The following extract is taken from the “Life of Hooke,” which precedes his “Posthumous Works,” published in 1705, by Richard Waller, Secretary of the Royal Society: “In July the same year he (Dr. Hooke) showed a way of making musical and other sounds by the striking of the teeth of several brass wheels, proportionally cut as to their numbers, and turned very fast round, in which it was observable that the equal or proportional strokes of the teeth, that is, 2 to 1, 4 to 3, etc., made the musical notes, but the unequal strokes of the teeth more answered the sound of the voice in speaking.” [26] Galileo, finding the number of notches on his metal to be great when the pitch of the note was high, inferred that the pitch depended on the rapidity of the impulses. [27] When a rough tide rolls in upon a pebble beach, as at Blackgang Chine or Freshwater Gate in the Isle of Wight the rounded stones are carried up the slope by the impetus of the water and when the wave retreats the pebbles are dragged down. Innumerable collisions thus ensue of irregular intensity and recurrence. The union of these shocks impresses us as a kind of scream. Hence the line in Tennyson’s “Maud” “Now to the scream of a maddened beach dragged down by the wave.” The height of the note depends in some measure upon the size of the pebble, varying from a kind of roar—heard when the stones are large—to a scream; from a scream to a noise resembling that of frying bacon; and from this, when the pebbles are so small as to approach the state of gravel, to a mere hiss. The roar of the breaking wave itself is mainly due to the explosion of bladders of air. [28] The error of Savart consists, according to Helmholtz, in having adopted an arrangement in which overtones (described in Chapter III.) were mistaken for the fundamental one. [29] “The deepest tone of orchestra instruments is the E of the double-bass, with 41-1/4 vibrations. The new pianos and organs go generally as far as C^{1}, with 33 vibrations; new grand pianos may reach A^{11}, with 27-1/2 vibrations. In large organs a lower octave is introduced, reaching to C^{11}, with 16-1/2 vibrations. But the musical character of all these tones under E is imperfect, because they are near the limit where the power of the ear to unite the vibrations to a tone ceases. In height the pianoforte reaches to a^{iv}, with 3,520 vibrations, or sometimes to c^{v}, with 4,224 vibrations. The highest note of the orchestra is probably the d^{v} of the piccolo flute, with 4,752 vibrations.”—Helmholtz, “Tonempfindungen,” p. 30. In this notation we start from C, with 66 vibrations, calling the first lower octave C^{1}, and the second C^{11}; and calling the first highest octave c, the second c^{1}, the third c^{11}, the fourth c^{12}, etc. In England the deepest tone, Mr. Macfarren informs me, is not E, but A, a fourth above it.