Throughout the whole history of architecture, the concept of harmony has been the subject of numerous studies and long-lasting discussions. Harmony may be defined as a correspondence between parts, the result of the composition (or the division) of a whole into consonant parts. Its ancient link with music, where ‘agreeable’ combinations of sounds can be read as mathematical relationships, seems to seal the connection between harmony and mathematics. In art and architecture, however, this correspondence is not easily described. Although it is undeniable that a link between architecture and geometry (and therefore mathematics in general) exists, in different periods the nature of this connection has been identified and judged in different ways.

To Pythagoras and the Pythagoreans is attributed the discovery that tones can be measured in space – that is, that musical consonances correspond to ratios of small whole numbers. If two strings vibrate in the same conditions, the resulting sounds depend on the ratios between their length. The ratio 1:2, for instance, generates a difference of one octave (diapason), the ratio 2:3 produces an interval of one fifth (diapente), and the ratio 3:4 corresponds to a difference of one fourth (diatessaron). The addition of two intervals results in the multiplication of the two numerical ratios, the subtraction corresponds to a division and, therefore, halving an interval equals extracting a square root.

The Pythagorean interest in numbers, as filtered by Plato, generated a tradition that linked philosophy and mathematics in the interpretation of the cosmos.