grave harmonic, while all the other intervals have, shows that the natural laws are not confined to one style of working.
When the major scale has been generated, with its three chords, the subdominant, tonic, and dominant, by the primary mathematical ratios, it consists of forms and orders which in themselves are adapted to give outgrowth to other forms and orders by the law of duality and other laws. All the elements, orders, combinations, and progressions in music are the products of natural laws. The law of Ratio gives quantities, form, and organic structure. The law of Duality gives symmetry, producing the minor mode in response to the major in all that belongs to it. The laws of Permutations and Combinations give orders and rhythms to the elements. The law of Affinity gives continuity; continuity gives unity; and unity gives the sweetness of harmony. The law of Position gives the notes and chords their specific levities and gravities; and these two tendencies, the one upward and the other downward, constitute the vital principle of music. This is the spiritual constitution of music which the Peter Bell mathematicians have failed to discern: [Scientific Basis and Build of Music, page 37]
"The organic structure of music is formed by the three ratios of 1:2, 1:3, and 1:5, from the laws of quantities and motions; but as it is only the ratio of 1:2 that has a pure, unmixed, invariable character, and as the notes produced by the first, second, and third powers of THREE have different degrees of centrifugal force, and the character of the notes produced by the first power of FIVE depends on the character of the notes from which they are derived, so the final character of the notes and chords is determined by the amount of force which they have acquired from the way in which they have been derived, and from their position in the system; and no matter how these notes may be afterwards placed, like chemical elements, they never lose their original force. [Scientific Basis and Build of Music, page 95]