Here is a comparison of the new scale put between the other two popular scales I've mentioned:
In this new scale every note is a multiple of 1/16th of the distance between 1 and 2. That would be 16 multiples though, and the scale only has 12 notes. The ones that are skipped are 7,12, and 15 parts of 16.
The light grey boxes in the diagram are where this new scale exactly matches the just temperament scale, and the dark grey are where the new scale matches the equal tempered scale more closely than the just scale does.
So the nice thing is evident when you look at how the notes are arranged when you think of them going around a circle; after all once you pass B you are back to C so a circle makes sense. A helix would make even more sense but that's too hard to draw :)
So you can see most of the notes are the same space apart like equal temperament with the exception of a few that are double that same amount. But I've marked off perfect just fifths in the diagram that are exactly a 3/2 ratio apart and will sound really good.
I guess there could be a 16 note scale that doesn't skip spaces like this one does. Maybe I'll try to find a program that you can play exact frequencies in and post a continuation of this showing what that would sound like.