Symmetry in Chinese Arts

Done by: Group 3 Lim Li Yan Yip Lixia, Sabrina Lee Weitian, Ivan Zhong Shengmin Goh Yoon Keong

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CONTENTS Introduction Symmetry in Chinese Literature

Chinese Paper Cuttings

Symmetry in Chinese buildings

Chinese Music Conclusion Bibliography

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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.

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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.

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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:

REVERSE

Example 2:

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Example 3:

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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

cicomposed by Wang Yuan Mei during Ming dynasty. Ci is a major form of

literature, second to poem. It is actually lyrics that can be sung. But Ci is much more

complicated than lyrics of a song. Many composers used it to express profound ideas and it is so

artistically expressed that ciis 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

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:

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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

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Example 5:

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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:

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Example 7:

82 6

Example 8:

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4 Example 5 is extracted from lecture notes on Chinese Rhetoric, prepared by A/P Lee Cher Leng 5 , : , 1995Complied by Chen Guo Qing & Zhang Ai Dong , Dao De Jing Chapter 81, Xi An: San Qin Publications, 1995 6 : , 1985 (Cao Xue Qin, Dream of the Red Chamber: Chapter 82, Beijing: Peoples Literature Publications, 1985)

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Note: Words in blue from example 6-8 are the key words.

Example 6 is from Dao De Jing of Lao Zi, a philosopher during the pre-

Qin dynasty, commonly known to be the founder of Taoism. Example 7 is from Dream of the

Red Chamber, Chapter 82, written by Cao Xue Qin during the Qing

dynasty. Example 8 is from Learning and Being a Person, written by

Liang Qi Chao 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

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 9 C2 patterns: There is 2-fold rotational symmetry and no reflection symmetry.

10 11C3 patterns:

8 http://www.artisticchinesecreations.com/papercut.html9 http://www.delicraft.com/10 http://www.artisticchinesecreations.com/papercut.html11 http://www.delicraft.com/

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http://www.delicraft.com/http://www.artisticchinesecreations.com/papercut.htmlhttp://www.delicraft.com/

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.

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12 http://chineseculture.about.com/library/weekly/aa020900a.htm13 http://www.delicraft.com/14 http://www.artisticchinesecreations.com/papercut.html

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http://chineseculture.about.com/library/weekly/aa020900a.htmhttp://www.artisticchinesecreations.com/papercut.html

D1 patterns: There are 1-fold rotational symmetry and reflection symmetry.

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D2 patterns: There are 2-fold rotational symmetry and reflection symmetry.

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15 http://chineseculture.about.com/library/weekly/aa020900a.htm16 http://www.funalliance.com/all/papercut/papercut.htm17 http://www.funalliance.com/all/papercut/papercut.htm

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http://chineseculture.about.com/library/weekly/aa020900a.htmhttp://www.funalliance.com/all/papercut/papercut.htmhttp://www.funalliance.com/all/papercut/papercut.htm

D4 patterns: There are 4-fold rotational symmetry and reflection symmetry.

18 19 The most common types of rosette patterns seen in Chinese paper cuts are C1 and D1.

Distribution Of Rosette Patterns

0%5%

10%15%20%25%30%35%40%45%50%

C1 C2 C3 C4 C5 C6 D1 D2 D3 D4

18 http://gift2all.zoovy.com/category/papercutting19 http://www.funalliance.com/all/papercut/papercut.htm

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http://gift2all.zoovy.com/category/papercuttinghttp://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.

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'.

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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 L

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."

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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 L, 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

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Hence, the spiral of fifths gave rise to continuous rotational symmetry of the notes

through repetitions and eventually formed the 60 L.

The seven-notes (Heptatonic) Chinese scale

C D E+ (F) L+F# G A+ B+ C

1/1 9/8 81/64 (4/3) 729/512 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.

Doesnt the below show reflectional symmetry when placed on a musical scale?

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Figure 1: Scale of Great Dragon tuning.

22 http://www.cechinatrans.demon.co.uk/ctm-psm.html

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http://www.cechinatrans.demon.co.uk/ctm-psm.html

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?

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In musical application, the notes will repeat accordingly as shown below.

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23 http://en.wikipedia.org/wiki/Symmetry#Music24 http://en.wikipedia.org/wiki/Symmetry#Music

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If the triangle in position I reflects to position II, what is the musical reflection of the notes?

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The notes will repeat. The triangle is reflected across the Y-axis. The musical counterpart of a horizontal reflection is called retrogression.

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Then there can also be a vertical reflection as shown.

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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 http://en.wikipedia.org/wiki/Symmetry#Music26 http://en.wikipedia.org/wiki/Symmetry#Music27 http://en.wikipedia.org/wiki/Symmetry#Music

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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 isnt 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.

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28 http://depts.washington.edu/chinaciv/home/3zgdsanp.htm

http://depts.washington.edu/chinaciv/home/3zgdsanp.htm

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Symmetry overview of the Forbidden City in Beijing

Its 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.

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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 http://solomon.cps.k12.5l.us/gallupindex.html30 http://solomon.cps.k12.5l.us/gallupindex.html

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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 3132dynasty, 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.

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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 33retain 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

http://library.thinkquest.org/10098/china1.htmhttp://library.thinkquest.org/10098/china1.htm

The Temple of Heaven33

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(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).

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Rotational symmetry as can be seen from the ceiling of the temple

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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.com35 http://www.beijingportal.com.cn/culture_architecture.htm36 http://www.beijingportal.com.cn/culture_architecture.htm

http://www.maths.adelaide.edu.au/people/pscott/place/pm4/pm4.htmlhttp://www.orientalarchitecture.com/http://www.beijingportal.com.cn/culture_architecture.htmhttp://www.beijingportal.com.cn/culture_architecture.htm

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.

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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

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http://www.beijingportal.com.cn/culture_architecture.htm

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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.

29

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

http://www.wfu.edu/~moran/G_tar2.htmlhttp://www.wholarts.com/music/ed/lect.htmhttp://www.sourcetext.com/pythagoras/mcclain.htmlhttp://www.cechinatrans.demon.co.uk/ctm-psm.htmlhttp://www.mathdance.org/symmetrygroups/symmetrygroups.htmlhttp://plato.stanford.edu/entries/symmetry-breaking/3http://chineseculture.about.com/library/weekly/aa020900a.htmhttp://www.delicraft.com/http://www.artisticchinesecreations.com/papercut.htmlhttp://www.funalliance.com/all/papercut/papercut.htmhttp://gift2all.zoovy.com/category/papercuttinghttp://members.tripod.com/vismath/kim/http://library.thinkquest.org/10098/china1.htmhttp://www.maths.adelaide.edu.au/people/pscott/place/pm4/pm4.htmlhttp://www.beijingportal.com.cn/culture_architecture.htmhttp://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Umberger/MATH7210/SymmArch/finalproject.htmlhttp://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Umberger/MATH7210/SymmArch/finalproject.html

30

Books

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its changing meanings, Rochester, N.Y. : University of Rochester Press, 1996

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North America, 2000

5. Jenny F. So, Music in the age of Confucius, Washington, D.C. : Freer Gallery of Art and

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Gordon Press , 1976

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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. , : ,

1995Complied by Chen Guo Qing & Zhang Ai Dong , Dao De Jing Chapter 81, Xi

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CHINESE PAPER CUTRelation of symmetry to Chinese Music, the Kung and Cosmic(4) The spiral of fifths and the scale of 60 LThe seven-notes (Heptatonic) Chinese scale