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As little as it is recognizably fantasy for the editor. Ok, just kidding. First you have to be aware of the fact that the "not strong enough fantasy element" wasn't the real reason why the editor ...
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#3: Attribution notice added
Source: https://writers.stackexchange.com/a/3318 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#2: Initial revision
As little as it is recognizably fantasy for the editor. Ok, just kidding. First you have to be aware of the fact that the "not strong enough fantasy element" wasn't the real reason why the editor dismissed the book. Even editors have problems pointing always precisely to the real problem. It could just be the most obvious thing which the editor felt uncomfortable about. Maybe he would have ignored that if another part of the book were superior. Back to the question: As soon as you use something supernatural, you are leaving the "mainstream" fiction, as you call it. That does not mean that it is automatically fantasy. It could be a horror book, which can contain elements from fantasy without being declared as such. Not to mention the diminishing difference between SF and fantasy in some areas. It would help if we knew what that "weak" fantasy element was. Let us assume you write a story about a girl with a sixth sense. She knows things that will happen in the next ten minutes, she feels, when she is observed. This is a supernatural gift (I don't have a better word). Readers of the mainstream novels could dislike it, because it is not realistic enough (which does not mean they wouldn't read James Bond novels). If you declare it as fantasy, would a fantasy fan (expecting a Tolkien story, witches, or vampires, etc.) be disappointed? Yes, probably. Fantasy readers like to "escape" the real world. They want to enjoy the possibilities which are not given in our world (and probably never will, to separate them from SF readers). Magic is the most obvious one. Creating fireballs out of nowhere. Meeting creatures like dragons and goblins, which you will never do on good old Earth. So your world need to be significantly different from our world to generate a complete new feeling to walk on that world. A girl with a sixth sense does not sound that extraordinary. That does not mean you can't write a really great book with that girl, but if you disappoint the expectation of your audience, you'll fail. As always it's hard to draw a line. Knowing your fantasy element might help if you (James) want to share it. But be prepared that we find out that your editor is wrong ;)