Sensuality and Proportion
A primer in sound for architects.

In the Pythagorean tradition, astronomy is interpreted as magnitudes in motion, geometry as magnitudes at rest, arithmetic as numbers absolute, and music as numbers applied.

I. Pythagoras of Samos was born about 569 BC - and died in about 475 BC. He was according to legend the son of a grain merchant who been granted Samoan citizenship for bringing grain to the city at a time of famine. Pythagoras evolved a whole way of looking at life from counting beans, or grains, and thinking these things are pretty much the same, what patterns can we make with them.. He founded a school of philosophy at Samos until a change of regime forced his exile to Crotona, an important Greek colony on the foot of Italy. Here his school flourished until it was suppressed in about 508BC. Pythagoras is said to have taken refuge in Metapontum where he died. His school was sacked and his followers persecuted. He was a true mathematician because he looked at the relevance of mathematics to the important questions of real life. An attitude imputing value to number will always be threatening to those who know the price of everything. We should look again to Pythagoras to find the relationship between numbers and meaning.

His teachings were transmitted orally and his doctrine is only available through later writings. He is said to be the first teacher to call himself philosophos, lover of wisdom, rather than sophos or wise man, and the first to use the term cosmos a word implying the beauty and order of the universe. 'Communion and friendship and orderliness and temperance and justice bind together heaven and earth and gods and men and this universe is therefore called cosmos or order.' [1] The Timaeus of Plato is accepted as a representation of Pythagorean thought. Pythagoreans are credited for having brought measure to music through the study of the monochord, pipes, and bells.

< Pythagoras is here shown quantifying the weight of the bells, and glasses, plucking the monochord with measured weights, and arguing the finest points of dissonance [comparing flute lengths] with Philolaus

Clockwise from top left: the hammers in Jubal [Tubalcain]'s smithy, playing tuned bells and water filled cups, experimenting with weights on the end of fixed length strings, and on the length of pipes to determine the exact ratios of consonant sounds one to another [from F Gafurio Theorica Musice 1492] [rep. Wittkower 1949.]

He is said to have been a vegetarian, hating the taking of sentient life, recognising 'the voice of a friend' - a dead friend - in the barking of a dog. Modern assessments of Pythagoras vary considerably. Legend has been attached to him. Burkert in 1972 observes that 'the material seems to fall into the pattern each enquirer is looking for. Pythagoras the scientist... the mystic... the Basic Idea... the shaman, etc.' He concludes that 'the tradition of Pythagoras as a philosopher and scientist is, from the historical point of view a mistake' [2] But the system of thought represented by a Pythagorean tradition has been of great importance to discussions of harmony , during the middle ages via Boethius, and the renaissance and Baroque periods, and into the modern age. Whilst exploring number and movement, it asks: what does this mean?

Archytas, a Pythagorean c428-347 BC describes mathematics as being composed of the four related studies: astronomy, geometry, arithmetic and music. [3] Boethius 480-524AD talks of the 'four mathematical disciplines of which music is one' and goes on to observe that 'the other three are concerned with the investigation of rational truth, but music concerns not only speculation but also human behaviour... so we can understand what was said.. by Plato, that the soul of the world is knit together by the harmony of music' [4] Music occupies a key position, it is the one mathematical discipline available directly and precisely to the senses and influencing the soul, a fulcrum between the material world and the meta-reality of number, contributing to the dialogue of correspondence between the two.

Andre Dacier in 1706 writes 'If we ought to measure the Glory of a Philosopher by the Duration of his Doctrine, and by the extent of the places that embraced it, nothing can equal that of Pythagoras, since most of his opinions are at this day literally followed in the greatest part of the whole world. ...Socrates and Plato followed his doctrine and his method of explaining it' [6].

In the Pythagorean tradition, astronomy is interpreted as magnitudes in motion, geometry as magnitudes at rest, arithmetic as numbers absolute, and music as numbers applied. In searching for the links between architecture and music we are trying, in a sense to link magnitudes at rest, with numbers applied. It perhaps worth exploring some Pythagorean concepts of number.

[1] Plato Georgias 507D - 508A]
[2] Burkert Lore and Science in Ancient Pythagoreanism Tr EL Minar, Harv. U.P 1972 p482.]
[3] Archytas 428-347 BC frag.1 in Kathleen Freeman 'Ancilla to the Pre-Socratic philosophers HUP 1948 p78]
[4] Boethius quoted in Acoustics. Historical and Philosophical development by RB Lindsay [ed] Dowden Hutchinson and Ross]
[5] SK Heninger Jr Touches of Sweet Harmony, Huntingdon 1974 p32]
[6] Andre Dacier Life of Pythagoras 1706 London 1707 reprinted 1981 ISBN 0-87728-286-2]

©Marcus Beale 2002

Sensuality and Proportion
A primer in sound for architects.