73 
number of harmonies which can be made amongst the various 
notes of the octave or of successive octaves; and these con- 
siderations are valuable; but there would seem to be a propriety 
in the arrangement of the notes independent of them; there is a 
stately march of sound in the ordinary gamut which is highly 
satisfactory to the ear, and for which considerations of harmony 
do not seem to me to account. 
One more point occurs to me as worthy of notice. I have 
spoken of the third and fifth of the scale as claiming their 
places before all other notes. There can be no doubt of this as 
regards the fifth ; it fully deserves the title of the dominant; 
when we listen to a piece of music, its sound is left upon the ear 
almost, if not quite, as clearly as that of the tonic itself; and 
mathematically speaking the numbers which denote the ratio 
of its vibrations to those of the tonic are simpler than in the 
case of any other notes. But there may be a demur to the same 
precedence being granted to the third, at least to the major 
third, because it may be argued that the succession of notes is 
as pleasing and satisfying to the ear if for the major we sub- 
stitute a minor third; that is, if we take as the basis of our 
system of notes the succession 
Crip GC, 
instead of 
C, HE, G, C. 
Let us, then, just examine the conclusions to which we shall 
be led, if we start with the minor third as one of the primary 
intervals. 
Our musical circle will now be as in Fig. vi.; and the 
question will be, where shall we put the semitones? In the 
ascending scale the demand for a leading note will lead us to 
put one of them below the upper C; and with regard to the 
other we easily perceive that the effect of the flat third is 
lost unless the note preceding it be distant by a small interval 
or by a semitone; not to mention that the juxtaposition of 
