Chapter V: Introduction (3)

Müller, and other investigators into the archæology of art, refer to the great difficulty which exists in discovering the principles which the ancients followed in regard to the proportions of the human figure, from the different sexes and characters to which they require to be applied. But in the system thus founded upon the harmonic law of nature, no such difficulty is felt, for it is as applicable to the massive proportions which characterise the ancient representations of the Hercules, as to the delicate and perfectly symmetrical beauty of the Venus. This change is effected simply by an increase in the fundamental angle. For instance, in the construction of a figure of the exact proportions of the Venus, the right angle is adopted. But in the construction of a figure of the massive proportions of the Hercules, it is requisite to adopt an angle which bears to the right angle the ratio of 6:5. The adoption of this angle I have shewn in another work[20] to produce in the Hercules those proportions which are so characteristic of physical power. The ellipses which govern the outline, being also formed upon the same larger class of angles, give the contour of the muscles a more massive character. In comparing the male and female forms thus geometrically constructed, it will be found that that of the female is more harmoniously symmetrical, because the right angle is the fundamental angle for the trunk and the limbs as well as for the head and countenance; while in that of the male, the right angle is the fundamental angle for the head only. It may also be observed, that, from the greater proportional width of the pelvis of the female, the centres of that motion which the heads of the thigh bones perform in the cotyloid cavities, and the centres of that still more extensive range of motion which the arm is capable of performing at the shoulder joints, are nearly in the same line which determines the central motion of the vertebral column, while those of the male are not; consequently all the motions of the female are more graceful than those of the male.

This difference between the fundamental angles, which impart to the human figure, on the one hand, the beauty of feminine proportion and contour, and on the other, the grandeur of masculine strength, being in the ratio of 5:6, allows ample latitude for those intermediate classes of proportions which the ancients imparted to their various other deities in which these two qualities were blended. I therefore confine myself to an illustration of the external contour of the form, and the relative proportions of all the parts of a female figure, such as those of the statues of the Venus of Melos and Venus of Medici.

The angles which govern the form and proportions of such a figure are, with the right angle, a series of twelve, as follows:—

Tonic. Dominant. Mediant. Subtonic. Supertonic.
(¹⁄₂) (¹⁄₃) (¹⁄₅) (¹⁄₇) (¹⁄₉)
(¹⁄₄) (¹⁄₆) (¹⁄₁₀) (¹⁄₁₄)
(¹⁄₈) (¹⁄₁₂)

These angles are employed in the construction of a diagram, which determines the proportions of the parts throughout the whole figure. Thus:—

[Sidenote: Plate X.]

Let the line A B (fig. 1, plate X.) represent the height of the figure to be constructed. At the point A, make the angles of C A D (¹⁄₃), F A G (¹⁄₄), H A I (¹⁄₅), K A L (¹⁄₆), and M A N (¹⁄₇). At the point B, make the angles K B L (¹⁄₈), U B A (¹⁄₁₂), and O B A (¹⁄₁₄).

Through the point K, in which the lines A K and B K intersect one another, draw P K O parallel to A B, and through C F H and M, where this line meets A C, A F, A H, and A M, draw C D, F G, H I, and M N, perpendicular to A B; draw also K L perpendicular to A B; join B F and B H, and through C draw C E, making with A B the angle (¹⁄₂), which completes the arrangement of the eleven angles upon A B; for F B G is very nearly (¹⁄₁₀), and H B I very nearly (¹⁄₉).

At the point _f_, where A C intersects O B, draw _f a_ perpendicular to A B; and through the point _i_, where B O intersects M N, draw S _i_ T parallel to A C.

Through _m_, where S _i_ T intersects F B, draw _m n_; through _β_, where S _i_ T intersects K B, draw _β w_; through T draw T _g_, making an angle of (¹⁄₃) with O P. Join N P, M B, and _g_ P, and where N P intersects K B, draw Q R perpendicular to A B.

On A E as a diameter, describe a circle cutting A C in _r_, and draw _r o_ perpendicular to A B.

With A _o_ and _o r_ as semi-axes, describe the ellipse A _r e_, cutting A H in _t_; and draw _t u_ perpendicular to A B. With A _u_ and _t u_, as semi-axes describe the ellipse A _t d_. On _a_ L, as major axis, describe the ellipse of (¹⁄₃).

For the side aspect or profile of the figure the diagram is thus constructed—

On one side of a line A B (fig. 2, Plate X.) construct the rectilinear portion of a diagram the same as fig. 1. Through _i_ draw W Y parallel to A B, and draw A _z_ perpendicular to A B. Make W _a_ equal to A _a_ (fig. 1), and on _a l_, as major axis, describe the ellipse of (¹⁄₄). Through _a_ draw _a p_ parallel to A F, and through _p_ draw _p t_ perpendicular to W Y. Through _a_ draw _f a u_ perpendicular to W Y.

Upon a diameter equal to A E describe a circle whose circumference shall touch A B and A _z_. With semi-axes equal to A _o_ and _o r_ (fig. 1), describe an ellipse with its major axis parallel to A B, and its circumference touching O P and _z_ A.

[Sidenote: Plate XI.]

Thus simply are the diagrams of the general proportions of the human figure, as viewed in front and in profile, constructed; and Plate XI. gives the contour in both points of view, as composed entirely of the curvilinear figures of (¹⁄₂), (¹⁄₃), (¹⁄₄), (¹⁄₅), and (¹⁄₆).

Further detail here would be out of place, and I shall therefore refer those who require it to the Appendix, or the more elaborate works to which I have already referred.

The beauty derived from proportion, imparted by the system here pointed out, and from a contour of curves derived from the same harmonic angles, is not confined to the human figure, but is found in various minor degrees of perfection in all the organic forms of nature, whether animate or inanimate, of which I have in other works given many examples.[21]

THE SCIENCE OF BEAUTY, AS DEVELOPED IN COLOURS.

There is not amongst the various phenomena of nature one that more readily excites our admiration, or makes on the mind a more vivid impression of the order, variety, and harmonious beauty of the creation, than that of colour. On the general landscape this phenomenon is displayed in the production of that species of harmony in which colours are so variously blended, and in which they are by light, shade, and distance modified in such an infinity of gradation and hue. Although genius is continually struggling, with but partial success, to imitate those effects, yet, through the Divine beneficence, all whose organs of sight are in an ordinary degree of perfection can appreciate and enjoy them. In winter this pleasure is often to a certain extent withdrawn, when the colourless snow alone clothes the surface of the earth. But this is only a pause in the general harmony, which, as the spring returns, addresses itself the more pleasingly to our perception in its vernal melody, which, gradually resolving itself into the full rich hues of luxuriant beauty exhibited in the foliage and flowers of summer, subsequently rises into the more vivid and powerful harmonies of autumn’s colouring. Thus the eye is prepared again to enjoy that rest which such exciting causes may be said to have rendered necessary.

When we pass from the general colouring of nature to that of particular objects, we are again wrapt in wonder and admiration by the beauty and harmony which so constantly, and in such infinite variety, present themselves to our view, and which are so often found combined in the most minute objects. And the systematic order and uniformity perceptible amidst this endless variety in the colouring of animate and inanimate nature is thus another characteristic of beauty equally prevalent throughout creation.

By this uniformity in colour, various species of animals are often distinguished; and in each individual of most of these species, how much is this beauty enhanced when the uniformity prevails in the resemblance of their lateral halves! The human countenance exemplifies this in a striking manner; the slightest variety of colour between one and another of the double parts is at once destructive of its symmetrical beauty. Many of the lower animals, whether inhabitants of the earth, the air, or the water, owe much of their beauty to this kind of uniformity in the colour of the furs, feathers, scales, or shells, with which they are clothed.

In the vegetable kingdom, we find a great degree of uniformity of colour in the leaves, flowers, and fruit of the same plant, combined with all the harmonious beauty of variety which a little careful examination develops.

In the colours of minerals, too, the same may be observed. In short, in the beauty of colouring, as in every other species of beauty, uniformity and variety are found to combine.

An appreciation of colour depends, in the first place, as much upon the physical powers of the eye in conveying a proper impression to the mind, as that of music on those of the ear. But an ear for music, or an eye for colour, are, in so far as beauty is concerned, erroneous expressions; because they are merely applicable to the impression made upon the senses, and do not refer to the æsthetical principles of harmony, by which beauty can alone be understood.

A good eye, combined with experience, may enable us to form a correct idea as to the purity of an individual colour, or of the relative difference existing between two separate hues; but this sort of discrimination does not constitute that kind of appreciation of the harmony of colour by which we admire and enjoy its development in nature and art. The power of perceiving and appreciating beauty of any kind, is a principle inherent in the human mind, which may be improved by cultivation in the degree of the perfection of the art senses. Great pains have been bestowed on the education of the ear, in assisting it to appreciate the melody and harmony of sound; but still much remains to be done in regard to the cultivation of the eye, in appreciating colour as well as form.

It is true, that there are individuals whose powers of vision are perfect, in so far as regards the appreciation of light, shade, and configuration, but who are totally incapable of perceiving effects produced by the intermediate phenomenon of colour, every object appearing to them either white, black, or neutral gray; others, who are equally blind as to the effect of one of the three primary colours, but see the other two perfectly, either singly or combined; while there are many who, having the full physical power of perceiving all the varieties of the phenomenon, and who are even capable of making nice distinctions amongst a variety of various colours, are yet incapable of appreciating the æsthetic quality of harmony which exists in their proper combination. It is the same with respect to the effects of sounds upon the ear—some have organs so constituted, that notes above or below a certain pitch are to them inaudible; while others, with physical powers otherwise perfect, are incapable of appreciating either melody or harmony in musical composition. But perceptions so imperfectly constituted are, by the goodness of the Creator, of very rare occurrence; therefore all attempts at improvement in the science of æsthetics must be suited to the capacities of the generality of mankind, amongst whom the perception of colour exists in a variety as great as that by which their countenances are distinguished. Artists now and then appear who have this intuitive perception in such perfection, that they are capable of transferring to their works the most beautiful harmonies and most delicate gradations of colours, in a manner that no acquired knowledge could have enabled them to impart. To those who possess such a gift, as well as to those to whom the ordinary powers of perception are denied, it would be equally useless to offer an explanation of the various modes in which the harmony of colour develops itself, or to attempt a definition of the many various colours, hues, tints, and shades, arising out of the simple elements of this phenomenon. But to those whose powers lie between these extremes, being neither above nor below cultivation, such an explanation and definition must form a step towards the improvement of that inherent principle which constitutes the basis of æsthetical science.

Although the variety and harmony of colour which nature is continually presenting to our view, are apparent to all whose visual organs are in a natural state, and thus to the generality of mankind; yet a knowledge of the simplicity by which this variety and beauty are produced, is, after ages of philosophic research and experimental inquiry, only beginning to be properly understood.

Light may be considered as an active, and darkness a passive principle in the economy of Nature, and colour an intermediate phenomenon arising from their joint influence; and it is in the ratios in which these primary principles act upon each other, by which I here intend to explain the science of beauty as evolved in colour. It has been usual to consider colour as an inherent quality in light, and to suppose that coloured bodies absorb certain classes of its rays, and reflect or transmit the remainder; but it appears to me that colour is more probably the result of certain modes in which the opposite principles of motion and rest, or force and resistance, operate in the production, refraction, and reflection of light, and that each colour is mutually related, although in different degrees, to these active and passive principles.

White and black are the representatives of light and darkness, or activity and rest, and are therefore calculated as pigments to reduce colours and hues to tints and shades.

Having, however, fully illustrated the nature of tints and shades in a former work,[22] I shall here confine myself to colours in their full intensity—shewing the various modifications which their union with each other produce, along with the harmonic relations which these modifications bear to the primaries, and to each other in respect to warmth and coolness of tone, as well as to light and shade.

The primary colours are red, yellow, and blue. Of these, yellow is most allied to light, and blue to shade, while red is neutral in these respects, being equally allied to both. In respect to tone, that of red is warm, and that of blue cool, while the tone of yellow is neutral. The ratios of their relations to each other in these respects will appear in the harmonic scales to which, for the first time, I am about to subject colours, and to systematise their various simple and compound relations, which are as follow:—

From the binary union of the primary colours, the secondary colours arise—

Orange colour, from the union of yellow and red.

Green, from the union of yellow and blue.

Purple, from the union of red and blue.

From the binary union of the secondary colours, the primary hues arise—

Yellow-hue, from the union of orange and green.

Red-hue, from the union of orange and purple.

Blue-hue, from the union of purple and green.

From the binary union of the primary hues, the secondary hues arise—

Orange-hue, from the union of yellow-hue and red-hue.

Green-hue, from the union of yellow-hue and blue-hue.

Purple-hue, from the union of red-hue and blue-hue.

Each hue owes its characteristic distinction to the proportionate predominance or subordination of one or other of the three primary colours in its composition.

It follows, that in every hue of _red_, yellow and blue are subordinate; in every hue of _yellow_, red and blue are subordinate; and in every hue of _blue_, red and yellow are subordinate. In like manner, in every hue of _green_, red is subordinate; in every hue of _orange_, blue is subordinate; and in every hue of _purple_, yellow is subordinate.

By the union of two primary colours, in the production of a secondary colour, the nature of both primaries is altered; and as there are only three primary or simple colours in the scale, the two that are united harmonically in a compound colour, form the natural contrast to the remaining simple colour.

Notwithstanding all the variety that extends beyond the six positive colours, it may be said that there are only three proper contrasts of colour in nature, and that all others are simply modifications of these.

Pure red is the most perfect contrast to pure green; because it is characterised amongst the primary colours by warmth of tone, while amongst the secondary colours green is distinguished by coolness of tone, both being equally related to the primary elements of light and shade.

Pure yellow is the most perfect contrast to pure purple; because it is characterised amongst the primary colours as most allied to light, whilst pure purple is characterised amongst the secondaries as most allied to shade, both being equally neutral as to tone.

Pure blue is the most perfect contrast to pure orange; because it is characterised amongst the primary colours as not only the most allied to shade, but as being the coolest in tone, whilst pure orange is characterised amongst the secondaries as being the most allied to light and the warmest in tone. The same principle operates throughout all the modifications of these primary and secondary colours.

Such is the simple nature of contrast upon which the beauty of colouring mainly depends.

It being now established as a scientific fact, that the effect of light upon the eye is the result of an ethereal action, similar to the atmospheric action by which the effect of sound is produced upon the ear; also, that the various colours which light assumes are the effect of certain modifications in this ethereal action;—just as the various sounds, which constitute the scale of musical notes, are known to be the effect of certain modifications in the atmospheric action by which sounds in general are produced:

Therefore, as harmony may thus be impressed upon the mind through either of these two art senses—hearing and seeing—the principles which govern the modifications in the ethereal action of light, so as to produce through the eye the effect of harmony, cannot be supposed to differ from those principles which we know govern the modifications of the atmospheric action of sound, in producing through the ear a like effect. I shall therefore endeavour to illustrate the science of beauty as evolved in colours, by forming scales of their various modifications agreeably to the same Pythagorean system of numerical ratio from which the harmonic elements of beauty in sounds were originally evolved, and by which I have endeavoured in this, as in previous works, to systematise the harmonic beauty of forms.

It will be observed, that with a view to avoid complexity as much as possible, I have, in the arrangement of the above series of scales, not only confined myself to the merely elementary parts of the Pythagorean system, but have left out the harmonic modifications upon (¹⁄₁₁) and (¹⁄₁₃), in order that the arithmetical progression might not be interrupted.[23]

The above elementary process will, I trust, be found sufficient to explain the progress, by harmonic union, of a primary colour to a toned gray, and how the simple and compound colours naturally arrange themselves into the elements of five scales, the parts of which continue from primary to secondary colour; from secondary colour to primary hue; from primary hue to secondary hue; from secondary hue to primary-toned gray; and from primary-toned gray to secondary-toned gray in the simple ratio of 2:1; thereby producing a series of the most beautiful and perfect contrasts.

The natural arrangement of the primary colours upon the solar spectrum is red, yellow, blue, and I have therefore adopted the same arrangement on the present occasion. Red being, consequently, the first tonic, and blue the second, the divisions express the numerical ratios which the colours bear to one another, in respect to that colourific power for which red is pre-eminent. Thus, yellow is to red, as 2:3; blue to yellow, as 3:4; purple to orange, as 5:6; and green to purple, as 6:7.

The following series of completed scales are arranged upon the foregoing principle, with the natural connecting links of red-orange, yellow-orange, yellow-green, and blue-green, introduced in their proper places.

The appropriate terminology of musical notes has been adopted, and the scales are composed as follows:—

Scale I. consists of primary and secondary colours;
Scale II. of secondary colours and primary hues;
Scale III. of primary and secondary hues;
Scale IV. of secondary hues and primary-toned grays; and
Scale V. of primary and secondary-toned grays;

All the parts in each of these scales, from the first tonic to the second, relate to the same parts of the scale below them in the simple ratio of 2:1; and serially to the first tonic in the following ratios:—

8:9, 4:5, 3:4, 2:3, 3:5, 4:7, 8:15, 1:2.

_First Series of Scales._

----+------+-------+-------+-------+-------+-------+------+-------+-------
|Tonic.| | | | | | | |
| |Supertonic. | | | | | |
| | |Mediant. | | | | |
| | | |Subdominant. | | | |
| | | | |Dominant. | | |
| | | | | |Submediant. | |
| | | | | | |Subtonic. |
| | | | | | | |Semi-subtonic.
| | | | | | | | |Tonic.
----+------+-------+-------+-------+-------+-------+------+-------+-------
I. |(¹⁄₂) |(⁴⁄₉) |(²⁄₅) |(³⁄₈) |(¹⁄₃) |(³⁄₁₀) |(²⁄₇) |(⁴⁄₁₅) |(¹⁄₄)
|Red. |Red- |Orange.|Yellow-|Yellow.|Yellow-|Green.|Blue- |Blue.
| |orange.| |orange.| |green. | |green. |
----+------+-------+-------+-------+-------+-------+------+-------+-------
II. |(¹⁄₄) |(²⁄₉) |(¹⁄₅) |(³⁄₁₆) |(¹⁄₆) |(³⁄₂₀) |(¹⁄₇) |(²⁄₁₅) |(¹⁄₈)
|Green.|Blue- |Blue |Blue- |Purple |Red- |Red |Red- |Orange.
| |green |hue. |purple |hue. |purple |hue. |orange |
| |hue. | |hue. | |hue. | |hue. |
----+------+-------+-------+-------+-------+-------+------+-------+-------
III.|(¹⁄₈) |(¹⁄₉) |(¹⁄₁₀) |(³⁄₃₂) |(¹⁄₁₂) |(³⁄₄₀) |(¹⁄₁₄)|(¹⁄₁₅) |(¹⁄₁₆)
|Red |Red- |Orange |Yellow-|Yellow |Yellow-|Green |Blue- |Blue
|hue. |orange |hue. |orange |hue. |green |hue. |green |hue.
| |hue. | |hue. | |hue. | |hue. |
----+------+-------+-------+-------+-------+-------+------+-------+-------
IV. |(¹⁄₁₆)|(¹⁄₁₈) |(¹⁄₂₀) |(³⁄₆₄) |(¹⁄₂₄) |(³⁄₈₀) |(¹⁄₂₈)|(¹⁄₃₀) |(¹⁄₃₂)
|Green |Blue- |Blue- |Blue- |Purple |Red- |Red- |Red- |Orange
|hue. |green- |toned |purple-|hue. |purple-|toned |orange-|hue.
| |toned |gray. |toned | |toned |gray. |toned |
| |gray. | |gray. | |gray. | |gray. |
----+------+-------+-------+-------+-------+-------+------+-------+-------
V. |(¹⁄₃₂)|(¹⁄₃₆) |(¹⁄₄₀) |(³⁄₁₂₈)|(¹⁄₄₈) |(³⁄₁₆₀)|(¹⁄₅₆)|(¹⁄₆₀) |(¹⁄₆₄)
|Red- |Red- |Orange-|Yellow-|Yellow-|Yellow-|Green-| Blue- |Blue-
|toned |orange-|toned |orange-|toned |green- |toned | green-|toned
|gray. |toned |gray. |toned |gray. |toned |gray. | toned |gray.
| |gray. | |gray. | | gray. | | gray. |
----+------+-------+-------+-------+-------+-------+------+-------+-------

To the scales of chromatic power I add another series of scales, in which yellow, being the first tonic, and blue the second, the numerical divisions express the ratios which the colours in each scale bear to one another in respect to light and shade. Thus red is to yellow, in respect to light, as 2:3; blue to red, as 3:4; green to orange, as 5:6, and purple to green, as 6:7.

These scales may therefore be termed scales for the colour-blind, because, in comparing colours, those whose sight is thus defective, naturally compare the ratios of the light and shade of which different colours are primarily constituted.

The following is a series of five complete scales of the harmonic parts into which the light and shade in colours may be divided in each scale according to the above arrangement:—

_Second Series of Scales._

----+-------+-------+-------+-------+------+-------+-------+-------+------
|Tonic. | | | | | | | |
| |Supertonic. | | | | | |
| | |Mediant. | | | | |
| | | |Subdominant. | | | |
| | | | |Dominant. | | |
| | | | | |Submediant. | |
| | | | | | |Subtonic. |
| | | | | | | |Semi-subtonic.
| | | | | | | | |Tonic.
----+-------+-------+-------+-------+------+-------+-------+-------+------
I. |(¹⁄₂) |(⁴⁄₉) |(²⁄₅) |(³⁄₈) |(¹⁄₃) |(³⁄₁₀) |(²⁄₇) |(⁴⁄₁₅) |(¹⁄₄)
|Yellow.|Yellow-|Orange.|Red- |Red. |Red- |Purple.|Blue- |Blue.
| |orange.| |orange.| |purple.| |purple.|
----+-------+-------+-------+-------+------+-------+-------+-------+------
II. |(¹⁄₄) |(²⁄₉) |(¹⁄₅) |(³⁄₁₆) |(¹⁄₆) |(³⁄₂₀) |(¹⁄₇) |(²⁄₁₅) |(¹⁄₈)
|Purple.|Blue- |Blue |Blue- |Green.|Yellow-|Yellow |Yellow-|Orange
| |purple |hue. |green | |green |hue. |orange |
| |hue. | |hue. | |hue. | |hue. |
----+-------+-------+-------+-------+------+-------+-------+-------+------
III.|(¹⁄₈) |(¹⁄₉) |(¹⁄₁₀) |(³⁄₃₂) |(¹⁄₁₂)|(³⁄₄₀) |(¹⁄₁₄) |(¹⁄₁₅) |(¹⁄₁₆)
|Yellow |Yellow-|Orange |Red- |Red |Red- |Purple |Blue- |Blue
|hue. |orange |hue. |orange |hue. |purple |hue. |purple |hue.
| |hue. | |hue. | |hue. | |hue. |
----+-------+-------+-------+-------+------+-------+-------+-------+------
IV. |(¹⁄₁₆) |(¹⁄₁₈) |(¹⁄₂₀) |(³⁄₆₄) |(¹⁄₂₄)|(³⁄₈₀) |(¹⁄₂₈) |(¹⁄₃₀) |(¹⁄₃₂)
|Purple |Blue- |Blue- |Blue- |Green |Yellow-|Yellow-|Yellow-|Orange
|hue. |purple-|toned |green- |hue. |green- |toned |orange-|hue.
| |toned |gray. |toned | |toned |gray. |toned |
| |gray. | |gray. | |gray. | |gray. |
----+-------+-------+-------+-------+------+-------+-------+-------+------
V. |(¹⁄₃₂) |(¹⁄₃₆) |(¹⁄₄₀) |(³⁄₁₂₈)|(¹⁄₄₈)|(³⁄₁₆₀)|(¹⁄₅₆) |(¹⁄₆₀) |(¹⁄₆₄)
|Yellow-|Yellow-|Orange-|Red- |Red- |Red- |Purple-|Blue- |Blue-
|toned |orange-|toned |orange-|toned |purple-|toned |green- |toned
|gray. |toned |gray. |toned |gray. |toned |gray. |toned |gray.
| |gray. | |gray. | |gray. | |gray. |
----+-------+-------+-------+-------+------+-------+-------+-------+------

Should I be correct in arranging colours upon scales identical with those upon which musical notes have been arranged, and in assuming that colours have the same ratios to each other, in respect to their harmonic power upon the eye, which musical notes have in respect to their harmonic power upon the ear, the colourist may yet be enabled to impart harmonic beauty to his works with as much certainty and ease, as the musician imparts the same quality to his compositions: for the colourist has no more right to trust exclusively to his eye in the arrangement of colours, than the musician has to trust exclusively to his ear in the arrangement of sounds.

We find, in comparing the dominant parts in the first and second scales of the second series, that they are equal as to light and shade, so that their relative powers of contrast depend entirely upon colour. Hence it is that red and green are the two colours, the difference between which the colour-blind are least able to appreciate. Professor George Wilson, in his excellent work, “Researches on Colour-Blindness,” mentions the case of an engraver, which proves the power of the eye in being able to appreciate these original constituents of colour, irrespective of the intermediate phenomenon of tone. This engraver, instead of expressing regret on account of his being colour-blind, observed to the professor, “My defective vision is, to a certain extent, a useful and valuable quality. Thus, an engraver has two negatives to deal with, _i.e._, white and black. Now, when I look at a picture, I see it only in white and black, or light and shade, or, as artists term it, the effect. I find at times many of my brother engravers in doubt how to translate certain colours of pictures, which to me are matters of decided certainty and ease. Thus to me it is valuable.”

The colour-blind are therefore as incapable of receiving pleasure from the harmonious union of various colours, as those who, to use a common term, have no ear for music, are of being gratified by the “melody of sweet sounds.”

The generality of mankind are, however, capable of appreciating the harmony of colour which, like that of both sound and form, arises from the simultaneous exhibition of opposite principles having a ratio to each other. These principles are in continual operation throughout nature, and from them we often derive pleasure without being conscious of the cause. All who are not colour-blind must have felt themselves struck with the harmonic beauty of a cloudless sky, although in it there is no configuration, and at first sight apparently but one colour. Now, as we know that there can be no more impression of harmony made upon the mind by looking upon a single colour, than there could be by listening to a single continued musical note, however sweet its tone, we are apt at first to imagine that the organ of vision has, in some measure, conveyed a false impression to the mind. But it has not done so; for light, when reflected from the atmosphere, produces those cool tones of blue, gray, and purple, which seem to clothe the distant mountains; but, when transmitted through the same atmosphere, it produces those numerous warm tints, the most intense of which give the gorgeous effects which so often accompany the setting sun. We have, therefore, in the upper part of a clear sky, where the atmosphere may be said to be illuminated principally by reflection from the surface of the earth, a comparatively cool tone of blue, the result of reflection, which gradually blends into the warm tints, the result of transmission through the same atmosphere. Such a composition of harmonious colouring is to the eye what the voice of the soft breath of summer amongst the trees, the hum of insects on a sultry day, or the simple harmony of the Æolian harp, is to the ear. To such a composition of chromatic harmony must also be referred the universal concurrence of mankind in appreciating the peculiar beauty of white marble statuary. That the principal constituent of beauty in such works ought to be harmony of form, no one will deny; but this is not the only element, as appears from the fact, that a cast in plaster of Paris, of a fine white marble statue, although identical in form, is far less beautiful than the original. Now this undoubtedly must be the consequence of its having been changed from a semi-translucent substance, which, like the atmosphere, can transmit as well as reflect light, to an opaque substance, which can only reflect it. Thus the opposite principles of chromatic warmth and coolness are equally balanced in white marble—the one being the natural result of the partial transmission of light, and the other that of its reflection.

As a series of coloured illustrations would be beyond the scope of this _résumé_, I may refer those who wish to prosecute the inquiry, with the assistance of such a series, to my published works upon the subject.[24]

THE SCIENCE OF BEAUTY, APPLIED TO THE FORMS AND PROPORTIONS OF ANCIENT GRECIAN VASES AND ORNAMENTS.

In examining the remains of the ornamental works of the ancient Greek artists, it appears highly probable that the harmony of their proportions and melody of their contour are equally the result of a systematised application of the same harmonic law. This probability not being fully elucidated in any of my former works, I will require to go into some detail on the present occasion. I take for my first illustration an unexceptionable example, viz.:—

_The Portland Vase._

Although this beautiful specimen of ancient art was found about the middle of the sixteenth century, inclosed in a marble sarcophagus within a sepulchral chamber under the Monte del Grano, near Rome, and although the date of its production is unknown, yet its being a work of ancient Grecian art is undoubted; and the exquisite beauty of its form has been universally acknowledged, both during the time it remained in the palace of the Barberini family at Rome, and since it was added to the treasures of the British Museum. The forms and proportions of this gem of art appear to me to yield an obedience to the great harmonic law of nature, similar to that which I have instanced in the proportions and contour of the best specimens of ancient Grecian architecture.

[Sidenote: Plate XII.]

Let the line A B (Plate XII.) represent the full height of the vase. Through A draw A _a_, and through B draw B _b_ indefinitely, A _a_ making an angle of (¹⁄₂), and B _b_ an angle of (¹⁄₃), with the vertical. Through the point C, where A _a_ and B _b_ intersect one another, draw D C E vertical. Through A C and B respectively, draw A D, C F, and B E horizontal. Draw similar lines on the other side of A B, and the rectilinear portion of the diagram is complete.

The curvilinear contour may be thus added:—

Take a cut-out ellipse of (¹⁄₄), whose greater axis is equal to the line A B, and

_1st._ Place it upon the diagram, so that its circumference may be tangential to the lines C E and C F, and its greater axis _m n_ may make an angle of (¹⁄₅) with the vertical, and trace its circumference.

_2d._ Place it with its circumference tangential to that of the first at the point m, while its greater axis (of which _o p_ is a part) is in the horizontal, and trace the portion of its circumference _q o r_.

_3d._ Place it with its circumference tangential to that of the above at _v_, while its greater axis (of which _u v_ is a part) makes an angle of (³⁄₁₀) with the vertical, and trace the portion of its circumference _s v t_.

Thus the curvilinear contour of the body and neck are harmonically determined.

The curve of the handle may be determined by the same ellipse placed so that its greater axis (of which _i k_ is a part) makes an angle of (¹⁄₆) with the vertical.

Make similar tracings on the other side of A B, and the diagram is complete. The inscribing rectangle D G E K is that of (²⁄₅).

The outline resulting from this diagram, not only is in perfect agreement with my recollection of the form, but with the measurements of the original given in the “Penny Cyclopædia;” of the accuracy of which there can be no doubt. They are stated thus:—“It is about ten inches in height, and beautifully curved from the top downwards; the diameter at the top being about three inches and a-half; at the neck or smallest part, two inches; at the largest (mid-height), seven inches; and at the bottom, five inches.”

The harmonic elements of this beautiful form, therefore, appear to be the following parts of the right angle:—

Tonic. Dominant. Mediant. Submediant.
(¹⁄₂) (¹⁄₃) (¹⁄₅) (³⁄₁₀)
(¹⁄₄) (¹⁄₆)

When we reflect upon the variety of harmonic ellipses that may be described, and the innumerable positions in which they may be harmonically placed with respect to the horizontal and vertical lines, as well as upon the various modes in which their circumferences may be combined, the variety which may be introduced amongst such forms as the foregoing appears almost endless. My second example is that of—

_An Ancient Grecian Marble Vase of a Vertical Composition._

I shall now proceed to another class of the ancient Greek vase, the form of which is of a more complex character. The specimen I have chosen for the first example of this class is one of those so correctly measured and beautifully delineated by Tatham in his unequalled work.[25] This vase is a work of ancient Grecian art in Parian marble, which he met with in the collection at the Villa Albani, near Rome. Its height is 4 ft. 4¹⁄₂ in.

[Sidenote: Plate XIII.]

The following is the formula by which I endeavour to develop its harmonic elements:—

Let A B (Plate XIII.) represent the full height of this vase. Through B draw B D, making an angle of (¹⁄₅) with the vertical. Through D draw D O vertical, through A draw A C, making an angle of (²⁄₅); through B draw B L, making an angle of (¹⁄₂), and B S, making an angle of (³⁄₁₀), each with the vertical. Through A draw A D, through B draw B O, through L draw L N, through C draw C F, and through S draw S P, all horizontal. Through A draw A H, making an angle of (¹⁄₁₀) with the vertical, and through H draw H M vertical. Draw similar lines on the other side of A B, and the rectilinear portion of the diagram is complete, and its inscribing rectangle that of (³⁄₈).

The curvilinear portion may thus be added—

Take a cut-out ellipse of (¹⁄₃), whose greater axis is about the length of the body of the intended vase, place it with its lesser axis upon the line S P, and its greater axis upon the line D O, and trace the part _a b_ of its circumference upon the diagram. Place the same ellipse with one of its foci upon C, and its greater axis upon C F, and trace its circumference upon the diagram. Take a cut-out ellipse of (¹⁄₅), whose greater axis is nearly equal to that of the ellipse already used; place it with its greater axis upon M H, and its lesser axis upon L N, and trace its circumference upon the diagram. Make similar tracings upon the other side of A B, and the diagram is complete. In this, as in the other diagrams, the strong portions of the lines give the contour of the vase. The harmonic elements of this classical form, therefore, appear to be the right angle and its following parts:—

Tonic. Dominant. Mediant. Submediant.
(¹⁄₂) (¹⁄₃) (²⁄₅) (³⁄₁₀)
(¹⁄₅)
(¹⁄₁₀)

My third example is that of—

_An Ancient Grecian Vase of a Horizontal Composition._

This example belongs to the same class as the last, but it is of a horizontal composition. It was carefully drawn from the original in the museum of the Vatican by Tatham, in whose etchings it will be found with its ornamental decorations. The diagram of its harmonic elements may be constructed as follows:—

[Sidenote: Plate XIV.]

Let A B (Plate XIV.) represent the full height of the vase. Through B draw B D, making an angle of (²⁄₅) with the vertical. Through A draw A H, A L, and A C, making respectively the following angles, (¹⁄₅) with the vertical, (⁴⁄₉) with the vertical, and (³⁄₁₀) with the horizontal. These angles determine the horizontal lines H B, L N, and C F, which divide the vase into its parts, and the inscribing rectangle D G K O is (³⁄₈). This completes the rectilinear portion of the diagram. The ellipse by which the curvilinear portion is added is one of (¹⁄₅), the greater axis of which, at _a b_, as also at _c d_, makes an angle of (¹⁄₁₂) with the vertical, and the same axis at _e f_ an angle of (¹⁄₁₂) with the horizontal.

The harmonic elements of this vase, therefore, appear to be:—

Tonic. Dominant. Mediant. Submediant. Supertonic.
The Right (¹⁄₁₂) (²⁄₅) (³⁄₁₀) (⁴⁄₉)
Angle. (¹⁄₅)

My remaining examples are those of—

_Etruscan Vases._

Of these vases I give four examples, by which the simplicity of the method employed in applying the harmonic law will be apparent.

[Sidenote: Plate XV.]

The inscribing rectangle D G E K of fig. 1, Plate XV., is one of (³⁄₈), within which are arranged tracings from an ellipse of (³⁄₁₀), whose greater axis at _a b_ makes an angle of (¹⁄₁₂), at _c d_ an angle of (³⁄₁₀), and at _e f_ an angle of (³⁄₄), with the vertical. The harmonic elements of the contour of this vase, therefore, appear to be:—

Tonic. Dominant. Subdominants. Submediant.
The Right (¹⁄₁₂) (³⁄₄) (³⁄₁₀)
Angle. (³⁄₈)

The inscribing rectangle L M N O of fig. 2 is that of (¹⁄₂), within which are arranged tracings from an ellipse of (¹⁄₃), whose greater axis, at _a b_ and _c d_ respectively, makes angles of (¹⁄₂) and (⁴⁄₉) with the horizontal, while that at _e f_ is in the horizontal line. The harmonic elements of the contour of this vase, therefore, appear to be:—

Tonic. Dominant. Subtonic.
(¹⁄₂) (¹⁄₃) (⁴⁄₉)

[Sidenote: Plate XVI.]

The inscribing rectangle P Q R S of fig. 1, Plate XVI., is one of (⁴⁄₉), within which are arranged tracings from an ellipse of (³⁄₈), whose greater axis, at _a b_, _c d_, and _e f_, makes respectively angles of (¹⁄₆) with the horizontal, (³⁄₅) and (⁴⁄₅) with the vertical. Its harmonic elements, therefore, appear to be:—

Tonic. Dominant. Mediant. Supertonic. Subdominant. Submediant.
The Right (¹⁄₆) (⁴⁄₅) (⁴⁄₉) (³⁄₈) (³⁄₅)
Angle.

The inscribing rectangle T U V X of fig. 2 is one of (⁴⁄₉), within which are arranged tracings from an ellipse of (³⁄₈) whose greater axis at _a b_ is in the vertical line, and at _c d_ makes an angle of (¹⁄₂). The harmonic elements of the contour of this vase, therefore, appear to be:—

Tonic. Submediant. Supertonic.
(¹⁄₂) (³⁄₈) (⁴⁄₉)

These four Etruscan vases, the contours of which are thus reduced to the harmonic law of nature, are in the British Museum, and engravings of them are to be found in the well-known work of Mr Henry Moses, Plates 4, 6, 14, and 7, respectively, where they are represented with their appropriate decorations and colours.

To these, I add two examples of—

_Ancient Grecian Ornament._

I have elsewhere shewn[26] that the elliptic curve pervades the Parthenon from the entases of the column to the smallest moulding, and we need not, therefore, be surprised to find it employed in the construction of the only two ornaments belonging to that great work.

[Sidenote: Plate XVII.]

In the diagram (Plate XVII.), I endeavour to exhibit the geometric construction of the upper part of one of the ornamental apices, termed antefixæ, which surmounted the cornice of the Parthenon.

The first ellipse employed is that of (¹⁄₃), whose greater axis _a b_ is in the vertical line; the second is also that of (¹⁄₃), whose greater axis _c d_ makes, with the vertical, an angle of (¹⁄₁₂); the third ellipse is the same with its major axis _e f_ in the vertical line. Through one of the foci of this ellipse at A the line A C is drawn, and upon the part of the circumference C _e_, the number of parts, 1, 2, 3, 4, 5, 6, 7, of which the surmounting part of this ornament is to consist, are set off. That part of the circumference of the ellipse whose larger axis is _c d_ is divided from _g_ to _c_ into a like number of parts. The third ellipse employed is one of (¹⁄₄).

Take a cut-out ellipse of this kind, whose larger axis is equal in length to the inscribing rectangle. Place it with its vertex upon the same ellipse at _g_, so that its circumference will pass through C, and trace it; remove its apix first to _p_, then to _q_, and proceed in the same way to _q_, _r_, _s_, _t_, _u_, and _v_, so that its circumference will pass through the seven divisions on _c g_ and _e_ C: _v o_, _u n_, _t m_, _s i_, _r k_, _q j_, _p l_, and _g x_, are parts of the larger axes of the ellipses from which the curves are traced. The small ellipse of which the ends of the parts are formed is that of (¹⁄₃).

[Sidenote: Plate XVIII.]

In the diagram (Plate XVIII.), I endeavour to exhibit the geometric construction of the ancient Grecian ornament, commonly called the _Honeysuckle_, from its resemblance to the flower of that name. The first part of the process is similar to that just explained with reference to the antefixæ of the Parthenon, although the angles in some parts differ. The contour is determined by the circumference of an ellipse of (¹⁄₃), whose major axis A B makes an angle of (¹⁄₉) with the vertical, and the leaves or petals are arranged upon a portion of the perimeter of a similar ellipse whose larger axis E F is in the vertical line, and these parts are again arranged upon a similar ellipse whose larger axis C D makes an angle of (¹⁄₁₂) with the vertical. The first series of curved lines proceeding from 1, 2, 3, 4, 5, 6, 7, and 8, are between K E and H C, part of the circumference of an ellipse of (¹⁄₃); and those between C H and A G are parts of the circumference of four ellipses, each of (¹⁄₃), but varying as to the lengths of their larger axes from 5 to 3 inches. The change from the convex to the concave, which produces the ogie forms of which this ornament is composed, takes place upon the line C H, and the lines _a b_, _c d_, _e f_, _g h_, _i k_, _l m_, _n o_, and _p q_, are parts of the larger axis of the four ellipses the circumference of which give the upper parts of the petals or leaves.

This peculiar Grecian ornament is often, like the antefixæ of the Parthenon, combined with the curve of the spiral scroll. But the volute is so well understood that I have not rendered my diagrams more complex by adding that figure. Many varieties of this union are to be found in Tatham’s etchings, already referred to. The antefixæ of the Parthenon, and its only other ornament the honeysuckle, as represented on the soffit of the cornice, are to be found in Stewart’s “Athens.”