The connection between aesthetics and numbers dates back to pre-Socratic times. Pythagoras, Plato, and Aristotle worked on quantitative expressions of proportion and beauty such as the golden ratio. Pythagoreans, for instance, quantified" harmonious" musical intervals in terms of proportions (ratios) of the first few whole numbers: a unison is 1: 1, octave is 2: 1, perfect fifth is 3: 2, perfect fourth is 4: 3, and so on (Miranda 2001, p. 6). The Pythagorean scale was refined over centuries to produce well-tempered and equal-tempered scales (Livio 2002, pp. 29, 186).

Galen, summarizing Polyclitus, wrote," Beauty does not consist in the elements, but in the harmonious proportion of the parts." Vitruvius stated," Proportion consists in taking a fixed nodule, in each case, both for the parts of a building and for the whole." He then defined proportion as" the appropriate harmony arising out of the details of the work itself; the correspondence of each given detail among the separate details to the form of the design as a whole." This school of thought crystallized into a universal theory of aesthetics based on" unity in variety"(Eco 1986, p. 29).