How Are the Lengths of the Twelve Lü Calculated? Tonal Division × She Division

Earlier articles often treated the Twelve Lü as names governing measures of channel qi movement. In “Kuidu (III),” the text finally states directly how this measure is quantified:

The pulse-lü division of a normal person is the tonal division multiplied by the She division.

It then takes Huangzhong as the reference:

The Huangzhong measure of the vessel pathway is sixty fen. Receiving the normal person’s pulse-lü division, this is the constant of pulse lü.

This is one of the most important formula-like statements in the entire work.

Lü measure is not determined by tone alone

“Tonal division multiplied by She division” means that the pulse-lü scale is jointly determined by two layers:

• tone: the high-low and degree-of-concord of qi transformation;
• She: the position and state reached by qi interaction.

The same tone occurring at different She, or different tonal divisions at the same She, can therefore lead to different final pulse-lü divisions.

Why does a long numerical series appear after Dalü?

After Huangzhong at sixty fen, the source lists Dalü’s symbolic measure at fifty-seven and a half fen, then fifty-six fen, fifty-four point six, fifty-three point two, and so on in a descending sequence.

This series shows that “lü” in the Mirror Classic is not merely a borrowed musical label. It is a discrete quantitative framework that can carry different scales of qi movement.

The exact mathematical generation of every number, and how it connects in full with sanfen sunyi and Shou-She divisions, still requires a separate reconstruction; the passage itself does not provide every derivational step.

“Proper position is constant; lost position is change” is the clinical purpose

Immediately after the numerical sequence, the text says:

What obtains its position is constant; what loses its position changes. Pulse lü communicates and transforms through the Sixty Shou, and thereby the measures of tone, She, and joint meeting are known.

Mathematics is therefore not the endpoint. The purpose is to build a sufficiently fine normal scale that “lost position” can be detected.

The Twelve Lü connect sound, pulse, and channel position into one scale

At this point the design of the whole work is clearer: tone describes state, She describes position, lü turns the two into a scale of qi movement, and the Sixty Shou then track state transition.

The next article adds these local scales across the thirty-seven whole-body channel passages, returning to the early total of twenty-two zhang, three chi, and six cun.