In a footnote to Blaserna's “Theory of Sound in relation to Music” (p. 94), it is stated that Euler was acquainted with the importance of the numbers 2, 3, and 5, and that he “established upon them a rule for the development of our musical system.” To understand this statement it is necessary to know that a musical note is an effect of regular vibrations of a sounding body—that is to say, of vibrations occupying equal intervals of time; and that two notes cannot be consonant unless the proportion subsisting between their two rates of vibration is simple. These things being understood, it may be shown that the importance of the numbers 2, 3, and 5, employed for the purpose of expressing the ratios of vibration rates, cannot be overestimated. When the intervals between musical notes are expressed by the ratios of the vibration rates of the notes, these three numbers alone, with their squares, cubes, and other powers, and numbers arising from their intermultiplication, are capable of expressing the ratios of consonant notes; and not only so, but they alone are capable of expressing the ratios of all notes belonging to the same scale, and of all notes belonging to all scales into which it is possible to pass from the original scale by modulation.