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.
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.
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:—
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 Angle. | (¹⁄₁₂) | (²⁄₅) | (³⁄₁₀) | (⁴⁄₉) |
| (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.
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 Angle. | (¹⁄₁₂) | (³⁄₄) | (³⁄₁₀) |
| (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) |
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 Angle. | (¹⁄₆) | (⁴⁄₅) | (⁴⁄₉) | (³⁄₈) | (³⁄₅) |
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.
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).
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.”