Here's my story with rectangles.
(And some of the reason I got squares tattooed on my wrists.)
First, we must realize that rectangles happen less than 1% in a world without humans.
So why are they found in so many, if not all, cultures?
People's brains demand them.
We think in twos.
Even with three parts, we think of the middle as not being the ends.
We find 'the horizon' in their horizontals.
We find 'a majesty' in their veritcals.
Put together, that is my general rule on the hard-wired emotional content of aspect ratios.
Horizontals are comforting, reassuring and pleasing.
Verticals are imposing, present and cannot be ignored.
Anything in between, like the diamond or the parallelogram, is gonna fall over. Their corners become sharp dangerous points, instead of the ignorable norms that we find in reactangles.
The trapezoid is interesting, but for me it is just a rectangle from a funky perspective.
Second, we explore our brains, hands and eyes by enumerating some geometric principles about rectangles.
For irony, we will count one kind for each side. Each adds another layer of complexity onto the previous.
1 The square. The most basic of rectangles and easily my most beloved. Which to work optically needs to be a slight bit taller than it is wide. Jung said often in dreams the circle is symbol for the cosmos, and the square is the symbol for the conception of the cosmos.
2 Grided or unit-based rectangles. The "Twice as wide as it is tall." or "1 to 25" kind of thing. Look for these in Japanese everything, film and screen ratios, most every monolith and IKEA furniture.
3 Square root-based rectangles. By dividing a square along its diagonal, the length will be the square root of two. By turning this diagonal into a side, we create a more sophisticated, less common kind of rectangle. I recall seeing this in architecture (maybe Frank Lloyd Wright) and international paper sizes (like A4, A3 sizes).
4 The golden rectangle. This is one of the most overrated things ever. It's simply not the best rectangle for every use. And every psychology experiment, the movie "pi" or analysis of Van Gogh's canvases I have ever seen has been contrived to perpetuate this popular myth. People want to believe in it, despite all evidence to the contrary.
That said, the math involved with the golden rectangle is interesting. It's self-reflexive. It is in infinite harmony with itself. When things grow, they often grow in this fashion. The simplest example of this is the Fibonacci sequence (0 1 1 2 3 5 8 13 ...), but I feel the Lucas sequence is equally notable (2 1 3 4 7 11 18 29 ...). THE MAGIC IS NOT IN THE PATTERN, THE MAGIC IS THE PATTERN. The golden rectangle is remarkable, but that does not mean it is the most beautiful and everything should be based upon.
Third, it's all just a game. And the rules are:
1 Please the eyes of your audience.
Since you are making shelves for yourself, we're talking a core audience of one.
Let's explore this further with the principle of the optical center:
The optical center of any rectangle is a little higher than its geometric center. So if you consider this idea when you're putting the shelves in, putting a shelf at the exact center will make it hang a little low from the optical center.
But maybe you like it to hang a little low.
Maybe you like it to hang really low.
Maybe you're like me and you want your shelves to double as food storage devices.
My point is.. the four kinds of rectangles I listed are both the most popular and the ones I recommend using. I'd bet one of them will be the one you will use. But what really matters here is not what people claim is the best rectangle. Most people don't know what they hell they're talking about and just worried about fitting in enough or fitting in too much.
What matters is that you're happy with it. That your books and CDs and what-have-you look good to you in them. Maybe that is the golden rectangle (1.618) or maybe it's 5/3 (1.6) or maybe it's 1.6292462742728, as long it feels right, it is right.
ps I have found this approach relates very well to music, typography, cartography, political theory, writing, dancing and sex.
pps While writing this, I decided to post it in LJ cause it's good, so I apologize for the weird public tone.