notes which are produced by the two primes, 3 and 5. As the quadrant contains all the angles which give the different proportions in form, so does the ratio of 1:2, or the area of an octave, contain all the different notes in music. The ratio of 1:2 corresponds to unity, and, like the square and the circle in form, admits of no varieties. Half the length of a string gives an octave when the string is homogeneous and uniform; if the one half has more gravity than the other, the center of gravity of the whole string gives the octave. The ratio of 1:2 rests on the center of gravity.
While the ratio of 1:2 corresponds to rest, and to the force of gravity, the ratio of 2:3 corresponds to motion, and to the centrifugal force. The prime 2, by any of its powers, never produces a new note. The prime 3 always produces a new note, and on this account its powers are limited to the first power, the square, and the cube, and each of these powers of 3 produces one new note.
The prime 5, like the prime 3, produces new notes. One of these, namely A5, is derived from unity, i.e., the note produced by the ratio of 1:2; the second note is produced from the note derived from the first power of 3, namely E15; and the third is produced from the note derived from the second power of 3, namely B45. The notes thus produced by the prime 5 are the middles, that is, the thirds of the chords. As it is the second and third powers of 3 which possess great centrifugal force, and not the first power of that number; and as it is only the first power of the number 5 which Nature employs in this business, so this makes the character of the notes produced by the prime 5 to depend on the character of the notes from which they are derived. One of the 3 notes produced by the prime 5 is derived from unity, that is the note produced by the ratio of 1:2, and like that note it is strongly acted on by the force of gravity.1 A second note produced by the prime 5 is derived from the note produced by the second power of 3, and like that note it possesses increased
1 Gravity and levity, and centrifugal force; these musical forces do not here refer to the center of the earth, but the center of the musical system, e.g., E in the scale of C. - Editor.
See Also
4.8 - Centripetal Orthogonal Motions
4plusplus
centering
centripetal
centripetal force
centripetal pair
centripetal spiral
centripetally
centripetate
centripetence
centripetence-machine
constant of centripetal force
gravism
gravitation
gravitism
gravity
predominantly centripetally
syntropic
syntropy