Page:Harmony - its theory and practice.djvu/20

18 has by itself an incomplete effect. Let the student play the following dissonant chords, and he will feel this.

Now, as before with the dissonant intervals, let us put after each chord a consonant chord for its resolution. The satisfactory effect is felt at once. In general, it may be said that consonance is a position of rest, and dissonance a position of unrest.

19. Intervals are always reckoned upwards, unless the contrary be expressly stated. Thus "the third of C" always means the third above C; if the third below is intended, it must be so described. The number of an interval is always computed according to the number of degrees of the scale that it contains, including both the notes forming the interval. Thus from C to E is called a third, because it contains three degrees of the scale, C, D, E. Beginners are apt to get confused on this point, and to think of D as the first note above C, and E as the second. But the note C is itself counted as the first note of the interval. Similarly, from G to D is a fifth, from F to D a sixth, and so on in all other cases. The same reckoning, but in the reverse direction, applies to the intervals below. Thus A is the third below C, D is the fourth below G, &c. Let the student examine the major scale of C in §9, and he will find within the compass of the octave there given two 7ths, three 6ths, four 5ths, five 4ths, six 3rds, and seven 2nds. It will be a useful exercise for him to discover them for himself.

20. An interval larger than an octave is called a compound interval. Thus the interval

is compounded of the octave, C to C, and the third, C to E. (The octave is printed here as a small note.) Obviously, in addition to the third at the top, the interval contains the seven notes of the lower octave from C to B. The upper C is already counted as part of the third. Thus the number of a compound interval is always 7 more than that of the simple interval to which the octave is added. Therefore,