Where Do An, Fu, Gong, Ge, Zhi, Ling, Jie, Bian, Sui, and He Come From?

If one sees only the names “An, Fu, Gong, Ge, Zhi, Ling, Jie, Bian, Sui, He,” they are nearly impossible to guess.

But the text supplies a generating rule.

Using the degree Shao as an example:

Shao-Jue together with Shao-Yu is Shao-An; Shao-Zhi together with Shao-Gong is Shao-Fu; Shao-Shang together with Shao-Gong is Shao-Gong; Shao-Gong together with Shao-Jue is Shao-Ge; Shao-Jue together with Shao-Zhi is Shao-Zhi; Shao-Gong together with Shao-Yu is Shao-Ling; Shao-Yu together with Shao-Shang is Shao-Jie; Shao-Shang together with Shao-Jue is Shao-Bian; Shao-Zhi together with Shao-Shang is Shao-Sui; Shao-Yu together with Shao-Zhi is Shao-He.

It then summarizes:

An, Fu, Gong, Ge, Zhi, Ling, Jie, Bian, Sui, and He are the ten tones of qi transformation; they are distinctions in the shared degree of tone and voice.

The ten transformation tones are not a third independent musical scale

This is the key point.

“An” is not a new tone that appears from nowhere. It is a relation name produced when two existing tonal categories meet at the same degree.

Shao-An, for example, arises from Shao-Jue and Shao-Yu. Shao-Fu arises from Shao-Zhi and Shao-Gong. The Five Tones already exist; the ten degrees already exist; only then are relations between paired tones named through the ten transformation tones.

The coding of the second series therefore has three layers:

1. basic tonal class;
2. degree within the tone;
3. relation code generated when two tones share a degree.

Why is a relation code needed?

The body does not contain only one channel, one organ, or one source of sound. Qi transformation often involves interaction between two locations, directions, or systems.

If one records only “Jue” and “Yu,” one must still state how they interact. If common paired relations can be compressed into the code “An,” later systems such as the Sixty Shou and Eight She can record them more efficiently.

This is the classical method of “governing complexity through simplicity”: a small number of signs carry complex relationships.

“Same” should not simply be translated as physically identical

The text uses words meaning “same” and “sharing a degree,” but it does not say that the physical frequencies of the two tones are exactly identical. A safer reading is that they form a relation class at a particular qi-transformational scale.

Later passages speak of “the transformation by which different tones share the same qi and degree,” confirming that different tones can be grouped by a qi-transformational relation.

The core here is therefore not acoustic identity but a shared-degree relation within the medical coding system.

The value of the ten tones becomes fully visible later

In the Sixty Shou and Eight She, codes such as Zhi-An-Huangzhong, Zhong-Bian-Linzhong, and Zheng-Zhi-Taicu appear.

Here Zhi is a degree, An is a transformation-tone relation, and Huangzhong is a lü. Only when the three dimensions are layered together does a state code capable of localization and inference emerge.

The next article addresses another key question: why must the same transformation tone also be distinguished by left and right?