Grids galore

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[This is a guest post by Zhengyuan Wang]

Calligraphy Practicing Sheets and the Trussing Structure of Chinese Characters

One thing essential for every elementary-level Chinese learner is to learn to write the characters in the same size in one single passage. This is not a unique case that only exists in Chinese. But this can be a challenging task in reality, in regards to how different the Chinese characters can be to each other with the number of strokes ranging from as simple as characters with one stroke only (for instance, 一 yī and 丨gǔn [yes, this is a character]) to complex ones with up to twenty-eight strokes (矗 chù, the character with most strokes among the 3,500 common used Chinese characters). Not to mention, there are characters less common but with way more strokes, such as 麤 cū, with thirty-three strokes, 龘 dá/tà, with fifty-one strokes, and the most famous one biáng (as in figure 1) with forty-two or fifty-six strokes.

(figure 1: from left to right: biáng in traditional Chinese with 56 strokes, biáng in simplified Chinese with 42 strokes, and yī with only one stroke. How can you write them in the same size, which has to be not so big in the first place?)

Therefore, most children in China are introduced to certain kinds of calligraphy-practice sheets with grids to assist them in practicing writing the characters; among them, the Tian-shaped grid 田字格 tiánzìgé and the Mi-shaped grid 米字格 mǐzìgé are the most common two to be used (see figure 2).

(figure 2: left is a tiánzìgé and right is a mǐzìgé)

With rows and lines of these gridded squares, certain types of writing sheets are distributed to students (figure 3).

(figure 3: left is a practice sheet with tiánzìgé and right is one with mǐzìgé. Into each square, the student puts one character, regardless of whether it is a simple or a complicated one. In this way, they are trained to unify the size of characters.)

There are other types of practice sheets, including but not limited to, 井字格 jǐngzìgé, 回字格 huízìgé, or 九宮格 jiǔgōnggé, but these are far less popular (see figure 4).

(figure 4: from left to right are jǐngzìgé, huízìgé, and jiǔgōnggé)

Here is a simple way for us to see the popularity of each very straightforwardly. Below is a screenshot from taobao, the largest online shopping platform (see figure 5). The sales of tiánzìgé and mǐzìgé are much greater than other types.

(figure 5: from left to right are the search results for tiánzìgé, mǐzìgé, jǐngzìgé, huízìgé, and jiǔgōnggé. Each of them is sorted by “best-selling.” While the first two types sold more than 10,000 in the past month, the other three each had around 1,000 purchases.)

Is this result arbitrary? Not necessarily.

The choice of a specific type of grid is not made unreasonably. One fundamental principle of the design of these practice sheets is based on the trussing structure of Chinese characters (間架結構 jiānjià jiégòu), a concept introduced to children at a very early stage. Basically, it categorizes Chinese characters into different types according to how the character is capable of being separated. Here are some general ways for categorization:

  1. When the character cannot be further separated (or technically say, a character without a separable 偏旁 piānpáng ["component"] or 部首 bùshǒu ["radical"]), it is called a standalone character 獨立結構 dúlì jiégòu or 獨體字 dútǐzì:

1)    Long characters: 日 rì, 月 yuè;

2)    Flat characters: 曰 yuē, 二 èr;

3)    Inclined characters: 夕 xī, 力 lì;

4)    Radial characters: 水 shuǐ, 永 yǒng.

  1. When the character contains two major parts:

1)    Two parts juxtaposed vertically 上下結構 shàngxià jiégòu: 朵 duǒ; 多 duō; 忠 zhōng;

2)    Two parts juxtaposed horizontally 左右結構 zǔoyoù jiégòu: 地 dì; 胡 hú; 到 dào;

3)    One part enclosing the other part 包圍結構 bāowéi jiégòu.

a. Totally enclosed 全包圍結構 quán bāowéi jiégòu: 回 huí; 圍 wéi; 困 kùn;

b. Partially enclosed 半包圍結構 bàn bāowéi jiégòu (this one contains so many sub-categories depending on which side/sides are not enclosed):

      i. If only one side is not enclosed: 同 tóng; 區 qū; 凶 xiōng;

      ii. If two sides are not enclosed: 趙 zhào; 龐 pang; 句 jù.

  1. When the character contains three parts:

1)    Three parts juxtaposed horizontally 左中右結構 zǔozhōngyoù jiégòu: 湖 hú; 誰 shuí; 鄉 xiāng;

2)    Three parts juxtaposed vertically 上中下結構 shàngzhōngxià jiégòu: 章 zhāng; 器 qì; 蕉 jiāo;

3)    Other structures: For example, there can be characters with shàngxià jiégòu, but one of the two parts can be further regarded as a zǔoyoù jiégòu character, such as 花 huā (the bottom part 化 huà can be divided into 人 rén and 匕 bǐ), or the simplified 聂 niè (the bottom part 双 shuāng can be further divided into two 又 yoù).

Notably, a considerable portion of the three-part characters are a variation of a two-part character, where the middle part of the three can freely combine with either the top or the bottom, or either the left or right.

Having said that, I wish to return to the relationship between calligraphy practice sheets and trussing structure. Simply speaking, the argument is that the trussing structure of Chinese characters partially determines that tiánzìgé and mǐzìgé are the most popular ones.

Since the purpose of a practice sheet is to help an elementary learner to write and to unify the size of characters, the sheet functions in the way of providing the writer a pinpoint to put pen to paper 落筆處 luòbǐchù. As illustrated by the characters listed above, it is not hard to find that, especially mǐzìgé, which offers every single one of the characters an anchoring point to start the first stroke, which decisively leads to the other strokes of the character.

The problem with other types of practice sheets is that they are designed for some niche characters, making those sheets incapable of accommodating the needs of most characters. For instance, jǐngzìgé and jiǔgōnggé are probably good for a child to learn the quintessential zuǒzhōngyoù jiégòu characters (referring to those characters that have three radical parts, no two of which can combine into a new character). These characters have three parts that take almost the same space in handwriting, such as 街 jiē, 衔 xián, or 衚衕 hútong. But other characters, even though in shàngzhōngxià jiégòu can hardly fit into a jǐngzìgé and jiǔgōnggé all the time, since different parts may take up different portions of the space.

This is fairly self-explained by the difference between jǐngzìgé and jiǔgōnggé: the only disparity is that jǐngzìgé has a relatively narrowed middle row and column, while all three rows and columns in a jiǔgōnggé take the same space. This difference indicates that the two types of sheets are designed for different characters respectively, proving that they lack versatility.

A huízìgé is most adept for writing characters in bāowéi jiégòu, such as 国 guó, 田 tián, 周 zhoū, etc. But are tiánzìgé and mǐzìgé not capable of doing so? Not really. In a way, tiánzìgé and mǐzìgé might even do a better job than huízìgé. For instance, if a child is learning to write and to unify the size of 囚 qiú and 圕 tuǎn (the uncommon, polysyllabic way of writing the word for "library"), the decisive step for the child should not be trying to write the 人 rén and 書 shū in one size (if a child can do that already, they probably no longer need the gridded paper’s assistance). Instead, the point is that they have to make sure the big 囗 (口字框 kǒuzìkuàng) is in a proper size, so that they can fit either 人 or 書 into it. If this is the case, it is contradictory to the logic of huízìgé, because huízìgé focuses on framing the size of the middle part. A mǐzìgé turns out to do a good job for this purpose. The child simply needs to start the first vertical stroke from the mid-point (or slightly transferring it rightward) of the left-up part of the diagonal line, and end when the stroke touches the left-bottom diagonal line. Thereupon, the first stroke of the big 囗 is fixed, and all other parts can be written easily.

Another burgeoning type of practice sheet is the compound type (see figure 7).

(figure 7: practice sheet with some compound types of grids)

But these novel types may go too far toward the other end of the issue; that they contain too many auxiliary lines and, thus, confuse the students who has only encountered the character for a relatively short period of time.

Selected readings


  1. Michael Watts said,

    November 19, 2023 @ 6:57 am

    This is fairly self-explained by the difference between jǐngzìgé and jiǔgōnggé: the only disparity is that jǐngzìgé has a relatively narrowed middle row and column, while all three rows and columns in a jiǔgōnggé take the same space.

    What jumps out at me is that the "horizontal" lines in the 井字格 grid are markedly diagonal. This suggests to me that they provide a model for characters which have a left-hand component with a 横 stroke at the bottom, such as a 土字旁, a traditional 金字旁, or a foot radical. Horizontal strokes at the bottom of a character regularly become upward diagonal strokes in the radical form of the same character. Compare 堆 / 路 to 土 / 足 (though note that the bottom of the 足, in its radical form, is written 止).

    I'm a little surprised to see that 章 is thought of as being composed of three vertically aligned parts. I would have thought of it as 立 over 早, largely because the 日 and 十 elements are connected to each other. Judging by the zdic images, they are also connected in the Kangxi dictionary, though interestingly enough in that dictionary the 口 and 止 of the 足 radical are separate in 路.

    Is the reasoning behind the classification of 章 that the 早 is given more vertical space than the 立 is? Is it just traditional?

  2. Michael Watts said,

    November 19, 2023 @ 7:15 am

    丨gǔn [yes, this is a character]

    Is it? It has an entry in my electronic Hanyu Da Cidian, but there is no gloss. Here is the entry in full:


    I can't really opine on the 上下通也 gloss from the Shuowen, but the rest of it appears to explicitly deny that 丨 could be a character in its own right. It says "In the modern day 丨 is used as a radical in characters. It is also used as a stroke in characters, called "shu".

    (I'm not sure why the last two sentences aren't glosses. They are formatted as if they are part of the quote from the Shuowen, but they aren't actually part of it. Maybe just a formatting error? Maybe because they are not meanings associated with the 'character', but rather explanations of the fact that it isn't one?)

    On a totally unrelated note, I'm interested to see that 丨 is listed in the Kangxi dictionary with the pronunciation 古本切. Does that reflect the pronunciation during Kangxi's reign, or is it more ancient? (And if the first, what happened that it isn't supposed to be pronounced gen today?)

  3. Michael Watts said,

    November 19, 2023 @ 7:20 am

    Typo: the Hanyu Da Cidian entry I quoted does not say 一用作, it says 亦用作.

  4. Victor Mair said,

    November 19, 2023 @ 9:59 am

    According to Zhengyuan Wang's analysis and categorization, the character liè 鬣, discussed here, is indeed unusual and hard to classify.

  5. Michael Watts said,

    November 19, 2023 @ 11:11 am

    Just as a reference for squareness in handwriting, we can compare the first sample shown in the recent post Abbreviated and nonstandard kanji.

    In this sample, labeled "1", there are 5 characters. The fourth appears to be 友 with an additional dot and a 竹字头, and the fifth appears to be a simplified form of 機.

    That fourth character is, in my screenshot, about 69 pixels wide and 113 tall; these numbers might be off by up to 4 pixels or so. The fifth one, by contrast, is 96 pixels wide and 116 tall. They are almost exactly the same height, but character #5 is 40% wider than character #4 is.

    And while character #5 is close to being square, character #4 is not; it is more than 60% taller than it is wide.

  6. Richard Warmington said,

    November 19, 2023 @ 3:36 pm

    @Michael Watts. Re: "the rest of it appears to explicitly deny that 丨 could be a character in its own right."

    The Hànyǔ Dà Cídiǎn entry doesn't say it was never a character. It just says it's *now* used as a radical and as a stroke within other characters.

    The Shuowen definition implies that it *was* a character "in its own right". Its meaning is explained in French in the Grand Ricci dictionary as
    1. (Étymol.) communication entre le haut et le bas. (p. ext.) Du bas vers le haut : avancer.
    2. (p. ext.) Du haut vers le bas : reculer.

    And in 兩岸詞典 (the Cross-Straits Chinese Dictionary), 丨(gǔn) is defined as
    1. 上下貫通的樣子。
    2. 二一四部首之一。

  7. Michael Watts said,

    November 19, 2023 @ 8:45 pm

    And in 兩岸詞典 (the Cross-Straits Chinese Dictionary), 丨(gǔn) is defined as
    1. 上下貫通的樣子。
    2. 二一四部首之一。

    Is this different from the Hanyu Da Cidian entry? Sense 1 appears to be the gloss from the Shuowen, translated into more modern Chinese; sense 2 is "One of [the] 214 character radicals".

    Is sense 1 present in the Cross-Straits dictionary because it's part of the modern language, or because that sense is present in the Shuowen Jiezi?

    And is the sense present in the Shuowen Jiezi because it was part of the ancient language, or for some other reason? (Completeness??) I'd like to see a quotation that includes the word, but finding one is beyond the limits of my abilities. The admittedly hamhanded method of searching for "丨" yields two kinds of results: dictionary entries, and texts in which 丨 appears to have been used for some kind of visual effect, as here:

  8. Jonathan Smith said,

    November 19, 2023 @ 9:41 pm

    re: "丨", probably depends what "is/was a [Chinese] character" means. A narrow definition might be 'is conventionally used to write a word or part of a word of some modern Chinese language', broader would be, 'was in the past conventionally so used wrt some historical Chinese language', even broader 'was at least a single time so used'… etc…. maybe broadest of all 'was at least a single time used to fill a character-sized slot in some text'. "丨" passes the last test in Shuowen but no, reading the text there it's far from clear that Xu Shen is reporting on uses of this form to represent some word of his own or some earlier language. In general (sadly?) this is not his concern at all.

    The text is in fact weird and interesting, the language translated into French above actually says "引而上行讀若囟,引而下行讀若" 'if drawing [pen] from bottom upwards it is read [like] '囟' (don't know if this = xin4 'top of head'), drawing [pen] from top downwards it is read like " (don't know if this = tui4 'retreat')." Commentators go on to note characters within which (totally contrary to later practice) this *vertical stroke* is meant to be written either upwards or downwards, weirdly reflecting certain of Xu Shen's claims regarding the original referents of the character forms in question. (And none of this speaks to the later fanqie 古+文.)

    Anyway re: square characters, as far as a text as a whole, the notion of one "square" being allotted to each character, whether or not the square in question is "filled“ (it often isn't of course) is a reasonable pedagogical device… naturally violated left and right by the artists.

  9. Jonathan Smith said,

    November 19, 2023 @ 9:42 pm

    *missing final character in SW text is said to be variant of 退

  10. Victor Mair said,

    November 20, 2023 @ 10:19 am

    the notion of one "square" being allotted to each character, whether or not the square in question is "filled“ (it often isn't of course) is a reasonable pedagogical device


  11. DKlimenok said,

    November 20, 2023 @ 10:24 am

    (Must be a typo in the final paragraph: 'the students who has only encountered…')

  12. Michael Watts said,

    November 20, 2023 @ 11:11 pm

    More on the topic of character compositional classification, I see on zdic that 里 is considered to be its own radical. This appears to imply that it is composed of just one element.

    However, I also see that its composition is supposedly 上下结构, two elements arranged one above the other.

    The obvious way to interpret that would be that 里 consists of a 田 above a 土, but this is not really compatible with the stroke composition of 里, which includes only one vertical stroke that would need to be shared between the two elements. The top half of the stroke, I guess, would belong to the 田, and the bottom half would belong to the 土.

    The other way to interpret this compositional classification would be that 里 consists of a 甲 element positioned above an 二 element, but this suffers from many problems. That interpretation does not allow us to say that the two elements are positioned one above the other. The 甲 is written across both vertical halves of the available space, as if it were the sole element of the character, and the 二 is then written in the bottom half of the space, which would be normal except that this superimposes it across the bottom half of the 甲.

    What's the thinking here?

    I'm not sure how related this is, but it seems worth observing that foreign learners of Chinese tend to interpret the character 美 as having just one large pie stroke cutting through the entire thing, similar to the pie stroke of 天. In fact 美 is divided into a top half and a bottom half — and the shu stroke of the top half is not combined with the pie stroke of the 大 in the bottom half, though in writing they often do appear to connect.

  13. Victor Mair said,

    November 21, 2023 @ 8:13 am

    The radical / semantophore of měi 美 ("beautiful") is Kangxi 123, yáng 羊 ("ovicaprid", i.e., "sheep-goat") + the 3 strokes of dà 大 ("big") at the bottom for a total of 9 strokes. So its composition has nothing to do with the famous "piě 撇" (defined as "a stroke that falls downwards toward the left") — 丿– about which we have written so much recently. See "Extreme simplification and phoneticization" (11/19/23).

    Many seminal / fundamental concepts of Chinese civilization are written with sinoglyphs in which the ovicaprid radical / semantophore is featured.

    See "Lamb of Goodness, Goat of Justice" (pp. 86-93) in Victor H. Mair, "Religious Formations and Intercultural Contacts in Early China," in Volkhard Krech and Marion Steinicke, ed., Dynamics in the History of Religions between Asia and Europe: Encounters, Notions, and Comparative Perspectives (Dynamics in the History of Religion, 1 [Ruhr-Universität Bochum]) (Leiden: Brill, 2011), pp. 85-110 (available on Google Books) and elsewhere. Also see the many Language Log posts on "sheep", "goat", "ovicaprid", "wool", etc.

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