You already know most of this, I sure. I’ll say it anyway, because saying it will help me figure out more clearly why I disagree with you. While I am confident I disagree, expressing why is verbally frustrating —- which means it’s totally worth exploring. So:
Imagine the inside of a piano: all the strings tucked in next to each other.
When you whack the middle C string, all the other strings will vibrate, sympathetically, more or less. Those that vibrate most will be the other ‘c’ strings —- the ones that naturally vibrate twice (or half) as fast. Then, there are the strings that vibrate simple fractions faster: 3/2, say. This is all just a simple, boring, physical process, right? Air is hit by one string, and hits another string. Hit that second string at the right times, it moves more. Hit it at random times, it’ll barely budge. If you made a string that vibrated 131/127ths of the speed of that C string, it would not vibrate very much at all.
Our ears (and minds) find harmonies pleasing because our ears use exactly this process to perceive sound: the sympathetic vibrations of many oscillators with different fundamental frequencies. Hearing a C vibrates C-ish inner-ear-hairs lots, A-ish hairs some, and B-sharp-sharp-ish hairs almost none at all.
But sympathetic vibration happens even if there are no ears nearby to hear, or minds to percieve.
Thats what I mean when I say that harmonics are a physical process that we happen to describe mathematically using simple ratios.
The golden ratio is neat, and it pops up a lot —- but there’s no physical process that makes it pleasing. Our eyes don’t use continuing fractions in order to see, and rectangles of varying proportions are all just rectangular if there are no eyes to see or minds to percieve.
(As an aside, the precise, physical reality of harmonics shows up in our perception of them. It did so even before we knew what harmonics were. It’s easy to hear a single hz error off of a perfect harmony, on notes that are measured in hundreds of hz.
It’s nearly impossible to notice that a proportion is only .25% away from the golden ratio.)
So the golden ratio might be the most beautiful. There might be some part of out mind that prefers 1:1.61 more than any other visual relationship. But that would be particular to the human eye and mind —- and it would have to be demonstrated that it is so. That ratio is not inherently visually more special than, say, 1:2, or 1:1, or 16:9, each of which have their one intruiging and mathemystical properties.
Posted on 28 October 2011