From Ten Tones to Two Thousand One Hundred: Why Does the Mirror Classic Need Such a Large State Space?

After presenting the ten transformation tones, the Mirror Classic of Bian Que gives a striking set of numbers:

Gong, Shang, Jue, Zhi, and Yu each have ten qi and combine. Two tones and twenty qi transform into two hundred and ten tones; the Five Tones and two hundred qi transform into two thousand one hundred tones.

However the exact combinatorial arithmetic is eventually reconstructed through textual collation, one point is already clear: the author is not satisfied with coarse classes such as the Five Tones, Six Channels, or Five Zang. The aim is a very large state space.

Why are five classes insufficient?

If the body were described using only Gong, Shang, Jue, Zhi, and Yu, differences between many individuals and states would be compressed away.

But actual qi-transformational states also include:

• high-low distinctions within the same tone;
• shared-degree relations between two tones;
• different left-right positions;
• different Twelve Lü;
• different She and Hou positions;
• shifts over time.

Recording all of these details naturally produces rapidly increasing numbers of combinations.

The goal is not a large list; the goal is resolution

Long enumerations in ancient texts can be intimidating. From a modeling perspective, however, “two thousand one hundred tones” need not first be understood as “two thousand one hundred diseases to memorize.”

A more reasonable reading is that the author tries to prevent nearby but distinct physiological states from being forced into the same coarse category.

It is like describing temperature only as “cold” or “hot” versus distinguishing 18°C, 20°C, and 22°C. The resolutions are entirely different.

The Mirror Classic does not use a modern continuous numerical variable; it uses many discrete symbol combinations, but the intent is similarly to increase discriminability.

Shared degrees also have “fifty-five transformations”

The text later says that “all shared degrees among the tones take fifty-five transformations as their method,” and gives paired combinations among different degrees within the same tone.

This further shows that shared-degree transformation is not limited to different Five Tones. Different degrees within the same tone can also form relations.

The “ten transformation tones” are therefore not a simple lookup table, but a compressed labeling layer inside a much larger high-dimensional state space.

From here the book formally moves into the Sixty Shou

By this point, the second series has modeled “tone” as:

inherited tone → basic tone → ten degrees → paired shared-degree relation → left-right position → many combinations.

But these primarily answer “what state is qi presenting?” A further question remains: how does that state move along the channels?

The Mirror Classic next adds length, regulation, and Six-Channel structure through the Twelve Lü, then combines the ten transformation tones with the Twelve Lü into the Sixty Shou.

The core of the third series is therefore not music. It is how to combine “state” and “scale of movement” into a coordinate system capable of localizing the depth of disease.