74 
two semitones, which is our only alternative, would be intolerable. 
Hence we arrive at the arrangement Fig. VI. 
shewn in Fig. vi, which is that of the 
ordinary ascending minor scale; but it 
has been already pointed out that a 
scale of this kind does not admit of 
being changed into another, as does 
the diatonic arrangement; and it is 
fortunate that in the descending scale 
the ear does net by any means de- 
mand the small interval of the sem1- 
tone between the eighth and seventh of the scale; on the 
other hand the peculiar and indescribable effect of the minor 
key, of which the flat third is the mainspring, is increased by 
dropping a whole tone instead of half from the eighth to the 
seventh. Taking, therefore, the descending scale and beginning 
with a fall of a whole note, the position of the other semitone 
settles itself; for, whether we put it third in the scale or fourth, 
it will be seen from inspection of the figure that we get no 
different arrangement of the notes: in each case we shall have 
two groups of two and three tones respectively separated by 
two semitones; in other words, in each case we shall have the 
ordinary diatonic arrangement. 
In concluding this little essay, I will express the hope that 
the views which have been propounded, and the method em- 
ployed for their illustration, may tend to give simplicity and 
clearness to a branch of science, the fundamental principles of 
which, though in some respects easy and familiar, are in others 
not free from obscurity. 
H. GOODWIN. 
