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.