What the work claims
That 53 just fifths approximate 31 octaves with extraordinary accuracy; that the Moon emits no intrinsic light but reflects sunlight; and that Yijing hexagram lines can be systematically mapped to the Chinese calendar via the najia method.
How it was done
Jing Fang extended the Pythagorean comma calculation method from 12 fifths to 60, using iterative arithmetic based on powers of three. He rounded intermediate values to about six digits. He also correlated Yijing hexagram lines with elements of the Chinese calendar to formalise the najia method.
What holds up
His arithmetic demonstration that 53 just fifths converge closely to 31 octaves holds up as a verified numerical observation. His rounded calculation achieves 0.0145 cents accuracy. His ratio 177147/176776 is explicitly reported. His advocacy of reflected moonlight and formalisation of najia are both attested claims.
What does not
The material does not establish that Jing Fang’s 53-fifth temperament was implemented musically, nor that his lunar theory included optical or geometric modelling. It does not report experimental verification of the moonlight claim, nor any astronomical measurement supporting it.
Why it matters beyond the lab
It matters because it reframes Han dynasty scholarship as computationally sophisticated — not merely philosophical or calendrical — and exposes an early, explicit physical model of celestial illumination, decades before similar ideas appear elsewhere.
Is it worth your time
Yes — it reveals how pre-modern mathematical precision coexisted with cosmological insight, and shows that rigorous approximation was a deliberate, high-resolution practice in Han dynasty science.