Converting Platonic metaphysics — and the Pythagorean mysticism which lay at its heart — to Christianity, S. Augustine saw the City of God in terms of perfect number deduced from music. In his treatise on music, De musica, he defined the science of modulation in the arithmetical terms of ratio: the relationship between units of common measure or module in accordance with Pythagoras, especially the determination of the divine significance of the four numbers of the tetractys as 1:1, 1:2, 2:3, 3:4 (symmetry, octave, fifth and fourth). As the intervals of the monochord are marked off by divisions on a string, their ratios may be represented as linear proportions which, in turn, may readily be seen as applicable to the visual arts. Indeed, subscribing to the Pythagorean concept of cosmic order as based on these ratios — of beauty as God-given number — S. Augustine was bound to hear the eternal harmony of the divine in perfectly modulated music and to see it mirrored in architecture based on the same modulations: as music led reason towards the comprehension of God, so the church built in consonance with musical number must approximate God's City.