70 
in an ascending minor scale. The arrangements of the semi- 
tones in the ascending and descending scales of a minor key 
are, as every one acquainted with the elements of music knows, 
different, and the signature is that which corresponds to the 
descending scale, the semitones being put into their proper 
places in the ascending scale by means of two accidentals. 
The arrangement of the semitones in the descending scale, if 
represented according to the method of this paper, is the ordi- 
nary diatonic arrangement: for example, Fig. 1. would represent 
the descending scale of A minor, if we pass round the circle 
from A in the sense opposite to the motion of the hands of 
a clock; in other words the key of A minor has the same 
signature as that of C major; and as the signature is thus 
taken from the descending scale the modulations from one key 
to another in the minor scales follow the same rule as those 
in the major; but this would not be the case if the arrange- 
ment of semitones were that which, because it is more pleasing 
to the ear, we adopt in the ascending scale. 
These considerations seem valuable with reference to the 
question, What is the reason why in modern Europe the com- 
mon diatonic scale has gained such universal acceptance? It 
is a mistake to suppose that it is a scale founded upon any 
natural necessity ; if so, it would be universal, which is not 
the case. But this seems to be the fact, namely, that there 
is such a perfection in the arrangement as ensures its adoption 
as soon as known, and guarantees its permanence to the exclu- 
sion of all others, except so far as a different arrangement may 
sometimes produce a feeling of pleasure by its novelty or its 
eccentricity. Nor is it perhaps difficult to deduce the diatonic 
division from simple principles, and to shew that it is not so 
arbitrary as at first sight it may seem. 
The first principle must be the identity of a note with its 
octave. I speak of the octave, and by so doing appear to 
anticipate the existence of eight notes in the scale ; but I do not 
