Nos. 5, 6, 7, S, are different progressions produced by the rise or descent of the bass diatonically. In Nos. 5 and 7, we have allowed a third to be followed by a perfect con cord in similar motion between the bass and third part, which can hardly give offence, being so well covered by the upper parts. Besides a third followed by a fifth in similar motion, when the upper falls one degree, as in No. 5, is very good, and universally practised even between the extreme parts, or in two parts.
113. Rameau, and after him Mr. Kollrnann, lay it down absolutely as a rule, thin one fundamental concord cannot follow another diatonically. The latter gentleman accounts for such progressions, by saying that one or other of the chords is a discord from which the discord is re moved. This is that very convenient kind of reasoning which logicians call beggin,g the question, by which any thing may be made of any thin7; of which he is so fond, that he constantly uses it throughout his book. We are con tent with tea ching the procedure as classical, and of good effect, leming system-makers to account for it as they may. We must hov.-ever repeat, that chords succeed each other best, when they are connected by some connnon sound. On this subject we may quote the following- observations from Dr. Burney. " In old compositions the harmony of each note in the scale seems detached and unconnected by rela tive sounds ; and in the new, two chords seldom succectl each other, without being combined by some sound, in common with both. The following basse„ with no other harmony than common chords, perpetually occur in ancient music: DC, CE, EG, AGF. Of this last modulation I can give no better illustration than the following beginning of a chant of Palestrina, front a manuscript chiefly in his own hand writing.
arises to the thorough bass player from their being figured in the same way ; because he is to take the intervals indicated by the figures as they are found in the scale in which he is playing at the time as indicated at the clef. When the coin. poser intends any other interval, as when he changes the key , the change is intimated in the figures, which we shall explain more particularly afterwards. Common chords are not figured at all, except on some particular occasions, when it becomes necessary, as shall afterwards be shown. 'Fite imperfect chord on the seventh of the major and second ot the tninor scale, is usually figured with a 5, and generally with S011IC additional indication that the lesser fifth, and not the perfect, is intended, as Li 5, b 5, A or 3.
" The old masters," he observes, " often accompanied six of the seven notes in every key with common chords. The moderns, on the contrary, allow them only to the key note, and its fifth; to all the rest they (generally) give a sixth or a discord."
We shall now, therefore, proceed to exhibit the inver sions of the C0111111011 chords.
114. A common chord has only three real parts, for the eighth is only a doubling of the bass note. So long as this fundamental note is lowest, however the upper parts may be arranged, the common chord remains. But if we set either of the two remaining real parts in the bass, wc invert the chord; and thus the common chord has two inversions. From what we have said, art. 79. concerning the inversion of any interval, the reader will easily understand this pro ceeding, Let us begin with the major chord. If instead of :he fundamental note, we put the third of the common chord for bass, placing the fundamental sound an octave higher, that is inverting the interval, we shall have a chord consist ing of a minor third and minor sixth. This is called a chord 6 of the sixth, and in thorough bass is figured 3, or simply 6, the third to the bass being understood. If again we put the fifih of the common chord for bass we have a chord ing of the perfect (or minor) fourtit and major sixth; called the chord of the fourth and sixth, and figured thus These 4 two chords are called the first and second derivatives of the major common chord.
After the sante manner, by inverting the minor chord, we obtain its MO derivatives. Its first derivative consists of a major third and major sixth, and in thorough bass is figured 6 or simply by 6, the third being understood. The second 32 derivative of the minor chord consists of a perfect fourth and minor sixth, figured also 64. Although these derivatives of the major and of the minor chords differ so very essentially in their component parts, and in their effects, no confusion Mr. Kollman would have the last of these used solely to indicate the chord of the lesser fifth, when it is treated after the manner of a consonant common chord, and the other signatures to be employed to indicate the use of it as a discord, as will be explained in the sequel. By inverting this chord, we have two derivatives; 1st, when the third is made bass, a chord consisting of a minor third and a major sixth. This is figured 6 or simply by a 6, like- the 1st derivatives of perfect com 3' mon chords major and minor. To prevent ambiguity, a na tura! may. lie put under the 6, thus tl to indicate that the third is to be taken as in the scale; but this is not usually. done. When the fifth of the imperfect chord is put in the bass, we have a chord consisting of a major fourth and a major sixth, figured thus 6 the dash or cross added to the 4+ 4, indicating that it is the major and not the perfect fourth. However, we shall have occasion to speak of these chords, and their signatures or figures again, when we treat of the inversion of the seventh.