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I want to create a new logo for myself.
Because I love typographic logos, I'll create such a logo.
The most of the logos I see are square, but for a typographic logo it is sometimes hard to create a square logo (the logo should stand for "stage picture").
So is it good practice to create a non-square logo or why should I defently use a square logo?
I think you're mixing up logo and icon.
A logo doesn't have to be a square. There are several examples of famous non-square logos.
But an icon should be square. It is mostly used as gravatars or also favicons (the small images in the browser tabs).
But there is a strategy to design your logo similar to your icon. That means that your icon is also used in your logo. So the icon will be recognized to your logo.
As example Microsoft or also User Experience or Stackoverflow:
Microsoft logo
Microsoft icon
Stackoverflow logo
Stackoverflow icon
Or just look at the User Experience logo on this site and then on the favicon on this site.
The icon will be assigned faster than when the icon is different to the logo.
But also in this case there are some famous examples, e.g Google or Dribbble:
Google logo
Google icon
Dribbble logo
Dribbble icon
A lot of people were already on dribbble and would recognize the logo but not the icon. Same as google. Some (mostly older) smartphone users are confused about the g app, because they don't recognize google in it.
I give you the advise, design your logo as you want and try to design a similar icon for your logo.
A last example of a typographic logo / icon design by yahoo:
Yahoo! logo
Yahoo! icon
Last but not least, an article about the "square icon" for you by tweakyourbiz.
No, there is no such rules. But yes they are inside visible/non visible square area for size proposition like 16X16, 28X28,.....128X128 etc.Which helps in re-sizing or calculation in printing/html,css for better alignment.
For your help: http://www.1stwebdesigner.com/inspiration/72-creative-and-smart-typographic-logo-inspiration/
One version of it has to be square to be used in places that demand it, like icons.
A few rules for making a logo that will prevent future problems:
Should fit in a square, for icons.
Have a monochromatic version, for places like the notification bar.
Have a tiny version (down to 16*16 pixels) for use in places like browser tabs.
