[nonstandard key signatures]
Can you post an ABC of such a tune?

You'll know this one. There is one accidental (a lowered seventh) otherwise it's all in the hijazkar scale - like major, but with a flattened second and sixth. Copy it into the converter at mandolintab.net and you'll get it typeset the usual way a Greek musician would do it. (There is a leading-spaces problem - not sure why, probably something do with the Windows computer I'm using. Just delete the leading spaces in the header lines after pasting into the box).

With a short tune like this, it doesn't make a big difference. With something on a larger scale, like a piece of Turkish art music three pages long with modulations into four different makams, it's horrendously difficult to figure out what's going on if you don't use the right key signatures.

X:1
T:Misirlou
M:4/4
L:1/8
K:Dphr ^F^C
  D3 E F2G2|A3 B  c2B2|A8-|A8  :|
|:BA2B A2G2|AG2A  G2F2|F8-|F8   |\
  AG2A G2F2|FE2F  E2D2|D8-|D8  :|
|:G8-      |G6      FG|A8-|A6 GA|\
  B6     AB|c6      Bc|d8-|d8   |
  ed2e d2c2|dc2d =c2B2|A8-|A8   |\
  cB2c B2A2|AG2A  F2E2|D8-|D8  :|
  B6     AB|c6      Bc|d8-|d8  |]

Here's another one, a tune for the Romanian five-hole whistle. Its native scale is the Dorian mode with a sharpened fourth. The D sharps are not accidentals, they're obligatory - the instrument couldn't play a D natural if you tried (I've got one and I have tried). Putting them in the key signature means you can forget about them, much as music for the Highland pipes usually leaves the signature out entirely.

X:2
T:Hora ca la caval (on A)
M:4/4
L:1/8
K:ADor^d
|:ABcd   ede2|cAc2 Md3c|ed e2 cAc2|  Md3 c e2z2 |
  ABcd   ede2|cAc2 Md3c|ed e2 cdec|   Aece A2z2:|
|:efgf   aggf|feed Md3c|ec e2 cAc2|  Md3 c e2z2 |
  a2 Ma4   g2|fefe Md3c|ec e2 cdec|[1 Aece A2ze:|\
                                   [2 A4   A2z2||
|:Me2 d2 e2e2|cAc2 Md3c|e2 e2 cAc2|  Md3c  e2z2 |
  Me2 d2 e2e2|cAc2 Md3c|e2Me2 cdec|   A4   z4  :|