71 
intend to make this anticipation. I only use the word octave 
to describe that note which is produced by vibrations of air 
twice as rapid as those which produce the fundamental note. 
Experience teaches us that the coincidence of two notes so 
related is acoustically perfect, so that they may be regarded 
as the same, and we may with propriety speak of the upper 
C or the lower C, applying the same letter C to express two 
notes, which, mechanically speaking, differ from each other, but 
which musically may be regarded as identical. | 
The question of the musical scale therefore resolves itself into 
that of interpolating a convenient number of conveniently related 
sounds between a note and its octave. Of all possible sounds 
which may be interpolated there are two which seem to have 
a chief claim to admission. These are the third and fifth, 
according to the common nomenclature; but mathematically 
speaking they are sounds produced by vibrations bearing a 
very simple numerical relation to those which produce the 
fundamental note, and musically speaking they are sounds 
which produce a very perfect harmony with the tonic and 
octave ; and when the four notes are sounded successively, there 
is a simple and majestic progress from one to the other which 
every ear at once recognizes with pleasure. 
So far all is tolerably simple, but the problem still remains 
to interpolate notes amongst those four, which we admit without 
question as the chief in the scale ; and the problem branches out 
still further into the more complicated one of temperament; upon 
this many treatises have been written, and a compendious ac- 
count of the question may be found in Sir John Herschel’s 
Treatise on Sound in the Encyclopedia Metropolitana. It is not 
the purpose of this paper to enter into this difficult subject ; 
but without doing so, I think it may be shewn by reference 
to the mode of illustration which has been adopted, that we are 
(as it were) forced into the arrangement of tones and semitones 
which constitutes the ordinary diatonic scale. For if we admit 
