‘Most of the science of harmonies, to put it in a word, is concerned with consonances. That these are five and no more is proved by reason, as against the man who is all for strings and holes, and wants to explore these points irrationally by the senses; they all have their origin in numerical ratios. The ratio of the fourth is four to three, of the fifth three to two, of the octave two to one, of the octave and fifth three to one, of the double octave four to one. The additional consonance which writers of [Sidenote: E] harmony introduce under the name of octave and fourth, does not merit admission, being extra-metrical; to admit it would be to indulge the irrational side of our sense of hearing, and to violate reason, or law. Passing by then five arrangements of tetrachords, and the first five “tones”, or “tropes”, or “harmonies”, whichever name is right, by variations of which, made higher or lower, the remaining scales, high and low, are produced, is it not true that, though intervals are many, indeed infinite, the principles of melody are five only, quarter tone, [Sidenote: F] half tone, tone, tone and a half, double tone? In sounds no other interval of high and low, be it smaller or greater, can be used for melody. XI. ‘Passing over many similar points, I will’, I said, ‘produce Plato,[64] who, in discussing the question of a single universe, says that if there are others besides ours, and it is not alone, then the whole number of them is five and no more; not but that, if ours is the only universe in being, as Aristotle[65] also thinks, even this one is in a fashion composite and formed out of five; one of earth, one of water, a third of fire, and a fourth of air, [Sidenote: 390] while the fifth is called heaven or light or air, or by others “fifth substance”, to which alone of all bodies circular motion is natural, not due to force or other accidental cause. Therefore it is that Plato, observing the five perfect figures of Nature—Pyramid, Cube, Octahedron, Eicosahedron, and Dodecahedron—assigned them to the elements, each to each. XII. ‘There are some who appropriate to the same elements our own senses, also five in number. Touch, as they see, is [Sidenote: B] resistent and earthy. Taste takes in properties by moisture in the things tasted. Air when struck becomes audible voice or sound. There remain two: smell, the object of our olfactory sense, is an exhalation engendered by heat, and so resembles fire; sight is akin to air and light, which give it a luminous passage, so there is a commixture of both which is sympathetic. Besides these, the animal has no other sense, and the universe no other substance, which is simple and not blended. A marvellous [Sidenote: C] apportionment of the five to the five!’