Getting rid of some preconceptionsEdit
Shocking as it might seem to some people, the twelve tones you find in an octave on the piano don't actually reflect anything but an approximation of a certain selection of tones, that for some reason during the last 300 years became the backbone of western music.
There is nothing inherently natural about the 12 tone system, and it is a mistake to think that music only can be made in it, or using parts of it (like major and minor scales, or pentatonic scales). In fact, a culture won't develop the 'intonation' that we use until it has figured out quite a bit about how frequencies work, and a certain bit of math. The Chinese are as far as I know the only culture out of Europe to have developed the same scale, and they did it way before us, but didn't use it as extensively. I will explain why, eventually.
In the world, there are several different systems with all kinds of foreign tunings: Indian and Arabic which come quite close to having an additional step between our semitones, Thai which comes quite close to having seven equal steps to the octave, Balinese scales, which have somewhat unequal steps with a twist. But more on those, and the whys and hows of them.
If you want to write songs for your conculture, yet maintain a certain depth and uniqueness, copying the western system may not be a good idea. If you must use our scale, then it's possible to use chords in unusual ways or even constructing unusual chords.
If you are interested in a truly strange scale, take a look at this site which describes the Bohlen Pierce 13 note scale, which is very different from any scale attested in any culture.