Pythagoras & the Golden Ratio
Jeroen Seynhaeve 2019-09-14Not all that much is known with certainty about old Greek philosophers.
Some of them decided not to write anything down, while the written works of many others got destroyed and paraphrased along the ages and adverse ideologies. Skimming past the dubious legends and myths, we do, however, have fragmented factual knowledge of some of the focus points that distinguished one thinker from another.
For Pythagoras, this means skimming past stories of bean avoidance and reincarnation, and zooming in on his well-documented obsession with numbers. “All is number”. Pythagoras and his school of followers saw numbers everywhere, in geometry, arithmetic and perhaps most remarkably in music. They observed that strings of a different, but very particular length and weight, produce harmonious sounds, while others, of differing ratios, don’t. Exactly half or double the length produces exactly an octave lower or higher. Exactly a fifth or a third of a string, produces a perfect fifth or third harmony.
What is especially remarkable, is that whether or not our human ears and brains consider two sounds harmonious or discordant, can be explained by numerical ratios. What does this say about the relationship between human biology, morality, aesthetics and mathematics?
But of course, Pythagoras did not stop there. If this numerical explanation is true for music, why not for the rest of the world, the cosmos, and the way we should live in terms of ethics and health? Harmony is balance, and balance is good. And if harmony and balance are deemed good in the experience of music, the world and our lives, sure they play a crucial role in our appreciation of design, too.
One application of a numerical ratio in design, is the Golden Ratio – 1:1.618. Throughout history, as far back as the Egyptians, architects and mathematicians alike raved about the aesthetic qualities of design that stick to this Golden Ratio. In typography this ratio can be applied to the relative scale and ratios of typeface in a text (“vertical rhythm”): the font size and the line height. Using a consistent typeface styling and vertical rhythm, is necessary to create consistency, harmony and balance in text. So again, why we find a particular aesthetic experience – in this case a styled text – appealing, can be explained by numerical ratios.
An application such as modularscale.com shows you how this works, by applying musical terms and ratios to typeface. For example, a font size of 16pt, in a Golden Ratio of 1:1.618 (the ratio I use on this website), dictates varying font sizes and line heights of 9.889pt, 16pt, 25.888pt, 41.887pt and 67.773pt (etc)