1. No category

Symmetry in Chinese Arts
Done by:
Group 3
Lim Li Yan
Yip Lixia, Sabrina
Lee Weitian, Ivan
Zhong Shengmin
Goh Yoon Keong
1
CONTENTS
• Introduction
• Symmetry in Chinese Literature
• Chinese Paper Cuttings
• Symmetry in Chinese buildings
• Chinese Music
• Conclusion
• Bibliography
2
Introduction
“The use of the geometric principles of symmetry for the description and
understanding of decorated forms represents the union of two normally separate
disciplines – mathematics and design.” (Washburn et al., 1988)
Symmetry has been used in countless contexts, and with diverse shades of meaning.
Coming from the Greek symmetros, for "measured together," this word is most familiar to us as a
description of the similarity between the two halves of any form separated by a dividing line or
plane. The concept is not limited to science, of course. It has been, for example, a mainstay of
aesthetics from the beginning. Thus we speak of the symmetry of the human face, we can all
understand what it is and how it looks. Its influence in the arts is pervasive. In music, we hear the
symmetry of exposition and recapitulation in the so-called sonata form, where virtually the same
music is played and played again.
The creation of identities or equivalents is at the heart of the principle of symmetry in
music, as in the other arts. It is an emblem of the human predilection for just proportion in all
things, and the longing for rational comprehension of anything encountered. In the end,
somewhat subconsciously, the idea of symmetry is placed in opposition to chaos, and thereby to
ignorance as well.
Many studies have been done in this field; these have been outlined extensively in the
book, “Symmetries of Culture” by Washburn et al. (1988). The gist of it is that symmetry spans
spatial and temporal dimensions. In many cultures, it is used as an important factor in cultural
acceptance. Authors such as Hanson (1985)1 have traced how the lack of symmetry in Maori
society has resulted in instable social relationships. In the book itself, it was briefly mentioned
that certain types of symmetry were adopted in certain periods such as the “Snaketown Phase”
and the “Colonial Period”.
1
Taken from Washburn et al., 1988.
3
Extensive as the book may be, it leaves out study of a very significant culture – the
Chinese culture. Through our project, we hope to outline the different permeations of symmetry
in the different aspects of Chinese culture, namely in the Visual and Audio Arts. Symmetry in
Chinese literature is hard to spot for non-speakers of the language. Through a systematic
investigation of cultural order by using principles of linguistics as a model, it is hoped that we
can decode the structural systematic of various graphic systems. This is done in the analysis of
the structure of Chinese poems whereby words are replicated in such a unique manner that it
makes profound sense. For paper cut, we will illustrate how they use different forms of
symmetry-rotational and reflectional. In Chinese Architecture, we will show how bilateral
symmetry plays an important role in the construction of structures. Lastly, symmetry is shown to
be imperative in music through the tuning of instruments, the pentatonic scales and the structure
of the music itself.
4
Symmetry in Chinese Literature
Symmetry has an important role in Chinese literature. Maybe this is due to the preference
for things to be in even numbers, nobody exactly knows why. Regardless of the reason Chinese
literature, especially poems, has a strong tendency to include symmetrical elements.
Example 1:
花朵几枝柔倍砌，
柳丝千缕细摇风。
霞明半岭西斜日，
月上孤村一树松。
REVERSE
松树一村孤上月，
日斜西岭半明霞。
风摇细缕千丝柳，
砌倍柔枝几朵花。
（唐。薛涛《春》）
Example 2:
白杨长映孤山碧，
碧山孤映长杨白。
春暮伤别人，
人别伤暮春。
雁归迷塞远，
远塞迷归雁。
楼倚独深愁，
愁深独倚楼。
（明。王元美《菩萨蛮。暮春》）
5
Example 3:
难离别情万千，眠孤枕，愁人伴。闲庭小院深，关河传信远，鱼和雁天南，看明月，中肠
断。
断肠中，月明看。南天雁，和鱼远。信传河关深，院小庭闲伴。人愁枕孤眠，千万情，别
离难。
（明。王元美《卷帘雁儿落》）
2
Note: Words in blue from Example 1-3 are the reverse portions.
Example 1 is a poem by Xue Tao of Tang dynasty. Examples 2 and 3 are known as
ci（词），composed by Wang Yuan Mei during Ming dynasty. Ci （词）is a major form of
literature, second to poem. It is actually lyrics that can be sung. But Ci （词）is much more
complicated than lyrics of a song. Many composers used it to express profound ideas and it is so
artistically expressed that ci（词）is labeled as a major form of Chinese literature.
The poem in example 1 can be read in reverse order and becomes another poem. In
example 2, every sentence is made up of 2 parts and the two parts are made up of same words.
The only difference is that the words in the second half of the sentences are in reverse order
compare to the first half of the sentences. Example 3 is made up of two parts. The words in
second part are the words in the first part arranged in reverse order. All three examples have a
mirror image structure.
The three examples are instances where the Chinese literati tried to express symmetry in
Chinese literature in an interesting and amusing way. The essence of symmetry in Chinese
literature is actually in the sentence structure. Chinese poems best illustrate this symmetry in
sentence structure. In Chinese poems, all sentences are required to have symmetry sentence
structures. The sentence structure of the first part of the sentence is symmetrical to the second
part. And in order for the poem to look symmetrical as well, there is a strict rule to the number of
words in a sentence of a poem. There can only be even numbers of sentences and all sentences in
a poem must have the same number of words.
2
Example 1-3 are extracted from lecture notes on Chinese Rhetoric, prepared by A/P Lee Cher Leng
6
The meaning of being symmetrical in sentence structure is as follow:
For example we have a 5-word poem. (A 5-word poem is a poem whereby there is a pause after
every five words. Two 5- word parts made up a sentence of the poem.) In the first part of a
sentence, the first two words is an adjective, third and fourth word is a noun, and the last word is
a verb. Then in the second part of the sentence, the first two words must be an adjective, third
and fourth word must be a noun, and the last word must be a verb. If this structure is broken, for
example in the second part of the sentence, the first word is a verb, the second and third word is
an adjective and last two words is a noun. Even if the sentences rhyme, it will still not be
considered as a poem.
Example 4:
3
Example 4 is part of a poem by Wang Wei, a poet during the Tang dynasty. The sentences
clearly illustrate the idea of symmetry in sentence structure.
Besides poem, this symmetrical sentence structure is also seen in many other parts of
Chinese literature. One of those which are most commonly seen is couplets. In the past, Chinese
families would have two scrolls of words, pasted on either sides of door. Nowadays in
Singapore, people lived in HDB flat and this is not practice. But at Chinese temples like Thian
Hock Keng Temple, you will still get to see couplets pasted at either side of the door. And during
Chinese New Year, some Chinese families will still paste couplets inside the house.
3
Example 4 is extracted from lecture notes on Chinese Rhetoric, prepared by A/P Lee Cher Leng
7
Example 5:
4
Example 5 is one of those most commonly paste couplet during Chinese New Year. The
symmetry in sentence structure is clearly seen.
Sentences with mirror image structure are also frequently used in essays and novels. But
it is not totally mirror reflection of words, most of the time it is just mirror reflection of key
words. In such cases, it is normally used to expressed ideas like A is B, and B is A.
Example 6:
知者不言，言者不知。
知者不博，博者不知。
5
信言不美，美言不信。
（老子《道德经》）
Example 7:
不是东风压倒西风，就是东风压倒西风。
6
（曹雪芹《红楼梦》：82 回）
Example 8:
宇宙即是人生，人生即是宇宙。
7
（梁启超《为学与做人》）
4
Example 5 is extracted from lecture notes on Chinese Rhetoric, prepared by A/P Lee Cher Leng
陈国庆, 张爱东注译，《道德经》：第八十一章，西安 : 三秦出版社, 1995（Complied by Chen Guo
Qing & Zhang Ai Dong , Dao De Jing ：Chapter 81, Xi An: San Qin Publications, 1995）
6
曹雪芹，《红楼梦》：第八十二回，北京 : 人民文学出版社, 1985
(Cao Xue Qin, Dream of the Red Chamber: Chapter 82, Beijing: Peoples’ Literature Publications, 1985)
5
8
Note: Words in blue from example 6-8 are the key words.
Example 6 is from Dao De Jing（道德经） of Lao Zi（老子）, a philosopher during the preQin dynasty, commonly known to be the founder of Taoism. Example 7 is from Dream of the
Red Chamber（红楼梦）, Chapter 82, written by Cao Xue Qin （曹雪芹）during the Qing
dynasty. Example 8 is from 《为学与做人》（Learning and Being a Person）, written by
Liang Qi Chao （梁启超）during late Qing dynasty.
Symmetry can be seen in many parts of Chinese literature. One of the reasons of why is it
so could be because of the Chinese preference for even number objects. In Chinese literature,
mirror image symmetry is the symmetry that Chinese literati use. As a result of mirror image,
even numbers always results. Be it symmetry in meaning wise or structure wise, this symmetry
in Chinese literature produces the beauty of compare and contrast, and the beauty of balance.
Overall it enhances the beauty of Chinese literature.
7
Example 8 is extracted from lecture notes on Chinese Rhetoric, prepared by A/P Lee Cher Leng
9
CHINESE PAPER CUT
Paper cut is one of the most popular and characteristic folk arts in China. Papers are
folded, cut and unfolded to reveal sophisticated patterns, often with symmetry in them. Paper
cuts have rosette patterns — either Cn, which has n-fold rotational symmetry and no reflection
symmetry, or Dn, which has n-fold rotational symmetry and reflection symmetry. Ignoring the
Chinese characters in the center of the patterns, paper cuts give rise to various types of rosette
patterns.
C1 patterns:
There is 1-fold rotational symmetry and no reflection symmetry.
8
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C2 patterns:
There is 2-fold rotational symmetry and no reflection symmetry.
10
11
C3 patterns:
8
http://www.artisticchinesecreations.com/papercut.html
http://www.delicraft.com/
10
http://www.artisticchinesecreations.com/papercut.html
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http://www.delicraft.com/
9
10
There is 3-fold rotational symmetry and no reflection symmetry.
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C4 patterns:
There is 4-fold rotational symmetry and no reflection symmetry.
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C6 patterns:
There is 6-fold rotational symmetry and no reflection symmetry.
14
12
http://chineseculture.about.com/library/weekly/aa020900a.htm
http://www.delicraft.com/
14
http://www.artisticchinesecreations.com/papercut.html
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11
D1 patterns:
There are 1-fold rotational symmetry and reflection symmetry.
15
16
D2 patterns:
There are 2-fold rotational symmetry and reflection symmetry.
17
15
http://chineseculture.about.com/library/weekly/aa020900a.htm
http://www.funalliance.com/all/papercut/papercut.htm
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http://www.funalliance.com/all/papercut/papercut.htm
16
12
D4 patterns:
There are 4-fold rotational symmetry and reflection symmetry.
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19
The most common types of rosette patterns seen in Chinese paper cuts are C1 and D1.
Distribution Of Rosette Patterns
50%
45%
40%
35%
30%
25%
20%
15%
10%
5%
0%
C1
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C2
C3
C4
C5
C6
D1
D2
D3
D4
http://gift2all.zoovy.com/category/papercutting
http://www.funalliance.com/all/papercut/papercut.htm
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CHINESE MUSIC
It can be seen from the various dynasties of China, that music only thrives in the golden
era or the prime time of an empire. It has also been observed that the expansion of music leads to
extension of the idea of symmetry in both ancient music and its composition which we will
discuss promptly.
Relation of symmetry to Chinese Music, the “Kung” and Cosmic Influence
Music was the cornerstone in the Chinese civilization, which was the longest living
culture in history. It was considered to embody within its tones, elements of the celestial order.
The audible sound, including music, was but one form of manifestation of a much more
fundamental form of Super physical Sound. The Chinese believed that this Primal Sound, Kung
or "Huang Chung" (directly translated "yellow bell") was, though inaudible, present everywhere
as a Divine Vibration. Furthermore, it was also divided into 12 lesser Sounds or Tones. Each of
the 12 Tones was believed to be associated with one of the 12 zodiacal regions of the heavens.
For the ancient Chinese, the alignment with the divine prime tone was the emperor's most
important task. The alignment of earth with heaven and man with the Supreme was literally the
purpose of life. The entire State affairs and order was dependent upon the right tuning of the
fundamental tone, the yellow bell, or Kung. As an ancient text warns: "If the Kung is disturbed,
then there is disorganization; the prince is arrogant".
If the Kung was out of tune, because the celestial realm has changed, disorder and
inharmonious behavior in the society became obvious. Every instrument (also the measuring
instruments) was tuned and utilized in accordance with the holy tone.
The instrument, which could give to man the fundamental tone for a musical scale, which
was in perfect harmony with the universe, was the key to earthly paradise, and essential to the
security and evolution of the society. The Chinese was aware of the slow changing cosmic
influence and consequently the Kung has to change accordingly. The emperor had the task of
tuning the Kung so it was in alignment with the cosmic tone.
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However so, the Kung is found to be related to the frequency of the Platonic Year.
The duration of the Platonic Year, (The Pythagorean Great Year) is about 25,920 years
and represents the amount of time the axis of the Earth takes to complete a full rotation.
The vernal equinox is the point at which the equator (of Earth) intersects the ecliptic (or
zodiac), which is the position of the sun at the beginning of spring - March 21th.
The vernal equinox takes an average of 2,160 years to travel through one sign of zodiac.
This period of time is known as an age. It is not possible to state exactly when one age is
ending and a new beginning, because the signs overlap to a certain degree.
The journey of the vernal equinox through each of the 12 signs of the Zodiac equals one
great year of approx, 25,920 years.
This rotational cycle amazes us how the ancient Chinese could be aware of their sacred
fundamental tone, Kung, to be in accordance with the Platonic Year and choose the great rhythm
of the Earth.
The below illustrates how the ingenious Chinese has managed to link the 12 zodiac signs
with the invention of the Kung. However so, we need to note that they may have taken the 12
animal zodiac signs of the Chinese calendar into consideration instead, since the Western Zodiac
signs had not entered China yet.
15
All these show the innovation of Chinese and their obsession in symmetry, especially
rotational symmetry in this case, though we may not even live to experience the greatness of it.
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Significance of Chinese Pentatonic and Heptatonic scales in Music Symmetry
Melody and tone quality are prominent expressive features of Chinese music, and great
emphasis is given to the proper articulation and inflection of each musical tone. Most Chinese
music is based on the five-tone, or Pentatonic, scale, but the seven-tone, or Heptatonic scale, is
also used, often as an expansion of a basically pentatonic core. The Pentatonic scale was much
used in older music. The Heptatonic scale is often encountered in northern Chinese folk music.
In the pentatonic folk music, semitones do not exist. By practice have the people found
out, that the 5 notes scale gave the possibilities to play any key without significant disharmony.
Theorists would say that the scale was composed of ascending and descending fifths only in two
steps in each direction, which forms a reflectional symmetry from the left to the right. A
pentatonic scale can be played by only using the black keys on the piano.
20
http://www.sourcetext.com/pythagoras/mcclain.html
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(1) Definition of the Chinese Pentatonic Scale
As we know that 'pentatonic' means 'five', but there are many kinds folk music that have their
own set of 5 (eg. Japanese, Malay, Chinese etc). Hence, the best way to express the Chinese
Pentatonic is by understanding the fixed interval relation between the 5 notes.
Using the movable-doh concept, the basic of the Chinese pentatonic is doh, re, mi, soh, la (and
back to doh).
There is a name for each of the notes:
doh ('gong'), re ('shang'), mi ('jiao'), soh ('zhi'), la ('yu').
Now for the interval relation:
gong & shang (doh & re) is a major 2nd apart, shang & jiao (re & mi) is a major 2nd apart, jiao
& zhi (mi & soh) is a minor 3rd etc. So a basic 'formula' would be this:
Notes: gong shang jiao zhi yu gong
Interval: (Maj 2nd) (Maj 2nd)(Min 3rd)(Maj 2nd) (Min 3rd)
Therefore, if your doh (gong) is on a D flat, based on the interval relation, the following
arrangement would be:
Notes: Db Eb F Ab Bb Db
Interval: (Maj 2nd)(Maj 2nd)(min 3rd) (Maj 2nd) (Min 3rd)
We can memorize this fixed interval and try it on any starting note and we will get the same
pentatonic sound in different pitches. In terms of symmetry, it actually forms a translational
symmetry when repeating the scale.
(2) Not just one scale
From the above fixed interval relation (or structure), we can derive 5 kinds of Chinese pentatonic
scales. In the above examples, we start a scale using 'gong' (or doh). Remember that this is a
movable-doh concept. This is called the 'gong pentatonic scale'. We can also have a 'shang (or re)
pentatonic scale'.
17
Notes: shang jiao zhi yu gong shang
Interval: (maj2nd) (min3rd)(maj2nd)(min3rd) (maj2nd)
movable-doh: re mi soh la doh re
If you choose D flat as a 'shang' (like in this case) instead of a 'gong' (in the previous case), your
scale would be:
notes: Db(shang), Fb (jiao), Gb (zhi), Ab (yu), Cb (gong), Db (shang)
So we just need to remember that the interval relation is fixed, but we can choose where to
position the starting note and the respective scale which can be constructed as we fill in the other
notes according to the 'formula'.
(3) How to determine the 'gong' (or the doh) from a given Chinese scale.
If you are given a set of 5 notes, for eg, A,C,D,F,G,A, would you know which note is
'gong' and what scale is this? There is a secret to finding out. In every Chinese pentatonic scale,
there is a hidden Major 3rd. First, find the major 3rd. Here F and A is the major 3rd. In the
'formula', 'gong'(doh) and 'jiao'(mi) form the only major 3rd. This is fixed too. Hence, 'F' here is
your 'gong'. So, when you put the fixed interval structure, this would be a 'jiao pentatonic scale'
(since it starts on A and A is a jiao).
(4) The spiral of fifths and the scale of 60 Lü
Next, the pentatonic scale thus presents a structure that allows it to be an adequate
representation of the static influence of heaven on earth. But a static representation of a world in
motion could not be an instrument of action upon that world. It is necessary to evolve from the
motionless to the moving, from the angular to the circular, from the square to the circle. To
express the movements of the universe, the sounds will have to submit to the cyclic laws that, in
their own field, are represented by the cycle of fifths."
18
21
As we have already seen, the fifth is the third sound of the series of harmonics, the first
being the fundamental and the second its octave. According to the formula of the Tao-Te-Ching,
"One has produced two, two has produced three, three has produced all the numbers", we can
understand why the third sound, the fifth, must necessarily produce all the other sounds by its
cyclic repetitions. The first to be produced will be the four principal sounds, which form
comparatively simple ratios with the tonic.
The Chinese musical scale was developed by the circle of perfect fifths up to 60 degrees
or keys, the 60 Lü, though they usually only used the first 5 fifths in their pentatonic music,
because they knew that they represent the limit of consonance in modal music. In addition, the
ancient Chinese saw a symbolic representation of the pentatonic scale rooted from their belief of
music being the representation of the relationship between heaven and earth the five elements).
In practice, for reasons that are symbolic as well as musical, after the 52nd fifth (53rd note) the
Chinese follow the series only for the next seven degrees, which place themselves above those of
the initial seven-note scale, and they stop the series at the 60th note. The reason given is that 12
(the number of each cycle) * 5 (the number of the elements) = 60.
21
http://home22.inet.tele.dk/hightower/Kung#Kung
19
Hence, the spiral of fifths gave rise to continuous rotational symmetry of the notes
through repetitions and eventually formed the 60 Lü.
The seven-notes (Heptatonic) Chinese scale
L+
C
D
E+
(F)¤
1/1
9/8
81/64
(4/3) 729/512
F#
G
A+
B+
C’
3/2
27/16
243/128
2/1
The two auxiliary sounds - 243/128 and 739/512 - should not be used as fundamentals,
though they are needed for transpositions, because they belong to the scale of invisible worlds,
and therefore we can neither perceive their accuracy nor build systems upon them without going
out of tune.
Doesn’t the below show reflectional symmetry when placed on a musical scale?
22
Figure 1: Scale of Great Dragon tuning.
22
http://www.cechinatrans.demon.co.uk/ctm-psm.html
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Chinese Music and Song Composition
Chinese music writing should be based on various “modes”, seven-tonic scale instead of
only the pentatonic scale, and should be assisted with modal harmony and tooled with classical
symmetry. Furthermore, symmetric techniques advance the thoughtfulness of art songs.
Hence a basic approach to compose a song is to repeat a sequence of tones again and
again. If this is done correctly, the restatement of the sequence of tones will help to make the
musical piece easier to remember and more recognizable. Musical restatements are very similar
to geometric transformations. A geometric figure like a triangle can be relocated while
preserving its size and shape. These can include simple translations and reflections as shown.
Other than these, in modern composition of lyrics in Chinese Pop Songs, composers have a
tendency to separate a piece of song into 2 portions, where the 2nd part will just be a repetition of
the 1st part. There are also composers who only repeat the chorus part. All these can prove as
direct translational symmetry in terms of the lyrics and tune of the song, which lets singers have
an easier time memorizing them, as well as a plus point for teenagers who like to sing at karaoke
due to the easy grasp of the songs.
Below are 2 examples which musical scales can be symmetrical. If musical notes are
placed at the vertices of the triangle below and the triangle is moved horizontally from position
A to position B. What musical notes should be in position B?
23
In musical application, the notes will repeat accordingly as shown below.
24
23
24
http://en.wikipedia.org/wiki/Symmetry#Music
http://en.wikipedia.org/wiki/Symmetry#Music
21
If the triangle in position I reflects to position II, what is the musical reflection of the notes?
25
The notes will repeat. The triangle is reflected across the Y-axis. The musical counterpart of a
horizontal reflection is called retrogression.
26
Then there can also be a vertical reflection as shown.
27
Hence from the above examples, we can see that Chinese music, no matter in ancient
times, or modern times, it still deeply affects us, especially with the inclusion of symmetry to
enhance its longevity.
25
26
27
http://en.wikipedia.org/wiki/Symmetry#Music
http://en.wikipedia.org/wiki/Symmetry#Music
http://en.wikipedia.org/wiki/Symmetry#Music
22
SYMMETRY IN BUILDING
Although few examples of Chinese homes have survived from antiquity, using archeological
evidence, it can be determined that many of the basic principles of Chinese house design, such as
the emphasis on orientation, layout, and symmetry go far back in Chinese history.
28
The basic feature of Chinese architecture is
rectangular-shaped units of space joined together into
whole. The Chinese style combines rectangular shapes
varying in size and position according to importance
into an organic whole. As a result, traditional Chinese
style buildings have an imposing yet dynamic and
intriguing exterior.
Diagram of a four-sided courtyard house
The combination of units of space in traditional Chinese architecture abides by the
principles of balance and symmetry. The main structure is the axis, and the secondary structures
are positioned as two wings on either side to form the main rooms and yard. The area that the
house is built on is shaped like a rectangle or square, even if the entire plot of land isn’t perfectly
geometrical Residence, official buildings, temples, and palaces all follow these same basic
principles. The distribution of interior space reflects Chinese social and ethnical values.
"The design, layout and material of the old houses here reflect the ancient philosophy of
harmony between humans and heaven," said Liu Xiaoshi, a leading architect active in the
preservation of old Beijing.
28
http://depts.washington.edu/chinaciv/home/3zgdsanp.htm
23
29
Symmetry overview of the Forbidden City in Beijing
It’s apparent that the Chinese are concerned with geometry in architecture, merely by
viewing the archways or doorways of many buildings. Most examples have three bays: a larger
dominating portal forming the central axis with paired openings of lesser size and importance on
either side. They are often in the shape of semi-circles or near circles and have intricate designs
on or around them. The circles represent openness and hospitality in the Chinese culture, the
circular gate is said to be more inviting than a rectangular doorway. Presentation is a key
component in the Chinese culture. Expression of symmetry and geometry in architecture is a
traditional way for architects to express Chinese culture.
30
Paifang, an example of bilateral symmetry which is by far the most common form of symmetry
in architecture. In bilateral symmetry, the halves of a composition mirror each other.
29
30
http://solomon.cps.k12.5l.us/gallupindex.html
http://solomon.cps.k12.5l.us/gallupindex.html
24
Paifang, also called pailou, is an architectural design that is uniquely Chinese. The
paifang is an archway made of wood or stone and inlaid with glazed tiles. In feudal times,
calligraphers were requested to write moral inscriptions that were carved in the middle beam.
The paifang stand in downtown areas, entrances of mausoleums, temples, bridges, and parks.
They are also made in memory of virtuous people making them memorial structures. They can
also be made as a decoration.
The pagoda is another structure with symmetry. It was mainly used to house sacred
objects. These temples can take the form of a storied tower, or, more rarely, a upturned bowl. As
the centuries passed, however, the shape of these temples took new forms. In the second and
third century, the structures were basically made out of wood. Their shape took the form of a
tetragonal under Song during the 10th Century. The next
3132
dynasty, Tang,
decided to have their towers shaped into an octagon or diagonal. The number of
stories varied with each of the buildings. The height demised regularly from the
base to the summit but everything else remained the same.
In most buildings we find more than one kind of symmetry. For example, in the
Chinese pagoda, we can see at the same time both the cylindrical symmetry (found in towers and
columns) inherent in the building's organization about the vertical axis, and the similarity
symmetry (found where repeated elements change in scale but
33
retain a similar shape) of the
diminishing sizes of the layered roofs.
31
http://library.thinkquest.org/10098/china1.htm
32
http://library.thinkquest.org/10098/china1.htm
25
The Temple of Heaven33
(Tian Tan)
The temple was designed according to the
most advanced principles of mechanics,
geometry and fengshui (geomancy), and
incorporates a wealth of examples of
number, symmetry and geometric shape. It
has symmetry similar to the ones mentioned
with the pagodas. Furthermore, it also has rotational symmetry (Rotation and reflection provide a
sense of movement and rhythm in architectural elements and an emphasis on the central point of
the architectural space).
34
Rotational symmetry as can be seen from the ceiling of the temple
35
36
Cylindrical symmetry in round houses made of earth of Hakka Origin
33 http://www.maths.adelaide.edu.au/people/pscott/place/pm4/pm4.html#
34
www.orientalarchitecture.com
http://www.beijingportal.com.cn/culture_architecture.htm
36
http://www.beijingportal.com.cn/culture_architecture.htm
35
26
Translational symmetry falls in the category of space group symmetry, and is, after
bilateral symmetry, the most common kind of symmetry found in architecture. Translation of
elements in one direction is found in solemn rows of soldier-like columns, or in the springing
succession of arches in an aqueduct. Translational symmetry seems to carry with it an emphasis
on a superlative quality in architecture: the longest, the broadest, or the tallest. An example of
this type of symmetry will be the shophouses lined up in a row.
Chiral symmetry is perhaps less well-known than other types of symmetry but frequently
effectively used in architecture. Chiral symmetry is found in two objects which are each other's
mirror image and which cannot be superimposed, such as our hands. Chiral symmetry in
architecture is another way to place visual emphasis on the central element of a composition.
37
Twin pagodas (the two pagodas are all that remain of a large temple that was destroyed in the
British Opium War)
Hence, we can see that symmetry and balance are traditional Chinese techniques,. It is a
typical manifestation of harmony and tranquility which lie at the heart of Chinese traditional
thinking and on which Chinese civilization has been built.
37
http://www.beijingportal.com.cn/culture_architecture.htm
27
Conclusion
As shown through extensive analysis of the various examples of visual art as well as
audio art, symmetry perpetuates itself in many occasions. As mentioned, the Chinese favor
symmetry and things to exist in even numbers as it is a mark of harmony and continuity.
Through the paper cuts, symmetry is shown to exist in the reflectional and rotational properties;
and it is shown that C1 and D1 rosette patterns are more common than others. In the field of
literature, it has been illustrated how there is structural symmetry in the classes of words used
and the arrangement of such words. In architecture, the geometrical symmetry is symbolic; for
example, circles represent hospitality. Through the analysis of the structure of music, we see that
symmetry not only brings some sense of wholeness in the acoustic experience but it is a
reflection of a deeper hierarchical structure.
Hence, we can see that symmetry and balance are traditional Chinese techniques. It is a
typical manifestation of harmony and tranquility which lie at the heart of Chinese traditional
thinking and on which Chinese civilization has been built.
28
Bibliography:
Website Links
1. The Creation of Musical Scales, part II.
http://home22.inet.tele.dk/hightower/Kung#Kung
2. The Theory Behind Chinese Music
http://www.wfu.edu/~moran/G_tar2.html
3. Symmetry
http://en.wikipedia.org/wiki/Symmetry#Music
4. Fearful Symmetry
http://www.wholarts.com/music/ed/lect.htm
5. Music Theory and Ancient Cosmology
http://www.sourcetext.com/pythagoras/mcclain.html
6. Pitches, Scales and Modes
http://www.cechinatrans.demon.co.uk/ctm-psm.html
7. Introduction to Symmetry
http://www.mathdance.org/symmetrygroups/symmetrygroups.html
8. Symmetry and Symmetry Breaking
http://plato.stanford.edu/entries/symmetry-breaking/3
9. About Paper Cuttings
•
http://chineseculture.about.com/library/weekly/aa020900a.htm
•
http://www.delicraft.com/
•
http://www.artisticchinesecreations.com/papercut.html
•
http://www.funalliance.com/all/papercut/papercut.htm
•
http://gift2all.zoovy.com/category/papercutting
10. Symmetry in Architecture by Kim Williams, Architect
http://members.tripod.com/vismath/kim/
11. Chinese Architecture
http://library.thinkquest.org/10098/china1.htm
12. http://www.maths.adelaide.edu.au/people/pscott/place/pm4/pm4.html#
13. http://www.beijingportal.com.cn/culture_architecture.htm
14.http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Umberger/MATH7210/SymmArch
/finalproject.html
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Books
1. Yuan-Yuan Lee & Sin-yan Shen, Chinese musical instruments, Chicago : Chinese Music
Society of North America, 1999
2. Stephen Jones, Folk music of China : living instrumental traditions, Oxford : Clarendon
Press ; New York : Oxford University Press , c1995
3. Jonathan P.J. Stock, Musical creativity in twentieth-century China : Abing, his music, and
its changing meanings, Rochester, N.Y. : University of Rochester Press, 1996
4. Sin-yan Shen, China : a journey into its musical art, Chicago : Chinese Music Society of
North America, 2000
5. Jenny F. So, Music in the age of Confucius, Washington, D.C. : Freer Gallery of Art and
Arthur M. Sackler Gallery, c2000
6. Robert Wood Clack, Celestial symphonies : a study of Chinese music, New York :
Gordon Press , 1976
7. J. A. Van Aalst, Chinese music, Taipei : Chinese Classical Music Association , 1964
8. Ian Johnston, Measured tones : the interplay of physics and music, Bristol ; Philadelphia
: Institute of Physics Publishing, c2002
9. Dorothy K. Washburn & Donald W. Crowe, Symmetries of Culture: Theory and Practice
of Plane Pattern Analysis, United States of America: University of Washington, 1988.
10. 陈国庆, 张爱东注译，《道德经》：第八十一章，西安 : 三秦出版社,
1995（Complied by Chen Guo Qing & Zhang Ai Dong , Dao De Jing ：Chapter 81, Xi
An: San Qin Publications, 1995）
11. 曹雪芹，《红楼梦》：第八十二回，北京 : 人民文学出版社, 1985
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