HABMONY. 574 of the scale. When the same tone is sounded on two ditTorent instruments the interval is called a prime, both tones being on the same degree of the scale. The tone upon the second degree forms the interval of the second with the fundamental tone, and so on, until the eiglith degree is reached, which is the same as the first, one octave higher. Generally, all intervals are reckoned within one octave; thus C-e" is a third, although the two HAKMONY. INVERSION OF TRIADS. 6 Fundamental. First Inversion. EX. 7. Second Inveraion. tones composin.'? a chord, a distinction is made between close and open, spread or extended har- SKO' tones are separated by more than three octaves, mony. In example 9 the first chord (a) is in For theoretical purposes, however, the intervals close harmony because none of its tones can be of the ninth, tenth, eleventh, and twelfth are transposed an octave, and still fall within the recognized. Intervals are classed as consonant other tones of the. chord. The second chord (b) INVERSIONS OP CHORD OF SEVENTH. i -S2. 2 3 ^ bS= Faadamental First Inversion. Second Inversion. Third Inversion. and dissonant, and again as major, minor, aug- mented, diminished, and perfect. Chobds. Under this heading are treated the nature and formation of chords. The fundamen- tal chord is the triad consisting of three tones, the prime, third, and fifth. According as the major or minor third is used, the chord itself is major or minor. Tlie presence of an aug- mented or diminished interval renders the chord likewise augmented or diminished. All chords are constructed by means of thirds (ex. 5). By TRIADS. P ^^ Major. Minor. Augmented. KX. 5. Diminished. adding the interval of a third to any triad a chord of the seventh is obtained, so called because the last added tone forms the interval of a seventli with the fundamental tone of the chord (ex. 6) ^^ All chords can be inverted, i.e. I (m) ^ ~~ ~^S~~ ^"y t"'^^ of "■ chord can be in "iJ' ' "^' t'l^ t)ass or lowest part. When EX. 6. the fundamental tone is in the bass the chord is said to be in its fundamental position. With the third in the bass we obtain the first inversion : with the fifth in the bass we have the second inversion (ex. 7). Chords of the seventh admit three inversions (ex. 8). With respect to the relative position of the various m is in open harmony, because by transposing the E an octave, it falls between the tones C and G b of the chord (ex. 9). Likewise, -; transposing the G an octave g lower, it falls between C and E. Progression of Chords. Each tone composing a chord is regarded as belonging to a distinct voice or part. The rules governing the progres- sion of chords are exceedingly few and simple, yet it requires long and constant practice to ac- quire the art of leading the voices correctly. ( 1 ) Parallel octaves and fifths are strictly forbidden. This means that two tones of one chord forming the interval of an octave or a fifth must not progress in such a manner as to form the same interval in the next chord (ex. 10). The ex- ample under (a) is bad because the progressions c-d and f-g produce fifths in both chords. The correct progresssion is given under (b). Octaves EX. 10. and fifths may he open or covered. They are open, as in example 10 (a), when the forbidden inter- vals occur in both chords : covered when they oc- cur only in the second chord as the result of prrallel motion, as in the following (a) (ex. 11). These covered fifths can be avoided by leading the
