TREATISE I. BOOK III.

Here we have more precisely constructed the world monochord with its proportions, harmonies, and intervals. We have depicted its mover to be outside the world in this manner.

A complex cosmological diagram titled "The World Monochord" original: "Monochordum Mundanum". A large vertical musical instrument, a monochord, is superimposed over a circular map of the universe. At the top right, a divine hand reaches out from a cloud to adjust the tuning peg of the instrument. This signifies that God is the external mover who tunes the universe. The vertical neck of the instrument represents the cosmic axis. It is divided into two main halves: the lower material world and the upper formal or spiritual world. These two halves meet at the Sun, marked with the symbol ☉. The central axis lists the elements and celestial spheres from bottom to top. At the base is Earth labeled with the Greek letter Γ, followed by Water, Air, and Fire. Above the elements are the planetary spheres: the Moon, Mercury, Venus, and the Sun at the center. Continuing upward are the spheres of Mars, Jupiter, Saturn, and the Starry Firmament. The regions above the stars are labeled as the place of appearance original: "Epiphioma locus", the region of divine resonance original: "Epiphononia regio", and the part of the seat of manifestation original: "Epipheniae Sedis pars". Mathematical and musical ratios are shown by arcs on both sides. On the left side, a large outer arc spanning the entire length is labeled "Quadruple proportion" original: "Proportio quadrupla", a 4:1 ratio. Two medium arcs represent the "Double proportion" original: "Proportio dupla", a 2:1 ratio or an octave for each half of the cosmos. Inner arcs show the "Sesquialter proportion" original: "Proportio Sesquialtera", a 3:2 ratio or a perfect fifth and the "Sesquitertial proportion" original: "Proportio Sesquitertia", a 4:3 ratio or a perfect fourth. On the right side, the upper half is labeled the "Formal Octave" original: "Diapason formalis" and the lower half is the "Material Octave" original: "Diapason materialis". These are subdivided into their respective fifths original: "Diapente" and fourths original: "Diatessaron".