Using Network Analysis to Do Traditional Chinese Phonology Study

Traditional Chinese Phonology, lacking of alphabetic system of phonetic notation such as IPA, had to deal with large written materials in Chinese characters, and used Chinese characters as a tool to analyze sounds of words. This brings up a significant feature of its study, that is, the relationships of words’ sounds are more important than their phonetic values.
Xìli
án (literally: "inter-link") is one of the most important methods in traditional Chinese phonology. Its fundamental is to build networks of Chinese characters having same syllabic elements. This paper takes Xìli
án of Fǎnqiè in
Gu
á
ngyùn as an example to show how to use network analysis and visualization software to improve traditional Chinese phonology study.

In general, Chinese characters are monosyllabic. A Chinese syllable can be divided into three parts: the Initial (Shēngmǔ), the Final (Yùnmǔ), the Tone (Shēngdi
ào). The final can be further subdivided into the Medial (Jièyīn), the Main Vowel (yùnfù) and the Coda (yùnwěi), while the Medial and Coda are optional.

Fǎnqiè is a Chinese method to indicate the pronunciation of a monosyllabic character by using two other characters. The first one, known as Fǎnqiè-Sh
àngzì, has the same initial as the desired character, known as Bèiqièzì. And the second one, known as Fǎnqiè-Xi
àzì has the same final and tone as Bèiqièzì. Here is an example. “端(du
ān), 多(du
ō)官(gu
ān)切”. The Bèiqièzì is “端”. The Fǎnqiè-Sh
àngzì is “多” indicating that the initial of “端” is “d”. The Fǎnqiè-Xi
àzì is “宗” indicating that final of “冬” is “u
ɑn” and the tone is “-”.

Naturally, any Fǎnqiè was meaningful when it was created, but may not keep its perfection as time goes by, due to phonetic changes. For example, “東(dōng), 德(dé)紅(hóng)切”. “德” still has the same initial as “東”, while “紅” has the same final but different tones. Thus, the systematic use of such Fǎnqiè in ancient rime dictionaries is an invaluable resource for the work of historical linguists.

Guǎngyùn is a Chinese rime dictionary compiled in 1008AD. It is a revision and expansion of
Qièyùn, the influential rime dictionary published in 601AD. It is generally accepted that
Qièyùn recorded the voice of Chinese at that time, maybe not as a spoken language, but rather how characters should be pronounced when reading the classics. So
Guǎngyùn, as the most accurate available account of
Qièyùn in the past, was used by traditional scholars as a major source on the reconstruction of
Qièyùn system, the code name of Middle Chinese.

Guǎngyùn is split into four tones in five volumes (Two for Píng tone, and one each for other three: Shǎng, qù, rù). Each tone is split into rimes, with total of 206 rimes (including final and tone). Each rime is divided into groups of homophonous characters, with a character as the representation, and the pronunciation of each group given in
Fǎnqiè formula.

It is Chénlǐ, in his masterpiece
Qièyùn-Kǎo published in 1842, who first introduced Xìli
án method in the study of Fǎnqiè in
Guǎngyùn. The Principle of Fǎnqiè-Xìli
án comes from the idea that the relation between Bèiqièzì and Fǎnqiè-sh
àngzì or Fǎnqiè-xi
àzì is an equivalence relation.

In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive. Any equivalence relation provides a partition of the underlying set into disjoint equivalence classes. Two elements of the given set are equivalent to each other if and only if they belong to the same equivalence class.
That means, if we look for the Fǎnqiè-sh
àngzì of each Fǎnqiè-sh
àngzì and link them together with one another, we can obtain equivalence class of Fǎnqiè-sh
àngzì representing a same initial. By systematically applying this method, it becomes possible to make classes of Fǎnqiè-sh
àngzì for the initials, and Fǎnqiè-xi
àzì for the rimes (including the final and tone) of
Guǎngyùn. When two classes were unable to link each other by any method, it may conclude that they represent distinct initials and distinct rimes.

Figure 1: A page in
Guǎngyùn

In old days, Fǎnqiè-Xìli
án of Guǎngyùn would cost a lot of time and the process is hard to display. So faced the same materials, researchers had to put lot of energy in repeating works to verify others’ results. It was often difficult to find out what went wrong when there were disagreements. Today, with the help of the network analysis and visualization software package like Gephi, it becomes much more easily to display one’s own work or review other’s work in both researching and teaching. Fǎnqiè-sh
àngzì (or Fǎnqiè-xi
àzì) are the nodes. The equivalence relation between them are undirected links. Then the components in the undirected network are equivalence classes of Fǎnqiè-sh
àngzì (or Fǎnqiè-xi
àzì) which represent different initials (or rimes).

The process is simple and repeatable. The first step is to convert the text of
Guǎngyùn to a structural form, see Table 1. The second step is to find the no repeated Fǎnqiè-sh
àngzì (or Fǎnqiè-xi
àzì) appeared in Guǎngyùn. The third step is to find the Fǎnqiè-sh
àngzì of each Fǎnqiè-sh
àngzì (or Fǎnqiè-xi
àzì of each Fǎnqiè-xi
àzì) in step 2, see Table 2. The fourth step is to transform the equivalence relations between Bèiqièzì and Fǎnqiè-sh
àngzì or Fǎnqiè-xi
àzì into links between nodes representing these characters. The fifth step is to convert those links in step 4 to a network with a network analysis and visualization software package, like Gephi, see Figure 2. The sixth step is find all the components in the network, Figure 3 shows an example.

However, it is not the end of our study of Middle Chinese Phonology, but only the beginning. Over more than 100 years, there is still no consensus on exactly how many initials and finals in Middle Chinese. The reasons are complicated, partly due to different versions of Guǎngyùn, partly due to various origins of Fǎnqiè in Guǎngyùn. Owing to digital method, it becomes much more convenient to demonstrate the works of key scholars and to locate the exact Fǎnqiè that caused their disagreements.

Table 1: The Structural Table of
Guǎngyùn

Rhyme
Homophonous Group

F
ǎ
nqiè-sh
à
ngzì

F
ǎ
nqiè-xi
à
zì

上平1東

東菄鶇䍶
𠍀
倲
𩜍𢘐
涷蝀凍鯟
𢔅
崠埬
𧓕
䰤

德
紅

上平1東

同仝童僮銅桐峒硐
𦨴𧱁
筒瞳㼧
𤭁
罿犝筩潼曈洞侗橦烔䴀挏酮鮦㼿
𦏆𦍻
眮蕫穜衕
𩍅𢈉
䆚哃
𢏕
絧
𨝯𨚯𪔝𩦶𪒿

徒
紅

上平1東

中衷忠
𦬕

陟
弓

上平1東

蟲沖种盅爞
𦬕
翀

直
弓

上平1東

終衆(眾)潨
𣧩𧑄𩅧
䝦䶱䈺螽鼨蔠柊鴤泈

職
戎

……
……
……
……

Table 2: The Fǎnqiè-sh
àngzìof each Fǎnqiè-sh
àngzì in
Guǎngyùn

ID

F
ǎ
nqiè-sh
à
ngzì in
Guǎngyùn

F
ǎ
nqiè-sh
à
ngzì of F
ǎ
nqiè-sh
à
ngzì

1
德
多

2
徒
同

3
陟
竹

4
直
除

5
職
之

6
敕
恥

7
鋤
士

8
息
相

9
如1
人

……
……
……

Figure 2: The Network of Fǎnqiè-sh
àngzi

Figure 3: A Component in the Network of Fǎnqiè-shàngzi

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ò
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ě
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ǎ
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Huang Yiqing, Wang Ning, Cao Shujing.
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