The intervals, or relative pitches of the notes to the tonic C, appear expressed in the fractions, which are determined by assuming the wave length or amount of vibration of C as unity, and finding the ratio of the wave length of any other note to it. The value of an interval is therefore found by dividing the wave length of the graver by that of the acuter note, or the number of vibrations of the acuter in a given time by the corresponding number of the graver. These fractions, it is seen, comprise the simplest ratios between the whole numbers 1 and 2, so that in this scale are the simple and satisfactory elements of harmony in music, and everybody knows that it is used as such. Now nature exposes to us a scale of color to which we have adverted; it is thus: Red, Orange, Yellow, Green, Blue, Indigo, Violet. Let us investigate this, and see if her science is as good as mortal penetration; let us see if she too has hit upon the simplest fractions between 1 and 2, for a scale of 7. We can determine the relative pitch of any member of this scale to another, easily, as the wave lengths of all are known from experiment. The waves of red are the longest; it corresponds, then, to the tonic. Let us assume it as unity, and deduce the pitch of orange by dividing the first by the second. The length of a red wave is 0.0000266 inches; the length of an orange wave is 0.0000240 inches; the fraction required then is 266/240; dividing both members of this expression by 30, it reduces to 9/8, almost exactly. This is encouraging. We find a remarkable coincidence in ratio, and in elements which occupy the same place on the corresponding scales. Again, the length of a yellow wave is 0.0000227 inches; its pitch on the scale is therefore 266/227; dividing both terms by 55, the reduced fraction approximates to 5/4 with great accuracy, when we consider the deviations from truth liable to occur in the delicate measurements necessary to determine the length of a light vibration, or the amount of quiver in a tense cord. A green wave is 0.0000211 inches in length; its pitch is then 266/211, which reduced, becomes 4/3; in like manner the subsequent intervals may be determined, which all prove to be complete analogues, except, perhaps, violet, whose fraction is 266/167, which reduces nearer 16/9 than 15/8. But these small discrepancies, which might be expected in the results of physical measurements, do not cripple the analogy which appears now in the two following scales: DIATONIC OR NATURAL SCALE OF MUSIC. C, D, E', F, G, A, B, C' D' E', &c. 1 9/8 5/4 4/3 3/2 5/3 15/8 2 18/8 10/4 DIATONIC OR NATURAL SCALE OF COLOR. Red, Orange, Yellow, Green, Blue, Indigo, Violet. 1 9/8 5/4 4/3 3/2 5/3 16/9