In former periods, the trust in music as effect and iconic sign was so strong that music formed part of the MA quadrivium along with Astronomy, Geometry, and Mathematics (following the BA Trivium of linguistic disciplines). Church architects, wishing to make a cathedral a microcosm of the universe, trusted to the musical intervals and their analogous mathematical and geometric proportions to guide them in building. Thus Bishop Suger seems to have constructed Chartres Cathedral on the principle of the proportions 3:5:8 variously multiplied. And music itself was composed not to appeal to the ear, but to recreate celestial harmonies and intervals in an imitation of the music of the spheres through to boom away all the time, but inaudible because of habit. As late as 1726, Jonathan Swift, in his satire upon the overly theoretical Fellows of the Royal Society depicts the scientists of Laputa as wholly caught up in astronomy and music; and shows how the music actually produced sounds awful because it is purely theoretical.

Strangely enough, however, the theoretical music of the Middle Ages, in so far as it may be reconstructed, sounds quite good. There is an enigma here – the result of pure theory neglecting what we might call ’beauty’ or aesthetic criteria, does create ’beauty’. This suggests that the universe – or nature – is beautiful in a certain sense;  that ”truth is beauty, beauty truth”. This is weird, and metaphysically interesting! 

One interval used to be theologically problematic: the so-called diabolus in musica (tritonus), which pointed in two directions at one and the same time and was therefore thought duplicitous, double-tongued like the serpent. Another problem, I imagine, must have been the untempered scale – but this is something I do not know about and would like to find out about.