Practical harmony is the science of uniting tones agreeable to method and rule. While melody is made up of notes in succession, harmony is composed of notes in combination. Its study demands a complete knowledge of such rudiments of music as the stave and clefs, notes and intervals, time varieties, keys and their signatures, etc. The initial step is made with the diatonic, chromatic, and enharmonic scales and intervals.
Of intervals there are several kinds, both within the compass of the octave and beyond it.
The following list illustrates the principal intervals:
Of these intervals of 2nd, 3rd, 4th, etc., there are several qualities – distinguished according to the number of semitones they contain.
There are major, minor, perfect, augmented and diminished intervals which is shown in the following:
These intervals are classed under the heads consonant and dissonant. The unison (that is, a coinciding note on the same degree of the scale), the perfect intervals of the fourth, fifth and octave, or eighth, are designated perfect consonances; while the major and minor thirds and sixths are called imperfect consonances. The seconds, sevenths and ninths are dissonant intervals.
In harmony the first or keynote of a scale is called the tonic, the second the supertonic, the third the median, the fourth the subdominant, the fifth the dominant, the sixth submediant, the seventh the leading note, the eighth the octave. The principal chords in harmony are the triad, the chord of the seventh, the chord of the ninth, and the chord of the eleventh, and some authorities add the chord of the thirteenth.
A bass note or root, with its major, or minor, third and perfect fifth is called a train or common chord.
Other triads may be built upon each note of the scale; but the species of triad, and the number of intervals in is constituent parts vary according to the note of the scale which forms the bass. After the key-note triad, the next in importance, in its scale relationship, is the dominant triad.
This chord, possessing for its third the major seventh, or leading note of the scale, has a great leaning towards the key-note triad, and on this account is generally used, with an added seventh, to close a composition and to bring it to its original key. The subdominant triad is also used, though not so commonly, to precede the key-note triad in a final close or ending.
It should be noticed that all the interval of the scale are contained in the key-note, subdominant, and dominant triads, which chords, therefore, possess the property of giving tonal character to the keys to which they belong.
When the octave of a bass note is added to a triad, it is a complete chord in four parts, and can be ‘inverted,’ or made to appear in three different positions.
This is done by taking either of its notes instead of the original root for the bass.
Chord of the Seventh
A chord of the seventh is formed by adding an interval of a seventh, which may be either major, minor or diminished to the triad. The following combination of notes is a chord of the diminished seventh.
A complete study of harmony is necessary to an understanding of the several forms and uses of this species of chords of the seventh.
The principal form of it is the chord of the dominant seventh, consisting of the root, the major third, the perfect fifth, and the minor seventh.
It is called ‘dominant’ from its peculiarly assertive character, from being formed upon the fifth, or dominant note of the scale, and from its embodying the four principal tone elements of the octave scale or key. There are three inversions of this chord.
The first inversion with the third of the chord in the bass is called the chord of the ‘sixth and fifth’; the second inversion, with the fifth in the bass, is known as the chord of the ‘six, four, three’; the third inversion with the seventh in the bass is named the ‘six, four, two’ chord.
Chord of the Ninth
The chord of the ninth is generally built upon the fifth, or dominant of the scale and consists of a chord of the seventh, with an added ninth.
The ninth may be major or minor, according to the scale from which it is taken. Chords of the ninth may be formed upon other notes of the scale, subject to certain rules concerning suspensions in harmony.
This chord has three inversions – on the third, fifth, and seventh of the chord. In four part harmony constituent elements of this chord are the root, third, seventh and ninth.
Chord of the Eleventh
The construction of the chord of the eleventh consists in adding an eleventh to the chord of the dominant ninth. The eleventh must always be sounded in the uppermost part, and the ninth and seventh intervals must form parts of the chord.
The first inversion has the fifth in the bass; the next the seventh, as the root; the third inversion has the ninth in the bass; and the last inversion, the eleventh becomes the bass.
Progression, Preparation and Resolution
The progression of chords in harmony demands specific study. As a broad rule, all discords, except the chord of the dominant seventh, must be ‘prepared’ and ‘resolved’ according to the rule of harmony; and the progression of concords must be made without producing consecutive perfect fifths, octave, or unisons between any of the parts. Thus such a passage as the following would be inadmissible because of the consecutive perfect fifths between the soprano and the alto parts.
Many other restrictions, rules and licenses affect the progression of parts in harmony.
‘Preparation’ as applied to a discord means its introduction, in the same part, in a previous chord. Thus, in the case of the following chord of the seventh, the discord E is prepared by its presence in the preceding chord as shown by the tie.
The ‘resolution’ of a chord is the term applied to the due progression of the parts which constitute it. Take the chord of the dominant ninth. In the following passage, the dissonant notes, the seventh and ninth in the second chord on D, are prepared in the previous chord, and the ninth and seventh duly resolve upon the fifth and third respectively in the next chord upon G – as a bass note at a distance of a fourth above the previous root.
In this same chord on G, one note, B, called the ‘leading’ note has an inviolable progression upwards to C, the key-note of the following chord.