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.

[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 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)