Phoneme Order

Following the gods, the phonemes are ordered n, g, q, f, s, x, h, p, t, k, ʔ, v, r, j.  Tones are ordered 1, 2, 3 i.e. low, mid, high.

Initials

The order of initials is derived first from consonant, then semivowel.  Plain consonants are treated as if they had a semivowel at the same articulation.

Core-Final pairs

The order of core-final pairs is derived from consonant, semivowel, core (vn, rn, jn, vjn, rjn, rvg, jvg etc.). 

Syllable Order

Syllables are ordered in a list derived from cycles of initial-tone and core-final pairs.  Lining up the ordered lists provides the first great cycle:

nv1vn (1st initial-tone nv1, 1st core-final vn)
nv2rn (2nd initial-tone nv2, 2nd core-final rn)
nv3jn (3rd initial-tone nv3, 3rd core-final jn)
n1vjn (4th initial-tone n1, 4th core-final vjn)
...

This continues for 162 syllables: two cycles of the initial-tone list and three of the core-final list.  This provides the first ordered list of syllables.  After this the pattern starts to repeat.  27 different great cycles are required to cover all syllables.  Each one shifts the list of  initial-tones by 28 places and leaves the list of core-finals in place.  The second great cycle (syllables 163 to 324) starts:

q2vn (29th initial-tone q2, 1st core-final vn)
q3rn (30th initial-tone q3, 2nd core-final rn)
f1jn (31th initial-tone f1, 3rd core-final jn)
f2vjn (32nd initial-tone f2, 4th core-final vjn)
...

The reckoning of the list shifting is circular: 1st, 29th, 57th, 4th, 32nd, 60th, 7th etc.  Each shift causes the list to begin with a different one of the 27 initials, in the order nv, q, x, n, f, hv, nj, fr, hr, gv, fj, hj, gr, sv, h, g, s, ʔv, qv, sj, ʔr, qr, xv, ʔj, qj, xr, ʔ. 

All 27 derived lists, placed in order from first to 27th, provide the full ordering of 4374 syllables.