The relative position of the notes of a chord, and consequently its intervals, may be altered by raising one or more of them an octave; and, on the whole, the nearer the intervals approach to their position in the harmonic scale, the purer is their harmony. Close, in contradistinction to dispersed harmony, is when the notes of a chord are so near that no component note could be placed between them. When the fundamental bass of a chord ceases to be its lowest note, the chord is said to be inverted. Thus and — are inversions of the common chord, but not• —e9-- • where the fundamental bass is still the lowest note.
The minor triad is, as we have seen, a compound chord, whose ratio is 20, 24, 30, taking its minor third from the triad below, and its major third from the triad above. Its fundamental bass is the key-note. The minor mode has, like the major, three triads. in each key—those of the tonic, subdominant, and dominant; and the minor common chord admits of the same inversions as the major, by making the third or fifth the low est note.
The first seven notes of the harmonic scale contain the chord next in consonance to the common chord, the chore of the seventh or dominant harmony. Rejecting octaves, it is the harmonic triad with the addition of the grave seventh, 4, 5, 6, 7, C E G or G B D F, and admits of three inversions, according as the third, fifth or seventh is taken instead of the root as the lowest note. This chord belongs to the key of which its fun damental note is the dominant; and in order to satisfy the ear, it requires to be followed by a resolution into the common chord of the key, or one of its inversions, the major third rising a semitone to the key-note, and the.seventh descending one degree --,,,,,,0 • The dominant seventh note is flatter by an interval of 63, 64, than the subdominant of the key. though the two are not distinguishable on keyed instruments. The chord of the dominant seventh is the same in the tonic minor as in the major mode, but differs in . .
_V _ 0 its resolution, in respect that it descends a tone instead of a semitone .. ,,,-,1 mt. — The dominant harmony affords numerous means of modulating from one key to another. For example, the addition of a dominant seventh to the common chord of a key, effects , . a modulation into the key of the subdominant In modulating Ir —0 —0 —e9 into the key of the dominant, the supertonic bears the dominant harmony, and becomes dominant of the new key " 0-11 For other modulations, we must refer to works on the theory of music.
The following more complex harmonies are also in general use ; ; __ in — .., 1 P a 4 5 6 7 8 1, the chord of the added ninth, consisting of the dominant harmony (its root generally omitted) with the fifth of the adjacent triad above; 2, 3, and 4, the different forms of the added sixth, or chord of the subdominant; 2 is the triad of the subdominant, with the third of the adjacent triad below, or rather its octave; 3 is the triad of the subdominant, minor mode, with the third of the adjacent triad below; and 4, the same triad with thil third of the tonic major to the adjacent triad below; 5, the diminished seventh, a corn. pound of the characteristic notes (B F) of the dominant harmony of the major mode with those (G..r.'; D) of the relative minor; 6, 7, and 8, the augmented sixths, all dominant har. monies, resolving into the major tonic; 6, called the Italian sixth (F A D',;;), is a com pound of the characteristic notes (A DM of the dominant harmony of the minor mode (11 D-:. F A) inverted, with the dominant seventh note (F) of the major triad (C E G) below
for a bass; 7, the French sixth (F A B D,1,), the same as the last, with the addition of the (soave to the fundamental bass; 8, the German sixth (F A C .11), compounded of the .characteristic notes of the dominant. harmony of the minor mode inverted, with the domi nant sevenths of the major triads below and above.
All classical harmonies can be reduced to the chords enumerated, varied by inver sions, omissions, suspensions, and pedal basses. A pedal bass or organ point is a bass note snstained through a progression of chords, to only the first and last of which it is the proper bass. The pedal bass of the tonic is often used with the chord of the domi nant seventh. the added ninth, and the diminished seventh, and occasionally with other -chords: sometimes the pedal harmonies are taken on the dominant instead of the tonic, and the holding note sometimes occupies an upper part instead of the bass • 7 _ ] A • r: ,...Y -so j 1 .._j_.;/ '7------- --...._— ----_____--- ---____--- ----....----- --)---..—. j----). 1 --.° 11 4 • A musical composition consists of a succession of notes or of chords subject to certair. laws. Like discourse, music has its phrases, periods, and punctuation. When a pima •of music continues in the same key, it is said to move by progression, a term used in con. tradistinction to modulation, where the key is changed. Progression in music of two parts is of three kinds—obliTte, when one part repeaqs or holds on tho same note, while the other moves it.tritiall down; direct,. where both parts move in the same way; an contrary, where one moves up, and the other down. Consecutive chords should in gen eral be connected, either as having some note in common, or as being the chords of closely connected keys. There are certain chords which require a special resolution—i.e., they must be followed by certain other chords; and there are certain progressions which, from harshness, are in ordinary cases to be avoided, more particularly consecutive fifths and consecutive octaves, the latter, however, admissible when used merely to strengthen a part. Modulation is generally effected by introducing the chords common to both keys, and the secret of good modulation consists in the skillful choice of interme diate chords. Every regular piece of music is composed in a particular key, in which it begins and ends, and which predominates over all the other keys into which it has.modu lated. The keys into which a key most readily modulates are those most nearly related to it—viz., the dominant, the subdominant, and the relative and tonic major or minor. We have seen how modulation may take place by introducing the dominant harmony of the new key or one of its inversions, and in this way the entire harmonic circle of the keys can be made, either by ascending or descending fifths; but in order to effect this change, it will be necessary, on reaching the key of C:',.: with seven sharps, to substitute, by what is called an enharmonic (q.v.) change, Dp with five flats, or vice versa, which on instruments with temperament produces no real change on the pitch, but merely on the names of the notes.