Counting front E, the first step to F is only a semitone. This is therefore called a minor second; and that of the in terval of a tone, CD or CE, is a major second. The third, EG, is a minor like DF, the fourth EA, and fifth, EB, will bc found to be of the same nature as those formerly reckoned. But the sixth, EC, consists of three tones and two semitones, and being thus reckoned a semitone less than the sixth be fore described, it is called a minor sixth, and the former a major sixth. The seventh, ED, is likewise minor.
If we reckon the intervals from F, shall find them all of the sante kind as when we reckoned from C, except the fourth, FB, which consists of three tones; and being. thus a semitone larger than the fonrth of our former reckoning, is called a major fourth, and the other a minor fourth. 'Fite major fourth is also sometimes called the tritone. The in tervals, as reckoned from G, are similar to those counted front C, except the 7th GF, which is minor.
The intervals reckoned from A, are similar to those counted front D, except the sixth, which is minor.
78. Lastly, reckoning from B, we find all the intervals like those reckoned from E, except the fifth, BF, which consists of two tones and two semitones. It is called a minor fifth; and the other fifth found in the other couplings, is called a major fifth. Thus we have major and minor seconds, ma jor and minor thirds, major and minor fourths, major and minor fifths, major and minor sixths, major and minor se venths. All these intervals have remarkably different ef fects; whether the extreme sottnds be played or sung in suc cession, or struck together. As it is of the greatest impor tance that the student should understand these distinctions well, and where the major and minor intervals lie within the scale, they are exhibited in notes in the following tables.
In these tables, the major intervals are denoted Joy the Roman numerals II, III, IV, &c.; and the minor intervals by the Arabic figures 2, 3, 4, &c. But the reader is not to understand that this manner of figuring is used in denoting the accompaniments to be played along with a fig,ured bass. The figure itt the three first tables, signifies the unison, which is not properly an interval, even when sounded by different instruments. In the fourth and succeeding tables, the bass is removed an octave lower, and then we begin with a real interval, the octave denoted by VIII; the other inter vals, though enlarged by octave, are still called seconds, thirds, &c.; and are here denoted accordingly, as. if reck
oned from a bass note octave higher.
79. These tables furnish some important remarks: They show what is called the inversion of all the intervals. 'l'o invert an interval, is to place the lower note an octave higher, so that it becomes the more acute of the two, or vice versa, in consecpience of which the interval between the sounds becomes very different. Thus the interval CI) is a major second; but if we invert it, by making D the bass, and C (in the octave above) the higher, we have a minor Seventh; and it is plain, that any interval and its inversion complete the octave. They are, therefore, calletl comple ments to each other. lIence, the smaller any interval is, the greater is the inverted interval, and vice versa. Thus Hence, to rise by one of the intervals united by the brackets, and to fall with the other, brings us to a note of the same name, hut distant by octave. Thus, to rise front C, a ma jor seventh, brings us to B; ancl to descend from C, a minor second, brings us to B octave below the former. The reader may be surprised that 7 and 2 added. should make 8, and not 9. The reason is, that in reckoning each interval, both sounds are included; and so in the two reckonings one of the notes is twice named, which is only reckoned once when the whole aggregate is reckoned. Thus, we say (3D 2, 1)C 7, and the two intervals added make 8; because counting from C to C, D is only once named among the eight sounds; and this will be found universally the cage in adding nuisical intervals together, as we shall have occasion to see in the sequel. 2tully, Within the diatonic scale, (extended through two octaves,) WC have five major seconds, CD, DE, FG, CA, AB, which, by inversion, become tive minor sevenths: two minor seconds, EF, BC, which give, by inversion, two major sevenths ; three major thirds, CE, FA, GB, which, inverted, become three minor sixths; four minor thirds, Dr, EG, AC, BD, by inversion, four major sixths ; six minor fciurths, CF, DG, EA, GC, _AD, BE, which, inverted, give six major fifths. Lastly, one major fourth. FB, by inver sion, a minor fifth. These oug,lit to be studied till they be come quite familiar. 3dly, 1Ve observe that in all these successive reckonings, the order of the sounds does not in any. one exactly correspond with the scale of C; nor are any two of them exactly similar. The order of sounds ascending front 0, and that from F bear the nearest resem blance to the scale of C, each differing from it only by one interval.