The following anomalous chords were found in the major mode, and are subjoined, to make the list complete:
8
5ths on C, and 1 on D.
5 5/4ths on D, 2 on E, and 1 on G.
The left hand column of the foregoing table contains the fundamental bases of the several chords. When any number is annexed to the letter denoting the fundamental, it denotes the quality of some other note belonging to the chord. E III, for example, denotes that the various chords on E, which stand against it, have their third sharped; G 3, that the third, which is naturally major, is to be taken minor, &c. Of the two columns in each of the four remaining pairs, the left contains the number of chords belonging to each root, of the kind specified at the top, which were found in 150 scores in the major mode; and the right, the corresponding results of the examination of 50 scores in the minor mode. The diminished triad, which is used in harmonical progression like the other triads, has its lowest note considered as its fundamental. The diminished 7th, in the few instances in which it occurred, was considered as the first inversion of the 9/7th, agreeably to the French classification, and was accordingly reduced to that head.
From this table, the number of times that each consonance of two notes would actually occur, were the 200 scores played, is easily computed. We will suppose three notes, besides octaves, to be played to each chord. The octaves played it is unnecessary to take into the computation, as it would only multiply the number of consonances whose temperament is the same, in the same ratio, and would have no effect on the ratio of the numbers expressing the frequency of the different consonances. In the chord of the 7th, which naturally consists of four notes, we will suppose, for the sake of uniformity, that one is omitted; and as the 7th ought always to be struck, we will suppose the Vth and IIId of the base to be omitted, each half the number of times in which this chord occurs. Considered as composed of three distinct notes, neither of which is an octave of either of the others, each chord will contain three distinct consonances. The common chord on C, for example, will contain the Vth CG, the IIId CE, and the 3d EG. The 9/7 on C will contain the VII CB, the IX, or (which must have the same temperament) the IId CD, and the 3d BD. Reducing all these consonances to their proper places, and adding those of the same name which have the same degree for their base, we obtain the following results:
TABLE II.
| Bases. | Vths, 4ths, and Octaves. | IIIds, 6ths, and Octaves. | 3ds, VIths, and Octaves. | |||
| Major. | Minor. | Major. | Minor. | Major. | Minor. | |
| B | 8 | 8 | 10 | 8 | 1141 | 214 |
B | 3 | 6 | 22 | 19 | —— | —— |
| A | 195 | 607 | 22 | 10 | 626 | 663 |
G | —— | —— | —— | —— | 32 | 310 |
| G | 1088 | 116 | 1090 | 125 | 22 | 23 |
| F | —— | —— | —— | —— | 78 | 10 |
| F | 395 | 78 | 486 | 301 | —— | —— |
| E | 59 | 308 | 40 | 284 | 1828 | 308 |
| E | —— | —— | 2 | —— | —— | —— |
| D | —— | —— | —— | —— | 7 | 9 |
| D | 197 | 156 | 60 | 7 | 403 | 213 |
| C | —— | —— | —— | —— | 26 | 12 |
| C | 1807 | 278 | 1959 | 870 | 4 | 1 |
| Bases. | 5ths, IVths, and Octaves. | 7ths, IIds, and Octaves. | VIIths, 2ds, and Octaves. | |||
| Major. | Minor. | Major. | Minor. | Major. | Minor. | |
| B | 256 | 265 | 25 | 17 | —— | —— |
| B | —— | —— | —— | —— | —— | —— |
| A | 2 | 1 | 34 | 7 | 3 | —— |
| G | 10 | 53 | —— | —— | —— | —— |
| G | —— | —— | 188 | 20 | —— | —— |
| F | 74 | 7 | 1 | 2 | —— | —— |
| F | —— | —— | —— | —— | 17 | 16 |
| E | 10 | 1 | 20 | 27 | —— | —— |
| E | —— | —— | —— | —— | —— | —— |
| D | 7 | 5 | —— | —— | —— | —— |
| D | —— | —— | 123 | 27 | —— | —— |
| C | 9 | 10 | 1 | —— | —— | —— |
| C | —— | —— | 5 | 1 | 10 | 1 |
Besides the following chromatic intervals: