EDIT: goddammit DormioBV
Working off those number guesses, I may have hit something.
I(一)ku, 1.
Ichi(一)rin, 1.
Ni(二)tori, 2.
San(三)ae, 3.
Ko(こ -> ご)machi, 5.
Ya(八)mame, 8.
Yep, it's the Fibonacci sequence! The next number would be 13, which is jyu-san. (十三) But since I don't know any touhous with that in their name I'll just say it's for Ten Desires.
now we know pesco's secret of using jappo in his puzzles so it took a few days less than the last oneWhich in turn screws us mere mortals out of participating in these puzzles.