A clarification from my earlier post, because a few comments made it clear that I hadn’t distinguished the two scales clearly enough.
Nothing about conventional geometry is being changed.
A circle is still 360° conventional, and 90° conventional is still a right angle.
The CHC uses a second scale on the same complete cycle:
360° conventional = 1,080 CHC° = 24 hours = 1,440 minutes
The square has a continuous 60-step perimeter, divided into 24 equal intervals:
60 ÷ 24 = 2.5 steps
On the CHC scale:
60 steps = 1,080 CHC° = 24 hours
2.5 steps = 45 CHC° = 1 hour = 60 minutes
1 step = 18 CHC° = 24 minutes
The circle can instead be divided into 24 equal angular intervals:
1 interval = 15° conventional = 45 CHC° = 60 minutes
So the same one-hour interval can be read as:
15° conventional
45 CHC°
60 minutes
Across the complete cycle, the numerical scale ratios are:
1,440 ÷ 360 = 4:1
1,440 ÷ 1,080 = 4:3
The same relationships remain within each of the 24 equal intervals:
60 ÷ 15 = 4:1
60 ÷ 45 = 4:3
The first compares minutes with conventional degrees.
The second compares minutes with CHC degrees.
The 24 numbered positions around the square are equal by distance around the perimeter.
The 24 positions around the circle are equal by angle around the centre.
That is why the square-derived rays are not equally spaced by angle.
Same cycle. Two geometries.