Yes. OS X keyboard drives me nuts sometimes, Karabiner can only fix some bits of the weirdness.

Hold the "e" key down for a few seconds: it will have a little dialog above where you can choose it, depending on your keyboard settings of course.

It's worth playing around with the option key when pressing letters on OS X. You're able to enter a ton of common (western) characters with that alone, without ever opening the "special characters" (ugh) palette.

Also the default configuration for a couple versions now (which I hate, but I know it benefits others) is if you hold a commonly (western) accented character, it'll suggest accents for it.

option-e and then a vowel will create {á é í ó ú}

option-u and then a vowel will create {ä ë ï ö ü ÿ}

option-n and then an 'n' will create ñ

Found this out while learning Spanish since holding down keys to select their alternate was way too slow.

For the record:

option-n and then 'a' will create ã

option-n and then 'o' will create õ

Thank you, this was driving me nuts.

On Windows[1], á é í ó ú are achieved by holding down Ctrl+Alt and then pressing the appropriate letter.

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[1] Yes, I know you are OSX, but someone else reading this might not be.