ee a ee ene ean epee Iran ener ara ena 
ES eee Oe ee nO eee ee ee ee ee ee Se eg eee ee ee 
On Musical Temperament. 29 
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, 
Sths on D, 2 on E, and i 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 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 dimi- 
nished 7th, in the few instances in which it occurred, was con- 
sidered as the first inversion of the 2th, 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 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. 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 1IId CE, and the 3d EG. The 
