Intervals may be inverted; that is, the lower note, by being raised an octave, may be placed uppermost; or the upper note, by being lowered an octave, may be placed undermost. By inversion, a second is changed to a seventh, and a seventh to a second; a third is changed to a sixth, and a sixth to a third; a fourth to a fifth, and a fifth to a fourth. Major intervals are changed to minor, and minor intervals are changed to major. A minor second becomes a major seventh, and a major second becomes a minor seventh. A major third becomes a minor sixth, and a minor third becomes a major sixth ; and so on, as in the following examples: Intervals are divided into Consonant and Dissonant. When two (or more) notes are heard at the same time, it is found that some of these intervals are agreeable and others disagreeable to the ear. The intervals which form the agreeable combinations are called consonant, the others dissonant. Harmony is not confined to the use of consonant intervals or concords only. On the contrary, the admixture of dissonant intervals, or discords, produces many of its greatest beauties. The consonant intervals are the major and minor third, the fifth, and the octave, with their inversions; namely, the major and minor sixth, and the fourth. The unison also may be included; because, though it cannot properly be called an interval, yet it is the inversion of the octave; and when used by two or more voices, is agreeable to the ear, and of use in harmony. It must, however, be remarked, that, though the inversion of the third (the sixth) is as agreeable to the ear as the third itself, yet this is by no means the case with the inversion of the fifth (the fourth); which is so much less agreeable than the fifth, that it requires 88 8 The notes of which a triad consists may be taken in different positions; for example În changing the position of a triad, the fundamental tote remains in the lowest place, or in the bass. But he triad may also undergo different inversions, by placng the third or the fifth in the lowest place, or bass. The third may be placed in the bass, producing the chord of the third and sixth * PROGRESSION OF CHORDS. Although every note of the scale may thus be made the foundation of a triad (or common chord, as it is also called), yet, in forming a harmonious series of triads, they cannot be made to follow each other at pleasure; but their succession must depend on certain rules deduced from the position of their fundamental note in the scale to which it belongs. In every scale, the most essential note is the key-note, or tonic. This note, or one of the notes contained in its triad, begins and ends every strain of melody or harmony, and recurs so frequently, that its impression is never lost upon the ear. Melodies frequently con The fifth may be placed in the bass, producing the sist entirely of the notes of this triadchord of the fourth and sixth. ୫ D And every other triad may be similarly inverted. Next to the key-note, or tonic, the most essential note is the fifth of the scale, called, from its importance, the dominant or ruling note. By adding this note, and the notes of its triad, to those of the tonic, a larger field of melody and harmony is thrown open. The triads, therefore, of the tonic and of the dominant are of the most frequent occurrence, and most easily alternate with each other. Alternations between the tonic and dominant, in different positions 80 Alternations between the tonic and dominant, in different inversions 8 After the tonic and dominant comes the fourth of the scale, called the subdominant, with its triad * In the present treatise, we make no use of the method of marking the different positions and inversions of chords by means of what are called thorough bass figures. It is a rude and clumsy contrivance, invented in the very infancy of the art of harmony, superseded by a better system of notation, and entirely discontinued in modern practice. It still continues to encumber books of instruction, because its acquirement is considered useful in order to read old music still extant, in the notation of which the figures were used. But this reason is becoming weaker every day as most of the classical compositions of the old masters have! (or are being) reprinted in the modern manner of notation Alternations of the tonic, dominant, and subdominant triads, in different positions Alternations of these three triads, in different inrersions The triad on the second note of the scale (called the supertonic) is the next, in frequency of use, to the preceding three. Its employment may be understood from the following example: 16 The above four triads-the tonic, dominant, subdominant, and supertonic-are the most essential. Pat the triads upon the third and the sixth notes of the scale (E and A in the scale of C) are also in frequent blended with the others; as thus The only remaining triad is that on the serenth note of the scale, or the imperfect triad. One of its interv (the imperfect fifth) being dissonant, it is much less frequently used than any of the other triads. In or to diminish its harshness, the dissonant note must fall, in the following chord, to the note immediately be it. Thus F, the dissonant note in the triad of B, must fall to E. This is called resol ring the discord Here, it will be observed, the tonic and subdominant are minor triads. The dominant is a major triad, and rep tonic an imperfect triad. The following examples will show how they are employed: Alternations between the tonic and dominant, in different positions and inversions 8 & Alternations between the four triads In forming progressions of chords, several conside- | Care, therefore, should be taken that the notes of each ations must be attended to. A chord must be regarded is a harmonious combination of notes sounded at the ame time by several voices or instruments; and a series of chords must be regarded as a succession of notes sounded by several performers, and forming several different parts or melodies, heard at the same time. part follow each other smoothly, as in the examples already given. It will be observed, in general, that the bass moves by larger intervals than the upper parts of the chord. The following is an example of the smoothest form in which a progression of triads can be arranged : 8 It is not permitted to make any two parts ascend or descend together by consecutive fifths, or consecutive octaves. Take, for instance, the progression from the tonic to the supertonic Suppose these notes sung by four voices, in the order D Here, while the bass rises from C to D, the second voice falls from G to F, and the highest voice falls from C to A. The progression of the triads is the same, with a different motion of the parts. This motion, when one part rises while the other descends, is called contrary motion. When both parts rise or fall, the motion is called similar; when one part rises or falls while the other part is stationary (that is, repeats or continues the same note), the motion is said to be oblique. It is not easy to explain why two fifths, heard consecutively in similar motion, should produce a bad effect, seeing that the fifth is, next to the octave, the most perfect consonance. But the fact is sufficiently ascertained by experience. The prohibition of two octaves in succession is of a different kind. They are not offensive in themselves, and are prohibited only when they would produce a poor and meagre harmony; for, a note and its octave being considered as the same, if two parts move in octaves, one of them is, in respect to fulness of harmony, thrown away. There is, consequently, no harm in making two parts move in octaves when the harmony is otherwise as full as is requisite. A whole strain of music may be performed in octaves (as when a man and a woman sing together apparently the same notes); but this is not regarded as harmony at all, in the technical sense of the term. CHORDS OF THE SEVENTH. Besides the chords called triads, or common chords, there is another class of chords, called chords of the secenth. From these two classes, every chord used in harmony is derived. The principal chord of the seventh is formed on the dominant, or fifth note of the scale. It is formed by adding a minor seventh to the major triad on that note Dominant of C major. Dominant of A minor. |