Experiencing Architecture

By Steen Eiler Rasmussen | Go to book overview

CHAPTER V
Scale and Proportion

Legend has it that one day when Pythagoras passed a smithy he heard the clang of three hammers and found the sound pleasing. He went in to investigate and discovered that the lengths of the three hammer-heads were related to each other in the ratio of 6:4:3. The largest produced the keynote; the pitch of the shorter was a fifth and that of the shortest an octave above it. This led him to experiment with tautly stretched strings of different lengths and he ascertained that when the lengths were related to each other in the ratios of small numbers the strings produced harmonious sounds.

This is only a legend and in my opinion it is too good to be true. But it tells us something essential about harmony and how it is produced.

The Greeks tried to find some explanation for the phenomena they observed. They said something like this: It makes the soul happy to work with clear mathematical ratios and therefore the tones produced by strings of simple proportions affect our ears with delight.

The truth is, however, that a person listening to music has no idea of the lengths of the strings that produce it. They have to be seen and measured. But whatever the Greeks' reasoning, they found that there was some relation between simple mathematical proportions in the visual world and consonance in the audible. As long as no one was able to explain what happens when a tone is produced and how it affects the listener, the relationship continued to be a mystery. But it was obvious that man was in possession of a special intuition which made it possible for him to perceive simple mathematical proportions in the physical world. This could be demonstrated as regards music and it was believed that it must be true of visible dimensions also.

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