Proceeding still by the system of thirds, we obtain the dominant major ninth composed of the major third, perfect fifth, minor seventh, and major ninth, all of which are dissonant, as before explained (see page 291.) By the application of a flat to the ninth interval of this harmonic combination, we have the harmony of the dominant minor ninth, composed of the major third, present fifth, minor seventh, and minor ninth, the whole of which sounds are also dissonant, and resolve in the following manner, viz.—

and the highest note ascends as usual, thus— Gis the root of the discord still, though D flat is termed the bass, because sung by the deepest voice, or played by a bass instrument; the second combination consists of the harmony of the major third, perfect fifth, and augmented sixth, when all intervals are dissonant, resolving sooner or later into perfect harmony, thusi.e. one after another, for reasons hereafter to be explained. It will be seen that this combination of dissonant sounds

is the same as the dominant minor ninth, with the exception of having the perfect fifth one degree, and omitting the root. The last harmonic combination of sounds, making the thirteenth, is expressed in the following manner, consisting of the union of the major third, minor seventh, and augmented fifth, and resolving thus

It must be observed that the resolutions of the various dissonant harmonies, arising from the dominant ninth, may be immediately effected

The

in minor as well as major perfect harmonies, with the exception of Nos. 4, 8, and 13. dissonances, therefore, of No. 11, may also resolve in the following manner, viz.—

From the harmony of the dominant minor ninth are derived two other combinations of sounds; the first is composed of the harmony of the major third, augmented fourth, and augmented sixth, which is effected by lowering the perfect fifth one-half tone, and omitting the note constituting the minor ninth, when the two gravest notes, as dissonances, descend one degree each,

Remarks upon the respective powers of the foregoing dissonant and consonant harmonies, and of the situations they occupy in the diatonic major and minor scales.

It has undoubtedly been remarked that the notes composing the several tonic harmonies, introduced for the proper resolution of the dis

number of inversions; it is placed upon the second degree of the major mode; the seventh interval must be prepared, and the whole of the component parts must regularly resolve upon the perfect harmony of the fifth below, or upon the dominant seventh of that fifth, thus

The harmony of the seventh of the third species (No. 7) is called that of the seventh of the sensible of the major mode, and composed of the minor third, diminished fifth, and minor seventh; it is placed upon the seventh of the major, and second of the minor mode, and produces three inversions, viz. the harmony of the minor third, perfect fifth, and major sixth; the harmony of the major third, augmented fourth, and major sixth; and the harmony of the major second, perfect fourth, and minor sixth, thus

For the resolution of these harmonic combinations, see example 8, plate I. When the bass of the third specimen rises one degree for the preparation of a perfect cadence.

The harmony of the fourth species (No 7), composed of the harmony of the major third, perfect fifth, and major seventh, produces also three inversions, viz. the harmony of the minor third, perfect fifth, and minor sixth; the harmony of the major sixth, major third, and perfect fourth; and the harmony of the perfect fourth, minor sixth, and major second, thus

The harmony of the diminished seventh is composed entirely of minor thirds, and is also denominated the seventh of the sensible of the minor mode. It is composed of the minor third, imperfect fifth, and diminished seventh, and produces three inversions, viz. the harmony of the minor third, diminished fifth, and major sixth; the harmony of the minor third, augmented fourth, and major sixth, called the harmony of the triton; and the harmony of the augmented second, augmented fourth, and major sixth. The whole of these intervals resolve upon the harmony of the tonic, and they are treated in every respect the same with those of the dominant seventh, thus

The harmony of the dominant major ninth (No. 9) comprises the whole of the notes constituting the dominant seventh, and is composed of the major third, perfect fifth, minor seventh, and major ninth. Being composed of five notes it is capable of four inversions, viz. the harmony of the minor third, diminished fifth, minor sixth, and minor seventh; the harmony of the minor third, perfect fourth, perfect fifth, and major sixth; the harmony of the major second, minor the harmony of the major second, perfect fourth, third, augmented fourth, and major sixth; and minor sixth, and minor seventh, thus—

00

This fundamental harmony, of which the fifth is omitted for the sake of a more grateful resolu tion, resolves, together with its three inversions, upon the harmony of the tonic; and, in the em ployment of this combination of sounds, the root of which is generally dispensed with, care must be taken to place its component parts at a considerable distance from each other; the last inversion only must be prepared, see example 12, plate I.

The harmony of the dominant minor rinth, composed of the major third, perfect fifth, minor seventh, and minor ninth, is also generally em ployed without its root, when it consists simply of the materials of the diminished seventh; the harmony of the dominant ninth has three inversions, thus

cable.

The harmony of the augmented sixth, major third, and perfect fifth, the eleventh of the classification, is employed in the formation of perfect cadences, but always upon the sixth degree of the scale. See example 15.

The harmony of the augmented fourth, and augmented sixth, and major third (No. 12), requires preparation as in example 16.

It has undoubtedly been observed that, as intervals are of themselves consonant and dissonant, harmony, which consists of the union of these intervals, must also be consonant or dissonant; that all dissonances which are essential, as producing variety, activity, and strength of character, must resolve, sooner or later, into consonances, minor or major, that the ear may be relieved from the harsh effects of dissonances; also that the different sounds and combinations of sounds we have been endeavouring to describe in the foregoing pages are capable of being reduced to nine notes. These may be again reduced to seven primary ones. As, therefore, in painting, we may blend the original colors as much as we please towards the production of another color; all the possible variety of tints being only different combinations of the seven primary colors as they are separated by a prism; so all the variety of melting sounds' which enchant us, must consist in a different succession,

or in a different union, of some of these seven natural notes, or their replications or varieties; such are the boundaries of these applications of sight and hearing.

APPLICATION OF THE FOREGOING OBSERVATIONS, AS APPLIED TO THE DIATONIC MAJOR SCALE.

As the major diatonic scale is composed of tones and half tones, it follows that the same figures, if placed upon its different degrees, would produce different species of harmonic combinations; thus by the application of the figures 3, 5, 8, upon those degrees, we obtain three major perfect harmonies, three minor perfect harmonies, and one imperfect harmony, corresponding to Nos. 1, 2, and 3; the first accompanying the tonic, dominant, and subdominant; the second accompanying the second, third, and sixth of the mode; and the last accompanying the major seventh of the scale (see example 17): the figures 3, 5, 7, produce one dominant seventh; three harmonies of sevenths of the second species; one of the third species of seventh; and two of the fourth species of seventh, corresponding to Nos. 4, 5, 6, and 7 (see example 18). The creation of this mode is explained page 289. The accompaniment given to it by Viedana will serve to show the different movements of parts required in the construction of counterpoint, as also the laws whereby two or more perfect harmonies are made to succeed each other with propriety and effect.

In counterpoint or harmony, no two fifths, nor two octaves, are allowed to succeed each other; the former because exceedingly offensive to cultivated ears, and the latter not only offensive

but productive of no result. These are avoided by the occasional doubling of some intervals, and of rejecting others; also in the observance of the rules appertaining to the four different species of movements of parts: viz. direct movement, when each part ascends or descends together; oblique movement, when one part ascends or descends during the time another remains stationary; contrary movement, which is the best, each part moving contrarywise; and parallel movement, each part remaining upon the same degree See example 19.

From these premises, in the accompaniment of the scale in four parts, as figured by Ludovico Viadana, the contrary movement must be taken in passing from the first to the second degree of the scale, thus