Here's a matrix of the ten notes and the ratios one to the other:
The ten note scale is from top to bottom on the left: 1:1, 15:13 8:7 26:21 9:7 10:7 3:2 12:7 13:7 27:14 and 2:1. This set can also be thought of as 14:14 15:14 16:14 26:21 18:14 20:14 21:14 24:14 26:14 27:14 28:14, almost all a part of the overtone series. The key difference is that the root of the scale, 14:14, is the seventh overtone of the other notes in the scale, instead of the first. Putting that 7th in the base shakes things up a bit. And I can move it around to reinforce the harmonic series for contrast.
The piece starts out with a mode made up of stacked fourths, and proceeds to change them. Here's the list, with the number indicating the scale degree out of the ten in the matrix.
For the second one, 26A583, I move the bass down to the 12:7, so it's consonant with the other notes in the series. 26A583 is made up of the ratios 15:14 10:7 27:14 9:7 12:7 8:7. But if you assume the 12:7 is in the bass, then the ratios relative to that 8:7 become 5:4 5:3 9:8 3:2 1:1 4:3. Those are all in the harmonic series relative to the A at scale degree 8, except for the 4:3, which is not. But it sounds so sweet I had to leave it in. All these five or six note scales, derived from the ten, were chosen because they sound good in stacked fourth chords. I just couldn't resist the 4:3 relative to the root on A. It's not too removed from the overtone series after all.
The bass moves back to the 1:1 for a while, until about 3/4 of the way through when it shifts to 615837, when I use the 8:7 in the bass. The ratios relative to the 8:7 for that set of six notes are 5:4 7:4 9:8 3:2 1:1 21:16. That 21:16 is not in the overtone series. And it's a 64:63 away from a 4:3 above the 1:1 in the scale. But it's close enough to fake it in this context as part of the melodic flow.
Play it here
or download this link