Sagittal and planar temperaments

Reflecting on the ease which with Sagittal could deal with 5120/5103
planar, I thought I'd look at what happens when you express some 5 and
7 limit commas in the apotome-Pythagorean comma-81/80-64/63 notation
and then look at the equivalences of commas you get from it. I got the
following list, which is suggestive of how the notation might work.

a = 2187/2048
s = 32805/32768
d = 81/80
c = 64/63

2048/2025

s = d

245/243

a = s d^2 c^2

126/125

s c = d^2

1728/1715

a = s d^2 c^3

1029/1024

a = s d c^3

15625/15552

a s = d^5

225/224

s c = d

3136/3125

s^2 c^2 = d^3

5120/5103

d = c

6144/6125

a = d^3 c^2

2401/2400

a = s^2 c^4

4375/4374

a = d^4 c

250047/250000

s^2 c^3 = d^4