Sixty Steps to Close the Circle, and a Death by Prediction

The tuning problem Jing Fang attacked is an old one and has no clean solution. Stack twelve perfect fifths and you arrive slightly above the octave you started from, by an amount small enough to ignore in practice and impossible to remove in theory. His response was to keep going, dividing the octave into sixty steps in pursuit of a point at which the cycle would close, and although it does not close, the calculation is a serious piece of mathematics and it was done in the service of a cosmological conviction rather than a musical one. In Han thought pitch, calendar and government are the same order expressed three ways, and a tuning that failed to close was a flaw in the world, not in an instrument.

That conviction is also what killed him. If irregularities in the heavens and in the weather report on the conduct of the ruler, then a specialist who can read them has a political weapon, and he used it, submitting memorials that interpreted portents as criticism of the court and of powerful officials. The weapon works both ways. He was accused in turn, his own predictions were used against him, and he was executed in 37 BCE. The atlas notes the case because it shows what correlative cosmology meant in practice: not a private symbolism but a public argument with consequences.