty and taste; but in nearly every case, with no other
effect than that of involving the subject in still greater uncertainty.
Even when restricted to the arts of design, they have failed to exhibit
any definite principles whereby the true may be distinguished from
the false, and some natural and recognised laws of beauty reduced to
demonstration. This may be attributed, in a great degree, to the neglect
of a just discrimination between what is merely agreeable, or capable
of exciting pleasurable sensations, and what is essentially beautiful;
but still more to the confounding of the operations of the understanding
with those of the imagination. Very slight reflection, however, will
suffice to shew how essentially distinct these two faculties of the mind
are; the former being regulated, in matters of taste, by irrefragable
principles existing in nature, and responded to by an inherent principle
existing in the human mind; while the latter operates in the production
of ideal combinations of its own creation, altogether independent of any
immediate impression made upon the senses. The beauty of a flower, for
example, or of a dew-drop, depends on certain combinations of form and
colour, manifestly referable to definite and systematic, though it may
be unrecognised, laws; but when Oberon, in “Midsummer Night’s Dream,” is
made to exclaim—
“And that same dew, which sometimes on the buds
Was wont to swell, like round and orient pearls,
Stood now within the pretty floweret’s eyes,
Like tears that did their own disgrace bewail,”—
the poet introduces a new element of beauty equally legitimate, yet
altogether distinct from, although accompanying that which constitutes
the more precise science of æsthetics as here defined. The composition
of the rhythm is an operation of the understanding, but the beauty of the
poetic fancy is an operation of the imagination.
Our physical and mental powers, æsthetically considered, may therefore be
classed under three heads, in their relation to the fine arts, viz., the
receptive, the perceptive, and the conceptive.
The senses of hearing and seeing are respectively, in the degree of
their physical power, receptive of impressions made upon them, and of
these impressions the sensorium, in the degree of its mental power, is
perceptive. This perception enables the mind to form a judgment whereby
it appreciates the nature and quality of the impression originally made
on the receptive organ. The mode of this operation is intuitive, and
the quickness and accuracy with which the nature and quality of the
impression is apprehended, will be in the degree of the intellectual
vigour of the mind by which it is perceived. Thus we are, by the
cultivation of these intuitive faculties, enabled to decide with accuracy
as to harmony or discord, proportion or deformity, and assign sound
reasons for our judgment in matters of taste. But mental conception is
the intuitive power of constructing original ideas from these materials;
for after the receptive power has acted, the perception operates in
establishing facts, and then the judgment is formed upon these operations
by the reasoning powers, which lead, in their turn, to the creations of
the imagination.
The power of forming these creations is the true characteristic
of genius, and determines the point at which art is placed beyond
all determinable canons,—at which, indeed, æsthetics give place to
metaphysics.
In the science of beauty, therefore, the human mind is the subject, and
the effect of external nature, as well as of works of art, the object.
The external world, and the individual mind, with all that lies within
the scope of its powers, may be considered as two separate existences,
having a distinct relation to each other. The subject is affected by the
object, through that inherent faculty by which it is enabled to respond
to every development of the all-governing harmonic law of nature; and the
media of communication are the sensorium and its inlets—the organs of
sense.
This harmonic law of nature was either originally discovered by that
illustrious philosopher Pythagoras, upwards of five hundred years before
Christ, or a knowledge of it obtained by him about that period, from
the Egyptian or Chaldean priests. For after having been initiated into
all the Grecian and barbarian sacred mysteries, he went to Egypt, where
he remained upwards of twenty years, studying in the colleges of its
priests; and from Egypt he went into the East, and visited the Persian
and Chaldean magi.[3]
By the generality of the biographers of Pythagoras, it is said to be
difficult to give a clear idea of his philosophy, as it is almost certain
he never committed it to writing, and that it has been disfigured by the
fantastic dreams and chimeras of later Pythagoreans. Diogenes Laërtius,
however, whose “Lives of the Philosophers” was supposed to be written
about the end of the second century of our era, says “there are three
volumes extant written by Pythagoras. One on education, one on politics,
and one on natural philosophy.” And adds, that there were several other
books extant, attributed to Pythagoras, but which were not written by
him. Also, in his “Life of Philolaus,” that Plato wrote to Dion to take
care and purchase the books of Pythagoras.[4] But whether this great
philosopher committed his discoveries to writing or not, his doctrines
regarding the philosophy of beauty are well-known to be, that he
considered numbers as the essence and the principle of all things, and
attributed to them a real and distinct existence; so that, in his view,
they were the elements out of which the universe was constructed, and to
which it owed its beauty. Diogenes Laërtius gives the following account
of this law:—“That the monad was the beginning of everything. From the
monad proceeds an indefinite duad, which is subordinate to the monad as
to its cause. That from the monad and indefinite duad proceeds numbers.
That the part of science to which Pythagoras applied himself above all
others, was arithmetic; and that he taught ‘that from numbers proceed
signs, and from these latter, lines, of which plane figures consist;
that from plane figures are derived solid bodies; that of all plane
figures the most beautiful was the circle, and of all solid bodies the
most beautiful was the sphere.’ He discovered the numerical relations of
sounds on a single string; and taught that everything owes its existence
and consistency to harmony. In so far as I know, the most condensed
account of all that is known of the Pythagorian system of numbers is the
following:—‘The monad or unity is that quantity, which, being deprived of
all number, remains fixed. It is the fountain of all number. The duad is
imperfect and passive, and the cause of increase and division. The triad,
composed of the monad and duad, partakes of the nature of both. The
tetrad, tetractys, or quaternion number is most perfect. The decad, which
is the sum of the four former, comprehends all arithmetical and musical
proportions.’”[5]
These short quotations, I believe, comprise all that is known, for
certain, of the manner in which Pythagoras systematised the law of
numbers. Yet, from the teachings of this great philosopher and his
disciples, the harmonic law of nature, in which the fundamental
principles of beauty are embodied, became so generally understood and
universally applied in practice throughout all Greece, that the fragments
of their works, which have reached us through a period of two thousand
years, are still held to be examples of the highest artistic excellence
ever attained by mankind. In the present state of art, therefore, a
knowledge of this law, and of the manner in which it may again be applied
in the production of beauty in all works of form and colour, must be
of singular advantage; and the object of this work is to assist in the
attainment of such a knowledge.
It has been remarked, with equal comprehensiveness and truth, by a
writer[6] in the _British and Foreign Medical Review_, that “there
is harmony of numbers in all nature—in the force of gravity—in the
planetary movements—in the laws of heat, light, electricity, and chemical
affinity—in the forms of animals and plants—in the perceptions of the
mind. The direction, indeed, of modern natural and physical science is
towards a generalization which shall express the fundamental laws of all
by one simple numerical ratio. And we think modern science will soon shew
that the mysticism of Pythagoras was mystical only to the unlettered,
and that it was a system of philosophy founded on the then existing
mathematics, which latter seem to have comprised more of the philosophy
of numbers than our present.” Many years of careful investigation have
convinced me of the truth of this remark, and of the great advantage
derivable from an application of the Pythagorean system in the arts
of design. For so simple is its nature, that any one of an ordinary
capacity of mind, and having a knowledge of the most simple rules of
arithmetic, may, in a very short period, easily comprehend its nature,
and be able to apply it in practice.
The elements of the Pythagorean system of harmonic number, so far as can
be gathered from the quotations I have given above, seem to be simply
the indivisible monad (1); the duad (2), arising from the union of one
monad with another; the triad (3), arising from the union of the monad
with the duad; and the tetrad (4), arising from the union of one duad
with another, which tetrad is considered a perfect number. From the
union of these four elements arises the decad (10), the number, which,
agreeably to the Pythagorean system, comprehends all arithmetical and
harmonic proportions. If, therefore, we take these elements and unite
them progressively in the following order, we shall find the series of
harmonic numbers (2), (3), (5), and (7), which, with their multiples, are
the complete numerical elements of all harmony, thus:—
1 + 1 = 2
1 + 2 = 3
2 + 3 = 5
3 + 4 = 7