> But I'm talking about the complete set of tones that divide up and
> constitute the entirety of an octave, like the pentatonic, the diatonic,
> the chromatic etc -- all of which include the fourth, fifth and octave.
>
No, the pentatonic does not include the fourth. True, the diatonic and
chromatic scales include the fourth and fifth. However, they are a
"drop in the ocean" of the vast panopoly of musical scales that people
around the world use to make music. Also, I'm not following your logic
about "the complete set of tones that divide up" the octave. Yes, the
pentatonic scale does that, but so do the scales and modes I mentioned.
The point I'm trying to make here is that there are many, many ways to
divide up the octave, using 5, 7, 12, 16, and (with microtonal music) as
many as 43 tones. They are all complete sets of tones that divide up an
octave, and no one of them is more "natural" than the others.
> And I believe that is true of the Indian and Arab scales even though they
> divide the octave into more than 12 units. For one thing, the Harmonic
> Minor, which includes the fourth and fifth of its corresponding major
> scale, is sometimes called the Mohameddan scale because it corresponds to
> a widely used Arabic maqam. So while there are more notes in the Arabic
> scale (which comes out as Ivesian quarter tones when you render them on
> Western instruments), it seems these two tones have to be in the complete
> set.
>
Sure, you can find some Arab scales that include the fourth and fifth;
however, you can find others that do not. There's nothing special and
universal about what Western music calls the fourth and fifth.
Miles