>Regarding 12/8, are you saying that the standard today is to use the GCM of the two signatures? I.e. the GCM for 3 and 4 would be 12. Just curious.
I think people who grow up with these rhythms don't need time signatures at all. Regardless, 12/8 works best (for some) for adapting western notation to this particular structure which has 4 main beats, and 6 beat overlay, and is divided into 2 cells.
The cells (2 main beats per) are a typical feature of all these types of rhythms which have no exact counterpart in Western music. You could write it as two measures of 6/8 (and its often done), but then the cells fall on alternating measures. It seems better to some to "translate" the structure so that the 4 main beats and the two cells fall into 1 western measure.
You also have to consider that the 4 main beats can be subdivided into triple pulse (3 per main beat) or duple pulse (4 per main beat). 12/8 works well for the triple pulse at least. I think that's what you are pointing to with your comments about GCDs.
You see, you can even write it in 4/4, but that's just notation. The notation doesn't capture all the nuances.
My friends will argue about which is the *correct* time signature, and I think they are somewhat missing the point. You have to hear/feel the whole structure that's there in the music. I think they hear *part* of what's going on, and want to label it quickly as one thing or another so they can forget about it and pretend they have it all figured out.