When the first sixteen harmonics are octave-displaced and compressed into the span of one octave, the result is an octatonic scale whose pitches have the following frequency ratios:
5:4 (a.k.a. 10:8)
3:2 (a.k.a. 6:4 or 12:8)
7:4 (a.k.a. 14:8)
An example of this scale can be heard here. Press and hold a tile labeled R0 and slide the cursor over to R1. Notice that it sounds similar to the major scale, except the perfect fourth is replaced with a lesser undecimal tritone and the major sixth is replaced with a tridecimal neutral sixth and a septimal minor seventh. These alternative pitches give the scale a steelpan-like, tropical-island-y feel (at least to my ears), with the septimal minor seventh in particular adding a jazzy flair.
Is there a name for this scale? If there isn't one, then the name "harmonic octatonic scale" might be the most logical choice. And is this scale at all useful? Are there any examples of songs which utilize this set of pitches, perhaps from non-Western cultures? Thank you.