338 On Musical Scales. [July, 
yet been detected by the eye of man, assisted even with his won- 
derful instrumental appliances—then may we accept it without a 
lingering doubt, and rely upon its power to advance us in the great 
task committed by his Creator to intellectual Man, of subduing the 
earth and holding dominion over it. 
Vv. ON MUSICAL SCALES. 
By Sir J. F. W. Herscuex, Barr., F.BS. 
Havine had my attention recently drawn to an ingenious attempt, 
by Mr. Jackson, to explain the relations between the Major and 
Minor scales in music, on the principle of the maximum of simplicity 
in the ratios of the vibrations of the several notes employed, I could 
not help being strongly impressed with the want of clearness intro- 
duced into the discussion of this subject by the employment of the 
fractions expressing the ratios of the vibrations, or of the lengths of 
the vibrating strings, and their multiplication or division one by 
another, to explain the relations of musical intervals. The elemen- 
tary fractions concerned, 4, 4, and +, are, it is true, of the simplest 
kind ; but their combinations, formed by multiplication and division, 
by whole numbers and by each other, present sufficient complexity 
to throw a kind of haziness over the perception of their magnitudes 
which distract attention. We have not quite so clear a perception 
of the magnitude of a fraction as of an nteger number ; and this 
indistinctness increases with the numerical increase of the numerator 
and denominator. ‘Thus, to say which of two proposed fractions is 
the greater, if their numerators and denominators exceed a few 
units, often requires some consideration, and reduction to a common 
denominator ; as for instance in the case of 7 and +2. The great 
majority too of those who study music do it as asubject sud generis, 
and not as a branch of mechanics. ‘Their thoughts are directed to 
musical intervals and not to the vibrations which give rise to the 
sounds, or to the lengths of the strings which vibrate; and accord- 
ingly they find it far easier to conceive the interval (say) from C 
to E as the sum of the intervals from C to D and from D to &, 
than as a ratio compounded of two ratios expressive of these in- 
tervals severally. The use of logarithms, by the intervention of 
which musical intervals are treated as magnitudes susceptible of 
addition and substraction, and, like feet and inches, measurable on 
a scale (that scale being the finger-board of an imaginary pianoforte 
capable of yielding every gradation of audible tone from the lowest 
to the highest ; the same interval corresponding to the same dis- 
