On Musical Temperament. 29 



The following anomalous chords were found in the major 

 mode, and are subjoined, to make the list complete : 

 8 >5t5ths on C, and 1 on D. 

 6 f ths 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 spe- 

 cified at the top, which were found in 150 scores in the major 

 mode ; and the right, the corresponding results of the exami- 

 nation of 60 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 dimi- 

 nished 7th, in the few instances in which it occurred, was con- 

 sidered as the first inversion of the |th, 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 play- 

 ed, is easily computed. We will suppose three notes, be- 

 sides 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 con- 

 sonances. In the chord of the 7th, which naturally consists of 

 four notes, we will suppose, for the salce of uniformity, that 

 one is omitted ; and as the 7th ought always to be struck, we 

 will suppose the Vth and Hid of the base to be omitted, each 

 half the number of times in which this chord occurs. Consi- 

 dered 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 Hid CE, and the 3d EG. The 



