/Vo, 6 47 A 9 A TRANSLATION OF SELECTED CHAPTERS OF HUANG TI-PEI'S PERSPECTIVES OF CHINESE MUSIC THESIS. Presented to the Graduate Council of the

Transcription

1 A 9 /Vo, 6 47 I HISTORY AND DEVELOPMENT OF THEORY OF LU: A TRANSLATION OF SELECTED CHAPTERS OF HUANG TI-PEI'S PERSPECTIVES OF CHINESE MUSIC THESIS Presented to the Graduate Council of the North Texas State University in Partial Fullfillment of the Requirements For the Degree of MASTER OF MUSIC by Whey-Fen Chen, B.A. Denton, Texas August, 1985

2 Copyright By Whey-Fen Chen 1985

3 Chen, Whey-Fen, History and Development of Theory of Lu: A ti Translation of Selected Chapters of Huang Ti-Pei"s Perspectives of Chinese Music. Master of Music (Theory), August, 1985, 120 pp., bibliography, facsimile, 56 pp. This study first narrates on the importance of theory of lu-lu (theory of tone generation) in the history of Chinese music from the Chou Dynasty (ca. 400 B.C.) to the Chin Dynasty (ca. end of 19th century), its symbolism and ramification. The main body of this study is devoted to critical translation of Huang Ti-Pei's Perspectives of Chinese Music, particulary those sections which give chronological narratives and comparative critiques of major theories of lu-lu, in order to provide the western scholarship with documents toward understanding the evolution of tone system of Chinese music. The study concludes with a comparison of Chinese tone systems from ancient time to present, and offers comments on comparison of tone systems between the eastern and western musics.

4 Acknowledgments I would like to express my apreciation to Dr. Chuang Pen-Li Professor and Head of the Chinese Music Section of the Chinese Culture University, for his courtesy in providing information and helpful comments regarding tonal generation theory.

5 TABLE OF CONTENTS Chapter Page I. HISTORY OF MUSIC AND MUSIC THEORY IN ANCIENT CHINA II. MAJOR LU THEORIES FROM LATE HAN TO CHIN DYNASTIES Section 1: Ching Fang's "chuen" producing sixty lu-s Section 2: Chien Yueh-Chih's 360 lu-s Section 3: Her Cherng-Tian's twelve even-tempered lu-s Section 4: Shyun Hsu's twelve "lu" pipes Section 5: Emperor Liang Wu's four "tong" (trichords) and twelve "dyi" (flute) Section 6. Liu Jwo's twelve equi-distant "lu" Section 7. Wang Pu's using "lu-chuen" to produce "lu" Section 8. Wei Han-Chin's lu using the emperor's finger length as measurement unit Section 9. Tsai Yuan-Ting adds the six altered lu-s Section 10. Chu Tsai-Yu's twelve well-tempered lu-s.. 69 Section 11. Emperor Kang Hsi's yueh-lu III. SOME OBSERVATIONS ON THE HISTORY OF TONE GENERATION APPENDIX BIBLIOGRAPH

6 CHAPTER I HISTORY OF MUSIC AND MUSIC THEORY IN ANCIENT CHINA An insterest of the western world in Chinese music has greatly increased during the last several decades, as evidenced by many publications particularly after the World War II. However, the focus has been on the traditional Chinese music--instruments and performance practice, and the aspect of Chinese music theory has largely been ignored by serious western music scholarship. This can perhaps be understood by the fact that much of Chinese writings on music theory, the earliest of which can be traced to remote antiquity of ca. third or fourth century B.C., is in a highly esoteric language, full of symbolic idioms which even the modern Chinese scholars find difficult to decipher. Unlike the history of western music where the main focuses are on music and composers, one overriding aspect of importance in ancient Chinese writing on music history is the theory of tone generation. It might even be said that the study of ancient tone generation systems is the sole concern of the theory of Chinese music, and indeed there are extant numerous treatises and chronicles on this subject--the theory of lu-lu, pitch series). Due to the narrow interest in Chinese music and the linguistic problem associated with such ancient writings, these invaluable historical theoretical sources have been largely unavailable to date to the western scholarship. According to legend, the origin of Chinese music theory was ascribed 1

7 2 to the Emperor Huang-Ti (4 ) who asked the minister Ling Lun ( * ) to cut a bamboo pipe between the nodes to a length of three tsun and nine fen from which the fundamental tone Huang-chung ( 44, yellow bell) was produced. One of the earliest references to the length of Huang-chung pitch and the calculation of the twelve lu-s is recorded in a historical book, The Spring and Autumn of Lu ( ) by Lu Bou-Wei ( ) in the third century B.C. In the chapter "Ancient Music," it states that the fundamental Huang-chung pitch is three tsun and nine fen. However, Hui-Nan-Tzu (5'f 4J} ) records the length of Huang-chung pitch as being nine tsun. Also, the name of the twelve lu-s is first mentioned in the Kao-Yu (II,4 ) in the end of the Chou Dynasty (ca. third B.C.). This account is according to Ling Chou-Chiu ) who referred to all the legendary information in order to answer the questions from Emperor Ching of the Chou Dynasty ( ) regarding the tonal system. The history of Chinese music is recorded mostly on calendars and astrological and topographical chronical treatises. That is, to ancient Chinese, music also represents the relationship between mythological (i.e. spiritual) and universal (i.e. material) realms. Therefore, the earliest theory established during the ancient time was in the context of symbolisms and rituals. Such symbolism relies in part on the philosophical doctrine of Yin-Yang ( 7?, female and male) represented by the numbers two and three. The number two represents earth, while the number three represents heaven. The other system employs five elements (, metal, wood, water, fire and earth) which are related to the

8 is later referred to as the system of san-fen-sun-i (., 3 five tones of the pentatonic scale, kung ($ ), shang ), chieh ( ), chih (fi(), and yu (1 ). This pentatonic scale pattern is equal to the solimization syllables of do-re-mi-sol-la or, transposed, sol-la-do-remi. With the addition of the two other altered tones, the heptatonic scale pattern was adopted in the late Chou Dynasty. This is recorded in Tong-Tien (, Comprehensive Resource) of Tu Yu (L1 ). These scale patterns and the yin-yang dualism provide the basis to explain symbolically the requisites of order and harmony in the universe. The yin-yang dualism, then, became the mathematical formula to calculate pitches, using the ratio of 2:3 or 3:4. This method of tuning adding and subtracting of one third of the length of the preceding tone) which resembles the spiral of fifths, as is in the Pythagorean system of consecutive fifths. This calculation process was first described in the chapter "Dyi-Yuan-Pien" ( ), written by Guan Chih -) in the fourth B.C. Resulting in a chain of ascending fifths and descending fourths, the twelve chromatic tones are derived, representing also the twelve months or the twelve hours. Also, the meticulously calculated standards of ancient Chinese tonal system were then expressed by way of sets of pitched pipes, silk strings, or lithophones, thus representing high levels of technical achievements and the concern for timbre sonorities. As stated above, the essence of standardization of the musical tone system was established in the Chou Dynasty. While the majority of ancient Chinese tone systems divide the octave into twelve lu-s, there were a number of tone-system theories

9 4 ti which went beyond the twelve-pitch octave, such as Ching Fang's sixty lu-s ), Chien Yueh-chih's three hundred and sixty lu-s ( six altered lu-s ), and Tsai Yuan-Ting's adding the ). These were, in essence, all an attempt to discover a point of closure in tone-generation process, at which point an octave equivalent of the Huang-chung pitch could be identified. Various such attempts were made during many dynasties, and none proved to be very successful until the end of the sixteenth century, with a revolutionary theory of twelve equal-tempered lu-s by Chu Tsai- Yu ( ) Although the numbers of tone ih these systems vary, their methods of tonal generation were all essentially based on the process of san-fen-sun-i. Additionally, all these tones have designated names and are symbolically and ritualistically associated with the months and days of the lunar calendar. In the Chin Dynasty ( 4-/,, ca B.C.), the Emperor Chin Shih-Huang burned virtually all the scholarly writings and thus practically destroyed all the ritual and ceremonial systems--including music--established during the Chou Dynasty. However, the ancient ritual music was revived during the Han dynasty (ca. 206 B.C.-211 A.D.). Since then, various foreign musics have entered into China and influenced the stylistic heritage of the traditional Chinese music. In order to accomodate the foreign musical characteristics with the traditional Chinese music style, theorists expanded modal constraints to the traditional tonal system. During the Tang and Song Dynasties ( ), Chinese music developed into a highly sophisticated art.

10 5 This study is a critical translation of selected portions of Huang Ti-Pei's ) Perspectives of Chinese Music ( the portions which deal with the development of the acoustical theory and tonal system in ancient China. Although, there exist several other summary accounts of Chinese music theory of lu, this book is selected due to the fact that the book deals with this subject in a greater detail and in a well organized chronological order. One of the purposes of this study, therefore, is to provide western scholarship with an access to investigate major theories of tonal generation in ancient China, from the Han, ca. B.C A.D. 220) to the Chin Dynasties (, ca. A.D ). These dynasties, although by and large in their attitude, did establish various individual pitch standards and revise the calendrical rituals, all in attempt to bring "harmony between heaven and earth" thus hoping ensure longevity of tiereigning dynasty. The different standards of pitch among various dynasties are explained in the third chapter of this treatise, entitled "The Evolution and Classification of Theory of Lu in Ancient China," This translation, in essence, will provide brief accounts of major literatures in the history of ancient Chinese music theory which have been largely overlooked by western scholars in the normal discourse on the history and development of theoretical thoughts. In addition to its significace to Chinese music history, this study will witness the fact that the theories of the lu or, rather, their counterpart-- the theory of temperamant--has played an important role in the history

11 6 of music theory, both East and West. During the course of this study, many other treatises--both ancient and modern--are consulted in order to clarify some critical matters which may not be quite as concisely stated in this treatise. Prefatory Note: 1) Portions of the text in brackets are editorial additions in order to more accurately convey the meaning of the original text and/or to render the translation more comprehensible. 2) In following the editorial format of the original text, all the figures and tables are not numbered. 3) The treatise included all quotations from ancient sources in its main body of text. This translation, therefore, will follow the format of the original treatise, instead of the format for quotations as in theses and dissertations. These quotations, however, are identified with quotation marks and indentation.

12 CHAPTER II MAJOR LU THEORIES FROM LATE HAN TO CHIN DYNASTIES Section I: Ching Fang's "Chuen" and the Producing of Sixty "Lu-s" In the remote ancient dynasty of Chou (ca B.C.), the yueh-lu0 4,the tonal system of ritual music) is based on [the tonal pattern of] tones and twelve [available] pitches, and that the seventone [scale pattern] is transposable. The tones of the five pitch pipes, Kung ( ), Shang (\J ), Chieh ( ), Chih ( ) and Yu ( ), that are produced by the san-fen-sun-i process can be said to be considerably accurate. [It may be said] that the accuracy [of intervallic relation between these tones] was due to the fact that pitch pipes were first created and, then, the pitch [or intervallic] ratio [between these tones] was established. This, in turn, resulted in the creation of the san-fen-sun-i process, (adding and subtracting of one-third [of the number -- i.e. length of pipe or string -- of the preceding tone]) which became the basis for further tone generation [process], producing pien-kung ) and pien-chih E9V() and, thus, forming the seven-tone scale system. These two additional tones were not "sanctioned" tones [such as the five others] in the scale system, and therefore, these two tones were not employed in ancient classic music. Further extension of this same process produced [other pitches to complete] the twelve lu-s; this [tonal system], however, is not equivalent to the twelve equal-tempered tone system and, therefore, the transposition [of tonal pattern] using these twelve lu-s would 7

13 8 become problematic. [This awkwardness in transposition] can be remedied by employing some special performace techniques, or by eventual acceptance of convention. In the absence of other tonal systems available for comparison, this tonal system, with a few established restrictions regarding transposition, was employed until the Chin ( ) and the Han Dynasties ( ), (ca. 255 B.C.-211 A.D., respectively). Although the Chin Dynasty was relatively short, foreign music had already begun to be imported. And in the Han Dynasty, invasion of foreign music increased which provided a source for comparison [between tonal system of foreign and native musics]. Thereupon, it became apparent that the problem in transposing ancient instrumental music is due to the problem inherent in the [tonal system of] yuehlu. Ching Fang, whose surname is Lee (4 ), and alias Chuen-Ming 9 US), lived in the city of Dun-Chou j3) during the reign of Emperor Han-Yuen4( ). In A.D. 45, he reached a rank of court official as the result of his being known for his filial respect. "Ching Fang" was the pen-name he used for his publication on his lu system. In the previous generations, the problem was recognized that the process of san-fen-sun-i produced the chung-lu which, however, will not produce the [octave equivalent of the] fundamental pitch of Huang-chung ( 4j ), and that this problem was thought to have been caused by the use of bamboo or pipe. Therefore, Ching Fang proposed to use strings instead of pipes and invented the instrument called "chuen" ( ). This Ching Fang's employment of chuen in producing lu's is recorded in the Lee-Lu-Chih of Hou-Han-Shu (

14 9 Treatise on the History of Lu of the History of Late Han Dynasty), "In the Han Yuen empire, minister Ching Fang stated that bamboo pipe should not be used for tuning and, for this reason, he created an instrument called chuen to determine the ratio of lu. The chuen is shaped like a zither (se ), ten feet in length and with thirteen strings stretched over [the sounding body]; [the ten-foot length according to the official measurement system] is equivalent to the traditional measurement of nine feet, thus accomodating the [requirement of] Huang-chung pitch being nine tsun ( ). Under the central string, there are marks which locate the sixty lu-s. Liu Hsin (At) submitted Ching Fang's system to imperial office and thus it became the officially sanctioned standard [for pitch measurement]." These statements describe the shape of chuen. In addition, the department which sanctioned the adoption was probably the Tien- Hou Boo ( 4j ). [The same document further states that,] "The prince Wei Hsuan-Cherng ( ) advised minister Chang Tzar (. ) to inquire on this matter, and Ching Fang responded by stating that, through study, he came under the influence of Chiao Yen-Shou (;, of consecutive generation of sixty lu-s. ) and his process That is, generating

15 10 [all successive] tones upward [by fifth] is by multiplying 2/3 [of the preceding tone length]; generating tones downward is by multiplying 4/3 [of the preceding tone length]. Downward generation from yang ( ) produces yin upward from yin produces yang, and the process terminates at the chung-lu pitch, whereby the twelve lu-s are complete. [Further generating process starting with] chung-lu produces chih-shih ( '), and chih-shih produces chu-mieh (,4 ), thus continuing, the process terminates with the nan-shih (1 ) pitch, thus completing the sixty lu-s." This describes the process which still adheres to but further extends the san-fen-sun-i method [of tone generation]. "In the first year of Yuan-Ho (x,'11, A.D. 84), a court official Yin Tong ( of [the office of] Ho-Chung-Lu ('f 44 ) submitted to the emperor that court officers are not aware of the fact the tuning of "sixty lu-s" is to be checked against the chuen. Therefore, the emperor summoned Yen Chung 4 ) to codify the system and to teach it to prince Hsuan ( ). Prince Hsuan comprehended thoroughly and willed that an academia be established to oversee the tuning of instruments. [However, when] the minister Hong ( ) examined the twelve lu-s pitches and discovered that only two pitches are accurate while four

16 11 are not, and the remaining six pitches could not be made to coincide with any [established] lu pitches. Therefore, prince Hsuan abandoned the proposal [of establishing and overseeing the office]. Henceforth, all the lu theorists were unable to determine the tuning of chuen's strings, but the office of Ho-Boo, not knowing [this dilemma,] continued to employ [chuen]." The above narrative suggests that, during this period, the correct tuning system was already lost. Ching Fang's use of strings to produce the lu series is still based on the process of san-fen-sun-i; he only extended the process from the last pitch in the series -- chung-lu -- to arrive at additional forty-eight pitches and, therefore, the total number of lu-s became sixty. However, these new additional forty-eight lu-s were to be within an octave gamut. In other words, an octave contains [or, is divisible into] sixty tones. Using the measurement in the treatise Hui-Nan-Tzu ( y$j- ) that chung-lu has [the length unit] of 60, and, applying this to Ching Fang's theory, the lu series can be expressed as below: 60 x (1 + 1/3) = 80 chung-lu produces chih-shih (chih-shih's pitch is higher than Huang-chung) 80 x (1-1/3) = 53.1/3 or chih-shih produces chu-mieh (the pitch of chu-mieh is lower than i-tse)

17 12 f1 If strings are used to replace pipes in producing the lu-s, the number can simply by multiplied by ten. The choice of this author's in using the Huai-Nan-Tzu's measurement unit is due to the fact that the pitch of chung-lu is given as 60 units and thus proves convenient in the calculation of subsequent pitches. According to the Lu-Lee Chih of Hou-Han-Shu, the name of Ching Fang's sixty lu-s are listed below: The original [twelve] pitches: Huang-chung ling-chung tai-tisu nan-lu ku-si ying-chung jui-ping ta-lu i-tse chai-chung wu-yi chung-lu The new pitches: chih-shih chieh-kung sheng-pien kai-shih ping-sheng kuei-chi lee-kuang tsu-chia fen-tung wei-mao chih-shih cheng-nan chih-wei chu-mieh' p ien-hs ien fen-fou pi-yen ann-tu lu-shih ling-yin ling-chi kuei-chia hs ing-shih shao-chu chi-pao fou-yu shih-hs i chih-nei chieh-hsing nan-chung chu-chi wei-yu chu-nan nei-fu sui-shih chin-shih fen-ling wu-ying hsing-chin 1 The exact implication of this "multiplication by ten" is not clear. The multiplication will not alter the intervallic relation between lu pitches but will greatly affect the register of the pitch series.

18 13 wei-han i-hsing se-yu chien-shih wei-chih pie-lu nai-sou fen-wu nan-shih (These pitches are listed in the order of successive generation of sixty pitches [to be read from left to right].) The above sixty lu-s are contained within an octave and therefore not all are suitable for practical use. This increase in the number of Lu-Lu (i.e. lu pitches) may be considered as an attempt to coincide with the number of the sixty-year cycle of Chinese calendrical generation Chai-Chih (f-} ). [Because it lacks practical application, the use of Ching Fang's sixty lu-s system] gradually declined after a century. It is recorded that, by the sixth year of Hsi-Ping ) during the reign of Emperor Ling ) of the East Han dynasty ( A.D. 177), chuen as [a musical] instrument was no longer in use and, it goes without saying, it is no longer extant. According to the description in the Hou-Han-Shu there is a drawing of the [chuen]. Since there are no clear markings under the central string, the proportions can not be indicated.

19 14 The drawing below is the present author's attempt at marking each position of the [lu], based on the proportion of frets on ancient Chinese zither (chin, ). Accordingly, on the upper side of the zither there are thirteen frets, with the seventh fret in the center.2 A marking is placed midway between the head [of the instrument] (yueh-shen,,i ) and the tail (long-yin, - ). The pitch thus produced is an octave higher than the san-yin (,open string). (tail I Do M Sol La Do i-i_ ~ -. ~I.i -~ I-. **-m~* - -- r~ I LS ; he (head) Chuen contains thirteen strings, with the central string not being used. By assigning each of the other twelve strings to pitches in the lu-lu series, the original twelve lu-s are properly distributed, and the interval between two adjacent strings is a semitone. From the seventh fret toward the head (in the direction of the zither's 2 This reading is assumed in the context of this passage. The original text has the word for string.

20 15 base), there [could] still be six more frets, and the pitch becomes higher as the fret position moves closer to the chin's head. 3 [However] the chuen is designed to measure the lu and, therefore, there is no need for the gamut of these tones to exceed an octave. Thus, from the seventh fret toward the head there is no need for additional frets. The location of the thirteenth fret on ancient chin is marked at 1/8 point of the whole length. This stopped tone is named "shang". In proper sequence, the twelfth fret is set at 1/6 of the whole length; the eleventh is located at the 1/5 position; the tenth fret is situated at the 1/4 position; the ninth fret is set at the 1/3 position; the eighth fret is set at the 2/5 position; the seventh fret is place at the 1/2 position. In producing this drawing, markings are indicated according to the proportional divisions for producing stopped tones, thereby these markings will coincide exactly with the original standard pitch series of "kungshang" ( ) [pentatonic] scale pattern. Tones on chin are not produced by pressing strings on the fret, but, rather, at certain subdivided points between two adjacent frets; the space between adjacent frets contains ten [such] "fen" points [for fingering]. These points are not marked on the chin itself; however, they can be so marked on the chuen: are marked according to the distance between [That is,] these "fen" the two particular adjacent frets and not in terms of specific measurement. Since the positions 3 In order to make the reading of this paragraph more easily comprehendable, order of sentences has been altered.

21 16 of chin's frets are arranged based on the process of san-fen-sun-i, the present author proposes to apply the system of fret positioning on chin to mark the "fen" on chuen. It has been two thousand years since the day of Ching Fang. And later generations realized that his use of chuen in establishing lu-s contributed little practical value to the system of lu-lu. In addition, Ching Fang's chuen system was quickly forgotten by later generations and became totally unknown about a hundred years after him. However, many treatises on music after the Han dynasty continued to record Ching Fang's system. What, then, is the reason [for this continuous reference]? It is probably because of the fact that Ching Fang was the first to use the string as a means of producing lu. Therefore, although his achievement was frequently criticized by later [writers], his contribution can not be totally ignored. The age of Ching Fang preceded that of Emperor Wu of the Han Dynasty by less than a hundred years. Even before the decline of the Han Dynasty, the foreign music (Mongolian music, already entered China and became increasingly popular. had On one hand, the two distinctly different musical systems influenced and accomodated each other; on the other hand, the rulers of this period, due to their religious beliefs and superstitions, applied the yin-yang calendrical numerology to all things [including music]. It is perhaps understandable, therefore, that, even to this day, there are those who subscribe to the [calendrical ramification attached to] chuen and tt the sixty lu-s [see preceding paragraph]. Further study into the

22 17 validy of the chuen system may perhaps be undertaken by establishing a special research office.

23 Section II: t, Chien Yueh Chih's 360 Lu-s In the chapter "History of Lu" ( v ) of the Sui Dynasty Chronical ( ) it is stated that "during the age of Yuan-Chia (ca. 438 A.D.) of the Sung Dynasty, the minister Chien Yueh-Chih extended beyond the last pitch of Ching Fang's [sixty lu-s], that is the pitch non-shih. He extended to the 360th lu-s, ending with the pitch named ann-yun ( ), the length for which is slightly less than four tsun and four fen. Thus, totaled, there are 360 lu-s, each pitch assigned [symbolically ] to each of the [360 calendar] days. The order of each lu follows the succession of kung-chih ($$ )[i.e. the circle of fifths]." "Nan-shih" is produced by Ching Fang's chuen. The name [nanshih] is given to the pitch which was arrived at the sixtieth [generation of tone via cycle of fifth] on the string, which, however, did not produce the [equivalent of the] origin (-al tone) [i.e., the fundamental pitch of Huang-chung] (the number of Huang-chung is eighty-one units). Chien Yueh-Chih made three hundred additional generative calculations from the nan-shih pitch and thus the total number including Ching Fang's lu is 360. The last lu [of Chien Yueh- Chih] is named ann-yun which [actually] has a lu-pipe length of slightly more than four tsun and four fen. [The discrepancy between the two -- the length being slightly more or less than four tsun and four 18

24 19 fen] is due to the fact that string was used to produce the lu, and the measurement unit for which is chih (,g). And the length slightly less than "four tsun and four fen" is [adopted to express the length of] the lu-pipe. It may be assumed, therefore, that, in following Ching Fang's system in which the calculation employed string length in expressing the lu, the number was applied to the lu-pipe and was [directly] recorded in the Sui-Shu. On this, there is no way of ascertaining. It can only be said that Ching Fang's system predated that of Chien Yueh-Chih's by five hundred years and historical chronicals only recorded Ching Fang's system a hundred years after his death, stating that the process of chuen had already been lost. Therefore, it appears more probable that Chien Yueh-Chih's lu system was based on the lu-pipe [instead of string]. Chien Yueh-Chih's 360 lu-s also employed the process of sanfen-sun-i. Therefore, it can be asserted that [Chien Yueh-Chih's lu] follows the nan-shih of Ching Fang. It can further be asserted that Chien Yueh-Chih's [360] lu pitches are all contained within an octave gamut. Because the last pitch arrive -- the ann-yun pitch -- has the length slightly less than four tsun and four fen, the length of ann-yun pitch is not sufficient enough to be the octave quivalent of Huang-chung. Therefore, [Chien Yueh-Chih's lu system] can not be applied in musical practice. According to [recent writings of] Wang Kuang-Chi (L), this system has the only significance of coinciding with the number of [calendrical] days. With regards to the names of these 360 lu-s, detailed information can be found

25 20 in the chapter "History of Lu" referred to earlier, and thus will be omitted here.

26 Section III: Her Cherng-Tian Twelve Even-Tempered Lu Her Cherng-Tian's system of tone generation, as recorded in the Lu-Lee-Chih of Sui-Shu (, Treatise on The History of Lu of The History of Sui Dynasty) reads as follows: "The san-fen-sun-i is a simple system used by the ancients. It can be likened to the ancient Chou calender of dividing a year into 360.1/4 portions. However, Ching Fang failed to comprehend the essence of this and, instead, realized into sixty portions. Furthermore, Her Cherng-Tian devised a new ratio that would allow the return of [the octave equivalent of] the fundamental pitch Huang-chung. Therefore, the twelve pitch series is complete in its circular system with no distortion. The length of Huang-chung is nine tsun (,; 9 tsun = ca. 27cm.), tai-tisu is 8.02 tsun; ling-chung is 6.01 tsun; and ying-chung is tsun. (The next ratio arrived from chung-lu is , which [if calculation is] reversed, will produce the fundamental.)" However, Sui-Shu gives only the measurements of four pitch pipes of Her Cherng-Tian which are: Huang-chung, tai-tisu, ling-chung and ying-chung. [Recently] Wang Kung-Chi also examined Lu-Chih-Hsu ( 21

27 22,f), the seventeenth volume of Song-Shu (, The History of Song Dynasty), and reported the calculation of pitch series according to this new system. Although he did not mention that the calculation is based on that of Her Cherng-Tian, the length of each pitch pipe is the same as the measurement of the four pitches mentioned in the Sui-Shu. In addition, Her Cherng-Tian established the Yuan-Chia calender ) for Emperor Wu of the Song Dynasty( ), thus there seems little doubt that the lengths of twelve pitch pipes were also produced by Her Cherng-Tian. Song-Shu, written by Shen Yueh ( t 9 ) of the Liang Dynasty (A.D ), is a highly scholarly work, containing the author's special personal opinions. The following chart gives the lengths of all pitch pipes as recorded in the Lu-Chih-Hsu of Song-Shu, expressed in the arabic numbers for easier comparison. Pitch Name Order of Length of Length of Generation Old Pitches New Pitches Huang-chung tsun =9.00 tsun ling-chung =6.01 tai-tiau =8.02 nan-lu =5.36 ku-si =7.15

28 23 ying-ching =4.79 jui-ping =6.38 ta-lu =8.49 i-tse chai-chung =7.58 wu-i 11 4, chung-lu =6.77 Huang-chung =9.00 From this chart, it can be seen that, starting from ling-chung, the length of each successive pitch increases by one lee, ca cm.). Accordingly, Huang-chung as derived from chung-lu will produce [the octave equivalent of] the fundamental pitch. This new pitch series, arranged in the order of decreasing length, can be shown as in the following table. (see next page)

29 24 Pitch Name Length of Difference Between Two Difference Pitch Pipe Adjacent Pitches In length Old New Old New Pitch Pitch Pitch Pitch Huang-chung ta-lu tai-tiau chai-chung ku-si chung-lu jui-ping ling-chung i-tse nan-lu wu-i ying-chung luang-chung *. I I I I

30 25 By examining the preceding table, one observes that, for each successively higher tone, the [length of] pitch pipe in the new series is seven lee shorter than the [corresponding] pipe in the old series. Or, for each successively lower tone, pitch pipe in the new series is five lee longer than the old. The length of the pitch pipe is in inverse proportion to its pitch register; that is, the longer the pipe the lower the pitch. Therefore, when the pipe length of [each] pitch is reduced by seven lee, it produces a higher pitch [of the successive tone in the series.] Through such an "even-out" process, the old, unequaltempered tone series [is being modified to] resemble closely that of the modern, equal-tempered tone series. Her Cherng-Tian's device should be regarded as a significant step in the development of Chinese tone system. The formulation of Her Cherng-Tian's new tone series, [though] based on the san-fen-sun-i system, is based on the formula of adding one lee to each successive tone [after the fundamental]. The principle is concise enough and the process is easily realized. It not only allows the return of the fundamental (its octave equivalent) but also conforms to some extent to the requirement of even-tempered [length]. Wang Kung-Chi regards the lu calculation using string length as a significant advancement in the history of Chinese music theory. Her Cherng-Tian's system [of equal-tempered tones series] predated the western twelve well-tempered tone system by ca years. Furthermore, the lengths of the new tone series as recorded in Sui-Shu and Song-Shu are all expressed in terms of unit tsun or smaller, and never chih or larger

31 26 and, therefore, is a system which did not rely on a string length. It seems natural that, since Her Cherng-tian did not rely on Ching Fang's system, the former chose not to employ the same tool (i.e. pipes vs. string length) [for tone generation].

32 it Section IV: Shyun Hsu's Twelve "Lull Pipes ( /, ), wo livedi g, Shyun Hsu (9 ), alias Kung-Tseng ( ), who lived in Yingg g Yin (j W ) of the Six Dynasties, was a learned scholar in Lu-Lu. 'I His tuning system using bamboo pipes in identifying lu is recorded in the Lu-Lee-Chih, of the Jin-Shu (, The History of Jin dynasty). It reads, [in part,] as follows: the court of Emperor Jin Wu ( "Shyun Hsu, who was an officier in 4) in 275 A.D., created twelve pipes based on the system of twelve lu-s, and commanded it to be adopted by the musical office Tai-Yueh (, a goverment association for collecting music). Shu Yang-Yuan (?4. k ) of the Chin Dynasty wrote the treatise Shyun Hsu Dyi-L-Tu-Chu The Pictorical Annotation of the Lu Pipes of Shyun Hsu), and further extended Shyun Hsu's theory. It states that Shyun Hsu created a flute [the hole location of which] was derived from the placement of the zither's frets. This resulted in unevenly placed hole positions and thus differed from the commonly used flute. The length of the common flute is two chih and four tsun f1 [approximately 2.2/5 feet]; however, the lu flutes may measure up to four feet. I Although the uneven distances of holes on the lu flutes enable them to be tuned to [other] musical instruments, it is doubtful whether these pipes could be used in musical performance along with other instruments. It also states that Shyun Hsu's flutes are much 27

33 28 like [the Ching Fang chuen]. The shape of chuen closely resembles that of se but has thirteen strings, thus it is called chuen [for differentiation]. The tuning flute [on the other hand], has seven holes, as does the common flute, thus it is simply referred to as a flute. Similar statements are found in She-Lu Kau (f ), by Hsu Hao (4 ). In discussing the [lu] pipes, Shyun Hsu rejected the flute with six evenly spaced holes. Shyun Hsu thereby produced twelve flutes with the hole positions altered. [The relocation of holes created certain problems:] Two holes are closely placed [nearly] side by side and can be stopped with either one or two fingers. Where holes are too widely spaced, fingers could not extend far enough to stop them properly. Even if tones were concordant [with one another], the [structure of the instrument] proved to be of little use; in actuality, however, no one tone proved to be harmonious [with one another]. Besides these books, there are other books dealing with Shyun Hsu's lu flutes; these include the Jin-Tai-Shih-Dyi-Kuan-Mou ( ) by Ling Ting-Kan ( ) of the Chin Dynasty, and the Tai-Lu ( j) by Gee Chung-Ming ( ) of the Ming Dynasty (4 ). All the criticism on Shyun Hsu's lu-flutes by his contemporaries as being unfit for performance due to the neven distances of holes is in reference to the matter of transposition [of ritual melodies]. Since there are twelve flutes and each flute is capable of producing [all tones in a given] pitch series (i.e. a key or a mode), this set [of twelve flutes] resembles the modern flute-set. The question as to why the ancients were adverse to using such a set of flutes -- the

34 29 matter of measurement system which gives the length of some flutes as up to four feet in length -- should be considered as worthy of further investigation. In the antiquity, flute was called "dyi" ) which was used in the performance of Ya-Yueh (, ritual music), and, according to legend, it was the instrument which was created by the minister Ling Lun of the court of Emperor Huang Ti (the legendary first emperor of China). However, the modern flute -- the type with six membraned holes -- is the creation of Cho Chung (1..4 ) during the reign of Emperor Han Wu4( y, B.C. 140). The most prevalent flute today is kun-dyi ($k ), the type with the fundamental G (i.e. all holes are stopped) and is also commonly called hsiao-kung-dyi (/lt). Due to the fact that this is the main melodic instrument in the performance of kung music ( 9 ), this particular type of flute is referred to when the [generic] term "flute" is used. The name [of another type of flute] hsiao-kung (/d \. ) actually refers to a mode (in D) of secular music. The fundamental pitch of this instrument is called her ('p) (equivalent to sol in the [pentatonic] solmization scale pattern), and is equivalent to pitch A of the western tone system. According to the Lu-Lu-Cheng-I (4 --, An Interpretation On The Lu Series) written in 1713, the fifty-second year of the Emperor Kang Hsi ( ) of the Chin Dynasty, there are two other types of flutes, called chung-lu-dyi (/ ) and ku-sidyi ( 7 ). The diameter of the chung-lu-dyi is chih, and the distance from mouth hole to the [longer end of the flute is chih, and was used in [the performance of music of] yin month(s)

35 30 (Pk ). The length of ku-si-dyi is [slightly] longer than chunglu-dyi, being chih, with the diameter chih, and was used in [the music of] the yang month(s) ( f). The difference between the two flutes is a semitone, which may be what is inferred to as the difference between the "tuning flute"4 and the "common flute". The lengths and sizes of these two flutes are [actually] nearly identical. The following illustrate the prevalent kung-dyi. From the above illustration, it is to be noted that, while the length of the entire flute is 68 cm., its sound column is actually only 34 cm. long. Previously, it has been mentioned that the lu flute of Shyun Hsu described by Shu Yanh-Yuen of the Chin Dynasty may measure up to four feet. [In the light of above discussion, it may be said that,] besides the matter of measurement system, that of the length from the mouth hole to the [longer] end of the flute requires further and deliberate study. As described in treatises, the structure [of the 4 This term actually means "melodic flute". However, tuning flute is adopted, due to the fact that the function of this instrument appears to be primarily for tuning or establishing a pitch standard.

36 31 flute in terms of number of] holes on Shyun Hsu's tuning flute is the same as that on the common flute (i.e. with a simple mouth hole and six other finger holes). The difference between the two flutes is the fact that, as compared to that on the common flute, the distance of the finger holes on the tuning flute is irregular. The fact that this [tuning] flute is regarded as less useful is in reference to this irregularity of distance between holes, and that such a particular [tuning] flute is suitable in playing only [note of a] certain [Fa] modal pattern. That is, a change in modality [in music] necessitates change from one flute to another. [The common flute, on the other hand,] with its more even-distant hole positions, is capable of playing various modal patterns, though only with employment of special techniques and somewhat awkwardly. With regard to the remarks of Hsu Hao concerning the difficulty of fingering, [it should be mentioned that] ancient players used the midsection of the fingers (also called finger waist) in stopping the holes and therefore resulting in the more restricted finger movement; instead, an improved finger motion can be obtained if the end section of fingers [the ball of fingers] is used in covering holes, as it will allow a longer reach. It goes without saying that a matter such as this is the choice between [adoption of] special technique and [following of] established custom. Even in Korea today, the longer flute ta-ling (K ) has remained in common usage, in spite of its longer length and the fact that the distance between holes are wider than that on kun-dyi. There indeed have been many criticisms on Shyun Hsu's tuning-

37 32 flutes with its six-holes structure and thus problematic for performance. From the contemporary view point, however, such a structure is in accordance with the requirement of twelve tempered-tone system. Recently, the "set flutes" ( ) have become prevalent. In each set the position of holes on each flute differs from other flutes, and some even assume that this may be an adaptation of Shyun Hsu's tuning-flute theory. Each of Shyun Hsu's flute represents one [particular] lu-lu series, and the uneven hole positions on flute(s) is recorded in many treatises. Since ancient flutes are made [or tuned] according to the current tone system of the day, and since the ancient tone system awaits further study, it can not be unequivocably said that the [modern] set flutes are [equal to] Shyun Hsu's tuning-flutes. However, it is undeniable that the method of Shyun's [improved] hole position is witnessing a revival today. [The history of] set flute is two thousand years old. Therefore, anyone who remarks that the contemporary set flute is a new invention or a new improvement ought to study further the historical development of lu instruments.

38 Section V: Emperor Liang Wu's Four "Tong-s" (Trichord)and Twelve "Dyi-s" (Flute) The Yin-Yueh-Chih (, Chronicle of Music) in the Sui-Shu records the following narrative: "Emperor Liang Wu'(, A.D. 502), [being] skilled in the [knowledge] of Lu-bell ('#4), gave a decree to collect information on ancient music. Having gained nothing, he took upon himself [the task of] establishing a system of music. He also created four instruments named "tong" (, similarly constructed as a resonant box). Its width is nine tsun; length is nine chih; height one tsun and two fen. Each of these tong-s has three strings. The first tong is called yun-ying-tong ({~ ) which includes ying-chung string ( 4 ), Huangchung string ( ) and ta-lu string ( 4 ). The second is named ching-yang tong ( ) which contains tai-tisu string ), chai-chung string and ku-si string ( t $). The third is chu-ming tong ) which has chung-lu g) stringw(icha jui-ping string ( J2 k ) and ling-chung string ( 4 ). The fourth is pai-tsang tong ( ) which possesses i-tse string ( nan-lu string ( 3 ) and wu-i string 33

39 34 ( 14t). As these tong-s are precisely correct [in their pitch standards] and in perfect accordance with the [ethos of] lunar calender (i.e. cosmology), each of these in turn allows transposition [of music according to the requisites of ethos]." In Tong-Tien written by Tu Yu of the Tang Dynasty (812 A.D.), it is recorded that the four tong-s created by emperor Ling Wu in 502 A.D. have the thickness [as indicated by the number of silk contained in a string] and the length of strings as shown in the following table. Name of Tong Number of Silk in Length of String Each String yung-ying ying-chung 140 thickness 4.74 chih huang-chung it ta-lu ching-yang tai-tisu chai-chung ku-si chu-ming chung-lu jui-ping ling-chung

40 35 pai-tsang i-tse nan-lu wu-i Although there is no description of the shape of tong, the [descriptive] term show sheng., reverberative sound) and hsuan sheng (, declamatory sound) imply the [construction of the] instrument to be similar to a resonant box. Also, since it has the nut (yueh, ) [as in all stringed instruments] and since strings are of different length, adjustable with [moveable] bridges, it also resembles the zither (s,: ; cheng, ). As the length and the thickness of strings are understood, it is not difficult to reconstruct the instrument. With regarded to the lengths and functions of the twelve flutes, Tong-Tien also gives the following account: "The length of Huang-chung flute is three chih eight tsun; the ta-lu flute is three chih six tsun; the tai-tisu flute is three chih four tsun, the chai-chung flute is three chih two tsun; the ku-si flute is three chih one tsun; the chung-lu flute is two chih nine tsun; the jui-ping flute is two chih seven tsun; the ling-chung flute is two chih seven tsun; the i-tse flute is two chih six tsun; the

41 36 I1 nan-lu flute is two chih five tsun; the wu-yi flute is two chih four tsun; ying-chung flute is two chih three tsun. The pitches of tong are represented by the tones on these flutes, and the tones [produced on tong] are in accordance with the pitch [standards] of these flutes, and these tones are [in turn] in accordance with the pitch [standards] produced on ancient gold [or bronze] bells and lithophone [i.e. jade instrument] as well as bells of the Chou Dynasty. [The tone system established by the dyi and tong] serves as the standard whereby music of eight tones [i.e. of different instrumental timbre] employing seven tones [i.e. heptatonic scale] will be harmonious." The next illustration gives the comparision of lengths of the twelve flutes based on the above statements: Note 1: The unit chih is that which was used during the reign of Emperor Wu of the Liang Dynasty. [i.e. the unit length of the chih differs from the contemporary chih length.] Note 2: The exact diameter and the length of flute and the placement of the holes need to be determined further through additional research.

42 37 Huang-Chung I Ta-Lu I I Tai-Tisu Chia-Chung Ku-Si it Chung-Lu Jui-Ping i i i. i _- I Ling-Chung I-Tse it Nan-Lu Wu-i Ying-Chung i i il i Emperor Liang Wu established the twelve flutes in order to represent the pitches of the tong as well as to allow transposition of music. The tonal system of the tong differs from that of the "chuen" [i.e. of Ching Fang; cf. Section I], as the tong pitches do not constitute any particular scale structure and therefore, require these flutes to represent [their tonal system]. The [tonal] system, through these twelve flutes, allows transpositional possibility and thus meeting the [ritual] requisites. The ancients used lu-pipes to set standard for tuning bronze bells and lithophones as well as the bamboo flutes. Various questions still linger, however: whether instruments were tuned [according to pitch standards set by] the string instruments; or that Emperor Liang Wu adopted the system of Ching Fang and Shyun Hsu?

43 38 Since the Chin and Han dynasties (4<''), foreign music, particularly that of northern region (Mongolian music) entered China. This continued until the Six dynasties, when Jin-Ling (4, presently Nan-Jing, Ji\ ) became the center of musical activity, and music became a commodity in the civic luxuries and festivities, chief among them was dance music solely for entertainment purposes. Since the secular festive and entertainment music emphasize decadent suaveness and variation, music [began to] incorporate various changes in the melody and rhythm. The instrument of hu-yueh proved to be more adept in performing music with such trendy characteristics than in performing the ancient music. The closer observations, however, indicate that there are no significant differences between the musics [and instruments] of ancient time and the new foreign, and the two [variously different musical characteristics] canbe blended harmoniously and equally appreciated. It must be noted, however, that the [tonal series of the] new music could not be fully justified on the basis of the traditional method of san-fen-sun-i (i.e. process of tone generation). Ching Fang is recognized as being the first to use string length instead of pipe length to identify [new] lu, and Chien Yueh-Chih continued with this adopted process, arriving at more pitches than are necessary in the practice of music performance. Her Cherng- Tian employed additive [length] process [in tone generation] while Shyun Hsu redistributed the holes of twelve-flutes in a way not reflective of the structure of the "common flute". All these new systems were an attempt at correcting inadequate [tonal system] of

44 39 the ancient time. The same can be said of Liang Wu's four tong-s and twelve-flutes. However, every theoretical system is found on the principle of san-fen-sun-i, and, therefore any attempt at modifying this sacro sanct system was met with criticism from scholars who subscribed to the tradition. This can be seen by the fact that Emperor Liang Wu's system is not recorded in the Liang-Shu ($, The History of Liang Dynasty) but only appears later in the writings during the Tang Dynasty (ja ). As the popular music (4 ) prevailed in the Tang Dynasty, the ancient ya-yueh began to decline. Even the emperor and all the court officers also preferred the new popular music. This popular music also employed a great number of foreign instruments, and, thus, led to the popularization of music [i.e. music with foreign elements] in general. As, Wang Kung-Chi observed: "It goes to prove that no musical system is a matter of course and of invariant statute. The established thought also can not escape from being affected and altered." It is only known that the length of the emperor Liang Wu's four tong-s is nine chih; its width is nine tsun; its height is one tsun and two fen, and that every tong contains strings of different lengths, each made from several entwined strands of silk. The description of twelve-flutes are even more succinct: only that of lengths and the function representing pitches of the tong are to be found. In studying Emperor Liang Wu's four tong-s and twelve-flutes, it will be easier to scrutinize the pitches of the strings than to examine the flutes. Wang Kuang-Chi records the formula of identifying

45 40 pitches from string, based on that of Chwolson as found in his Die Lehre vom Schall. This formula may prove helpful [in identifying] the pitches of each string of the four tong-s. The following explains the formula: N = G P II L N represents the frequency of vibration and, thus, the pitch. For instance: A = 440 Hz. G represents the gravitational acceleration which is 981 cm/sec2 Now it is called gravitation which is 980 cm/sec2 P represents the tensile force which is carrying strength of a string. The tension can be obtained by attaching a weight at the end of a string. The measure unit is by gram. For instance: the tensile force of a A string on a violin is 6870 cm/sec2 II represents the weight of a string which is equal to the circumference/diameter ratio (75 ) multiplied by its radius (R2), its length ( L ) and the density of the string ( D ). Therefore II = x R x L x D L represents the length of the string. For instance, the length of Huang-chung string is nine chih. Accordingly, the formula can be expressed as follows:

46 41 Pitch of = 981xtensile force of the string String 2N R 2 x L x D x The length of the string Therefore, one can first obtain the pitches of twelve-strings of the tong and then the pitches of the twelve-flutes. However, the following questions still remain: 1. What measurement system was adopted during the reign of Emperor Liang Wu in [producing] the music system? 2. Which kind of silk was used in making the strings of tong? 3. In Chwolson's formula, the pitch calculation is of metal strings. Could this formula be equally applied to silk strings? As an additional item of information, it is reported recently that Yang Yin-Lui ( ) has succeeded in calculating the Huang-chung pitch of the series of Liang Wu, which is said to be equivalent to the modern western G, with the frequency of Hz.

47 Section VI: Liu Jwo's Twelve Equi-Distant "Lu" Liu Jwo, alias Shih-Yuen ( ), lived in Hs in-du (j3) during the reign of emperor Sui-Wei ( 4 ). He was not only a well known Confucian scholar but also had researched into [the theory of] lu-lu. According to the Lu-Lee Chih of the Sui-Shu, Liu Jwo (J ) attained the rank of Tong-Kung ( ) in A.D He also dissertated on the aspects of Chang-Chou-Shyun-Lee (v ) and lu-lu. His main thesis is as follows: I' "Tone is the primary principle of music, and lu establishes [the system of] musical tone. If the tones are not [set according to] the lu, they will not become harmonious (or concordant with each other). [Furthermore,] pitches are [set according to] bell. fl The lu series ends with chung-lu and return to [the octave equivalent of] Huang-chung. However, as the older system [of tone calculation] was not precisely accurate, the last (tone -- i.e. chung-lu) did not return to the fundamental pitch Huang-chung. Therefore, Ching Fang of the Han Dynasty '9 futilely [extended the series to] the sixtieth lu and Chien '9 Yueh-Chih of the Song Dynasty to the 360 lu [all attempting to reach the point of return]. [The difficulty lies in 42

48 43 the fact that] it is not certain what measurement system [these theories] used in the pitch series calculation, and also that it is not always clear whether [the measurement of tone] was based on the string [length] or pipe [length/diameter]. Liu Jwo therefore formulated a new system. That is, the length of the fundamental pitch is set as sixty three (units). The pitch difference of each successive pitch in the series is obtained by reduction of three fen and, in addition, seven is used as divisive number of the measurement unit tsun of each pipe. Therefore, the length of Huang-chung would be nine tsun (i.e. 63 = 7 = 9); that of tai-tisu is 8.14 tsun, ling-chung six tsun and yingchung /7 tsun." According to this process, Liu Jwo's system is based on the cardinal number of 63, which, divided by seven, would give the Huangchung (unit) of nine tsun. All subsequent pitches from ta-lu, areobtained by subtracting three fen and dividing by seven, as can be shown below: Length of ta-lu Length of tai-tisu (63-3)-7= /7 2nd scale degree (63-6)-7= /7 3rd scale degree Length of ling-chung (63-21)+7=6.00 8th scale degree Length of ying-chung (63-33)-7= /7 12th scale degree

49 44 The chart given below shows the lengths of Liu Jwo's pitch pipes according to his system, compared with the lengths of pitch pipes of the older tone system. Also given is a comparison of differences between adjacent tones in Her Cherng-Tian's pitch series and that of Liu Jwo. (This chart is excerpted from History of Chinese Music by Wang Kuang-Chi). Pitch Name Length of Liu Jwo's Length of Length between Two Pitches Old Pitch Adjacent Pitches Liu Jwo's Her Cherng- Tian's Huang-chung 63+7=9.00 tsun = 9.00 ta-lu (63-3): 7=8.57 > 8.42 tai-tisu (63-6)+7=8.14 >8.00 chai-chung (63-9)+7=7.71 >7.49 ku-si (63-12)+7=7.28 >7.11 chung-lu (63-15):7=6.85 > 6.66 jiu-ping (63-18);7=6.42 >6.32 ling-chung (63-21);7=6.00 = fen fen i-tse (63-2L 7=5.57 <

50 45 nan-lu (63-27)=7=5.14 <5.33 wu- i (63-30)+7=4.71 < 4.99 ying-chung (63-33):7=4.28 < I, half-lu of Han-cungf (63-36)-7=3.85 <4.44 Huang-chung From this chart, it is to be observed that the length of Liu Jwo's Huang-chung is identical with that of the older system. From 'I ta-lu, however, the pitch difference between each successively ascending tone in Liu Jwo's system is proportionately greater than that in the older pitch system. The eighth tone ling-chung in Liu Jwo's system is identical with that in the old system. All the lengths of subsequent (higher) pitches [in Liu Jwo's system] become shorter than that of the older system. In other words, the pitches from ta-lu to jiu-ping 'I in Liu Jwo's system are lower than that in the old system while, from I, i-tse to the tone half-lu [higher than] Huang-chung, the pitches are higher. In addition, the difference between two adjacent pitches in Liu 'I Jwo's lu series is always the same, being 0.43 tsun. Hence, it is called "equi-distant". In contrast, none of the difference between any adjacent pitches in Her Cherng-Tian's series is the same -- the higher the pitches the smaller the difference. This principle of equidistant tone distribution is particularly observable in the placement

51 46 of frets on a stringed instrument. Pi-pa is an example (see illustration). first fret (shiang) irst fret (ping) Other instruments [with the same principle of fret position] are chingching ) and yueh-ching ( ), western equivalence of guitars and mandolins. Liu Jwo's lu series where differences between each adjacent tones are the same does not agree with the principle of acoustical science. One would discover that tones in this equi-distant system do not agree with that in the modern equal-tempered system.

52 47 However, Liu Jwo's system was in vogue during his generation. His system could possibly have been applied to the six-holes hsiao ( ) and dyi (flute). It should be noted that other instruments such as the kun-dyi, tong-hsiao (2/]) and chiang (Z ) which are used in ritual music, or the "secular" flutes as well as ensemble instruments such as so-na (44w) and chi-na (ji3), the placements of fingerholes are equal distances from one another. equal, the difference is negligibly small. Where the distance is not This could be seen as one of the reasons for the longevity of his system surviving into later. generations.

53 Section VII: Weang Pu's From "Lu-Chuen" to Produce "Lu" III Wang Pu, who lived during the reign of the emperor Shing-Tzung (- ) of the Late Chou (4 I ), one of the Five Dynasties ( l ) of the Late Tang ( ), attained the office of prime minister, whose duty is to transmit imperial edicts. According to the Biography of Wang Pu of The History of Five Dynasties, "In the sixth year of Hsien-Teh (01, A.D. 595), Emperor Shih-Tzung of the Chou Dynasty ordered Wang Pu to examine and to reestablish the ritual music. Wang Pu responded by saying that accurate tone could not be obtained from the twelve pitch-pipes playing together. Thereby, relying on the "lu-chuen"5 ( R ) of Ching Fang, he [established the tonal system] using thirteen strings of nine chih in length and placing bridges under these strings in order to mark the lengths of [corresponding] pitch pipes. [He adopted] the heptatonic scale pattern and thus accomplished the [task of reformulating] ritual music." From the above, it is clear that Wang Pu adopted Ching Fang's system of using string [length proportion] to produce tonal system. However, the difference is that Wang Pu's lu-chuen with bridges and 5 Lu-chuen: string instrument for acoustical measurement of tone. 48

54 49 shape as described resembles the ancient stringed instrument, the zither (cheng). bridges. The ancient cheng is nine chih in length and does not have Such cheng is still in use in Japan and Korea. Descriptions of chuen in greater details are found in Yueh-Chih ( Chronicle Music) of Wu-Tai-Shih ( i4fk, The History of Five Dynasties) as seen in the following quotes: Huang Ti played the pipe which is nine chih in length and produced the Huang-chung pitch, thus [laid the basic material for the] beginning of music. The pitch produced with half its (pipe) length is that an octave higher, and the pitch produced with double its (pipe) length is that an octave lower. Adding and subtracting of one-third (of the pipe length generates) successive tones. This process of permutation continues until twelve tones are obtained, thus the complete number [of tones generated from Huang-chung]." This is the principle on which Wang Pu establishes (his) tone system. The same chronicle also records that: "Wang Pu studied the system of lu. [Emperor Shih-Tzung of the Chou dynasty] ordered him to research the ancient and modern documents on lu and to submit the result. Although Wang Pu considered himself inadequate for such a task, he could not decline the royal request. Therefore, to represent

55 50 the Huang-chung pitch, he formulated a new system based on the Chou system and relied on the chu-shu of a grain of millet) as a standard measurement., the width The length of chu-shu is nine tsun, and its diameter three fen. This pitch is equivalent to (i.e. resonant with) the modern Huangchung pitch. The twelve pitch pipes are produced by the method of "adding and subtracting one-third". However, the twelve pitch-pipes [proved to be] not concordant; therefore, Wang Pu created "chuen-lu" with thirteen strings. each string on Wang Pu's chuen is nine chih. The length of The pitch of any unstopped strings is equivalent to Huang-chung." In other words, all thirteen unstopped string (i.e. without any bridges) has the same pitch as Huang-chung. "The eighth string with the bridge placed at sixth chih point produces the ling-chung pitch. The third string, with the bridge placed at eighth chih point produces the tai-tisu pitch. The tenth string, with the bridge located at chih point produces the nan-lu pitch. The twelfth string, with the bridge put at 4.75-chih point produces the ying-chung pitch. The eleventh string with bridge placed at 5.01-chih point produces the wu- i pitch. The six string, with the bridge located at 6.68-chih point produces the chung-lu pitch. The seventh string, with the bridge set at 6.33-chih point

56 51 produces the jui-ping pitch. The second string, with the bridge placed at 8.44-chih point produces the ta-lu pitch. The ninth string, with the bridge located at 5.63-chih point produces the i-tse pitch. The fourth string, with the bridge placed at 7.51-chih point produces the chai-chung pitch. The thirteenth string, with the bridge set at 4.5-chih point produces the Huang-chung pitch." The above describes the bridge placement of each string on luchuen. The Huang-chung string does not require a bridge. Accordingly, measurements of lu-chuen can be shown as in the drawing below. (ta-lu string) ~~~.44chih (head) Huang-chung (tail) ~ string (nine chih) 4.5 chih an have higher uan Snine chih inechi Huang-chung From the above drawing, it can be seen that the placement of bridges of the chuen is similar to that of cheng. However, it differs from the present-day cheng. On the current cheng, the string producing a higher pitch has the bridge located nearer to the nut, and the scale system on the modern cheng is that of pentatonic scale. From the twelve pitches, seven selected tones comprise a scale gamut, and primary tone [i.e. the tonic] is called kung ( ). The other notes [in this heptatonic pattern] are:

57 52 "Chich, shang, yu, chuen, pien-kung and pien-chih. Sounding and returning to this primary tone establishes the [pitchlevel of] tonality. Starting with one of these seven tones but [keeping their intervallic relationship] unaltered produces the modality. There are seven modes and twelve (available) pitches (within an octave gamut), thus, all told, there are eighty-four modes." 3f The above quotes explain the placement of lu-chuen's bridges and that the pitches can be altered by moving bridges. However, it is my opinion that the bridges can only be moved closer to the nut (i.e. moved to the right). This is due to the fact that the bridge of highest pitch is set at exactly the mid-point of the open string; moving the bridge closer to the nut will raise the pitch three octaves higher. Therefore, it is said that by moving bridges and thereby varying the kung pitch, eighty-four various keys will result; this is because of I' the limitation of using seven tones transposing to the twelve lu-s. It is not possible to transpose [twelve-tone chromatic scale to] twelve different pitch (lu) levels. Based on the above descriptions of lu-chuen's string length, 1t the following table lists string lengths of Wang Pu's lu-chuen and compares them with Ching Fang's system. The order of listing of strings is by register.

58 53 Order of Name of pitch Length String Wang Pu's Lu Old Lu 1 Huang-chung 9.00 chih 9.00 chih 2 ta-lu tai-tisu chai-chung ku-si chung-lu jui-ping ling-chung i-tse nan-lu wu- i ying-chung half-lu of Huang-chung

59 54 By examining this table, it can be seen that the system of Wang Pu's lu is the same as that of the old lu. The only difference is in the measurement of fen which has no appreciable effect on the pitches. Morever, Huang-chung, tai-tisu and ling-chung are exactly the same in both lu systems. in Chinese music. These three tones are the essential melodic tones (They are comparable to Do, Re, Sol or Sol, La, Re,) corresponding, as it were, to that in the old "pure pentatonic scale" system which is not transposable. Therefore, [since his system is identical with the old system,] Wang Pu's lu could not satisfy the requirement for transposition.

60 Section VIII: Wei Han-Chin's Lu Using The Emperor's Finger Length as Measurement Unit Wei Han-Chin ) lived during the reign of Hui's ( of the North Song Dynasty ( 1 ), and is contemporary with Yueh Fay ( ), a renown patriotic hero. In A.D. 1102, Liu Ping ( J ), a minister of the Office of Music, presented Wei Han-Chin to Emperor Hui, whereby Wei Han-Chin established the lu series of Ta-Cheng- Yueh () According to Yueh-Chih of Song-Shih (, The Music Chronology of The History of Song Dynasty), "'Wei Han-Chin stated that Yu (, Emperor of the Hsiung Dynasty, ) adopted the process of Huang-Ti in using the [pitch level of man's] voice as [the standard for] the lu and the body as unit(s) of measurement. Accordingly, Wei Han-Chin set the standard for Huang-chung lu by adding the lengths of Emperor Hui's middle, fourth and small fingers (each finger with three joints) which totaled to be nine tsun. By establishing the lu of Huang-chung, the other lu-s were arrived accordingly. Hence, the different lengths of strings and pipes [to express the lu-s] were thereby produced and the musical system established.' Further study indicates 55

61 56 that this musical system was completed in four years, and Emperor Hui conferred on it the name Ta-Cheng ( ), and, at the same time, discarded all other older musical systems." Wei Han-Chin's measurement for the pitch system based on the length of the Emperor's fingers was not only criticized by later generations, but also by contemporaries as well, as can be seen in the criticism of Chen Yang (A ) in his Yueh-Shu, Treatise on Acoustics and Music), and also, later, in the Syh-Ku-Ti-Yaw (i \ ) of the Chin Dynasty, which labelled it as heretic theory causing the fall of the dynasty. However, Ma Duan-Ling () Yz) of the k Ching Dynasty, in his Wen-Hsien-Tong-Kao (, Comprehensive Study of The History of Civilization), defended Wei Han-Chin's system, stating that, during the process of establishing a [new] tonal system, the craftsmen actually employed the old lu system instead of adopting that of Han-Chin, and Han-Chin himself appeared not to have recognized their "error." Therefore, although the musical system is said to have been revised, it actually changed little from the old system. It is my held viewpoint that there was already an accepted opinion regarding the length of Huang-chung before the establishment of Hanlu (2V ); otherwise, the reason for using the Emperor's three particular fingers in arriving at the Huang-chung length could hardly be understood. That is, the sum of the length of these three fingers of Emperor Hui happened to agree with the already-defined length [of Huang-chung]. Taking myself, for example, I am from Fu-Chou ($j) of south China, and

62 57 my height is 163 cm. The sum of the lengths of my three corresponding fingers is 22 cm. This length is very close to the length of Huangchung pipe of 23 cm. as determined by Hornbostal of Austria. A person taller than I would produce the length (of three fingers) which is closer to [that of Huang-chung]. Northern people are taller and their fingers are longer. Emperor Hui-Tzung ( ) was a Northerner. During the North Song Dynasty ( t1), there were diverse opinions regarding the pitch series, and many ministers [who were also scholars of classics in the court] participated in the dispute, among them, for instance, the prime minister Shy-Ma Kuang ( J $) ) and the officer of Civil and Military Affairs Fang Chen ( ~ ). As the result, the incessant dispute caused much controversy [in the court]. The proposal by Wei Han-Chin to employ Emperor's fingers as a measurement is, in one sense, an attempt to resolve these controversies. The proposal, with its good intention and considerable effect, finally restrained the dispute once and for all. In A.D. 1111, Ta-cheng yueh was disseminated in Korea. This tonal system is still perfectly preserved [and performed] at the Confucious Temple and the Hall of National Music (of Korea), the pien-chung (4 ) and pien-ching ) pitch series correspond to the western musical pitches as shown next.

63 58 Upper G# A A# B C C# D D# Order Pitch Lower G F# F E D# D C# C Order Pitch Note: Each set of Pien-chung and pien-ching consists of sixteen pieces (of lithophone). The interval between any two adjacent pieces of [tones] is a semitone. To pursue further research in Ta-cheng yueh, one needs only to examine the bells and sonorous stones in Korea. This will provide factual material for investigation, instead of futile and speculative theorization. Although there is much criticism on the system of Han- Chin, the investigation into the ancient and modern lu system can be best pursued by relying on the system of Han-Chin.

64 Section IX: Tsai Yuang-Ting '9 Adds The Six Altered "Lu" Tsai Yuang-Ting, alias Chi-Tong ) lived during the reign of Emperor Hsian-Tsung (4 ) of the South Song Dynasty ( ) (A.D ). He was a scholar whose activity was confined to Si-San ( JA ) area and did not attain any official position, and was known simply as Mr. Si-San (.\ ). It is reported that he had studied under Shu Si (!, one of the most renowned scholar of the day), and that, Chu Si, admiring his transcendent farsightedness and talent, regarded him not as his student but, rather, as a friend. Tsai Yuang-Ting's two famous books are Lu-Lu-Pen-Yuan The Original Sources of Lu-Lu Series) and Lu-Lu-Cheng-Pien ( A Dissertation on the Lu-Lu Series). Tsai Yuang-Ting regarded the system of transposable kung (the f1 tonic) [to any tone in the twelve lu-s] as awkwardly forced. He also regarded Ching Fang's sixty lu-s as being excessively complicated. Therefore, he derived six altered lu from the last pitch (chung-lu) in the twelve lu series by way of san-fen-sun-i process, and regarded these six altered lu-s as (more) appropriate [than the tones in the old system] for transposition. These six lu-s coincide with chih-shih ( ), chu-mieh (, ),-shih-hsi the chien-kung s y) pien-hsien ( ), chih-nei (7 t ) in the Ching Fang's sixty 1_u-s 59

65 60 system. These tones in the pitch nomenclature of Tsi Yuang-Ting's system, however, are pien-huang ), pien-ling (940'), piennan ), pien-ku ), pien-ying ) This is referred to as the "six altered pitches". According to Song-Shih, the theory of Tsai Yuang-Ting is stated as below: In the "Chapter on Altered-lu" (Pien-Lu-Pien,,), "Any one of the twelve pitches can be the primary tone kung [in an octave gamut]. From twelve pitches are selected five tones and two altered tones [in the diatonic tonal scale system]. The six lu-s are Huang-chung, ling-chung, tai-tisu, nan-lu, ku-si and ying-chung, which comprise the essential tones in the scale system. The other six lu-s -- juiping, ta-lu, i-tse, chai-chung, wu-yi, and chung-lu -- are obtained by altering Huang-chung, ling-chung, tai-tisu, nanlu, ku-si and ying-chung. [However,] because Tsi Yuang-Ting regarded this tonal series as not concordantly interrelated, he therefore proposed his series of altered tones. In this I system of twelve lu-s are six tones which can be altered: Huang-chung, ling-chung, tai-tisu, nan-lu, ku-si and yingchung; altered tones from above lu-s roughly approximate the "diatonic lu-s" but are slightly higher. Since these altered lu-s are not of the original [diatonic] scale tones, they may not assume the role of kung in a scale system.

66 61 /1 [Tones in] the twelve lu-s are obtained by successive generation. However, because the uninitated did not understand the [correct] ratio in the san-fen-sun-i process, the [last tone in the series thus produced] did not coincide with [the octave equivalent of] the fundamental. Chung-Lu [the last pitch in the 11 lu series] produces the Huang-chung pitch [approximately an octave above the fundmental] but its length being less than seven tsun and nine fen and, therefore, is not an accurate octave equivalent of the fundamental Huang-chung pitch. Ching Fang, realizing this, called the pitch which is produced by chung-lu as 'bhih-shih" and he continued the process in arriving at Forty-eight additional pitches. [However, Ching Fang] did not realize that the number of altered lu should only be six as [the limit of] naturally produceable, and should not have made further additions; any additional tones, though produceable, would be useless."..."her Cherng- Tian and Liu Jwo criticized defects in Ching Fang's theory, that he increased the ratio of eleven lu-s generated after ling-chung in attempting to ensure that chung-lu will produce [the accurate octave equivalent of] Huang-chung, with the correct number of 177,147. [In the corrective tone-generation system of Ching Fang as well as that of Her Cherng-Tian and Liu Jwo,] Huang-chung pitch [and its octave equivalent] remains the only correct lu; all other tones do not correspond with numbers [representing tonal ratios] in the san-fen-sun-i

67 62 process. [In fact] the defects of [Her Cherng-Tian and Liu Jwo proposals] is greater than that of Ching Fang." Note: Wang Kuang-Chi ( ) in his History of Chinese Music, states that the "Huang-chung" pitch generated from chung-lu will have the length of eight tsun and seven fen weak. I regard this to be inaccurate. Therefore it is corrected as seven tsun nine fen. stated that: In the chapter on "The Sixty Modes" (Liu-Shih-Diao-Pien), it is "Any one of twelve pitches can alternatingly become the tone (i.e. kung) and each [scale pattern] consists of seven tones. Therefore, altogether, there are eighty-four kungdiao ( ). There are twelve [transpositions -- one to each of the twelve lu-pitches], as well as twelve-transpositions for each shang-diao (3 e ), chueh-diao ( ), chich-diao yu-diao (J J), (these finalis being equivalent to Do, Re, Mi, Sol, La [in the solmization system]). The total amounts to sixty [different modal finalis] tones or sixty modes. The twelfth tone is the altered tonic kung '9 ), (equivalent to si [in the solmization syllables]), its position being between yu (La) and Kung (Do). Likewise, there is altered chih (F#) between chuen (Mi) and chih (Sol). These two "altered" tones may, combined, have twenty-four

68 63 transpositional levels [i.e. pitches]; however, they can not assume the role of finalis [of a mode] because F# and B are considered "altered" tones." Note: This is due to the fact that the classical [i.e. court music] as well as secular music do not use these two tones as [finalis of a] mode. Tsai Yuang-Ting advocated the addition of six [new] altered tones, based on the chapter of Pien-Lu-Pien [~J AV, see above], by producing a(nother) [altered] Huang-chung [and its subsequent "altered" tones] from chung-lu by the san-fen-sun-i process. The following table lists the six altered tones in order and in comparision with each other. Order Name of Pitch Length Chih Fang's Comparison Name 1 chung-1u recreates (1+1/3) chih-shih (cheng-huang) pien-huang-chung = = 81 2 pien-luang-chung (1-1/3) chu-mieh (cheng-ling) recreatespien-ling = = 54 chung 3 pien-ling recreates (1+1/3) shih-hsi (cheng-tai) pien-tai-tisu = = 72 4 pien-tai-tiau (1-1/3) chieh-kung (cheng-nan) recreatespien- = = 48 nan-u 5 pien-nan recreates (1+1/3) pien-hsien (cheng-ku) pien-ku-si = = 64 6 pien-ku-si recreates (1-1/3) chih-nei (cheng-ying) pien-ying-chung = = 42.67

69 64 More recently, Wang Kuang-Chi maintains that the system of Tsai Yuang-Ting must be upheld (i.e. the unequal-tempered tone system) in order to preserve the Chinese ancient musical system (twelve unequaltempered). Any one pitch can transpose as a kung (tonic). This system provides a good solution. Next are the eighteen pitches and their transpositional relationships.

70 H 4 H H Z cd hqh HP- P- OP-+ H P P+ -,C,. II HP 4 4 bia b.0 1 6, - - r N w.1,. U ' 2wwrpeetothe subrcig[f]13[ent](hu pe pthp~ Note: 1.-. represents the adding [of] 1/3 [length] (thus lower pitch, -p!,) 2. ww represents the subtracting [of] 1/3 [length] (thus upper pitch,j-

71 66 I This above diagram can, according to the system of twelve lu and the system of seven [diatonic] transpositions, be made into a pair of two concentric wheels, the upper one being turned to produce various pitch combinations, thus showing different modal patterns. (see Ex.) Si Do (inside wheel) (outside vs. inside wheels)

72 67 By adding altered tones of Tsai Yuang-ting to the original twelve pitches, eighteen pitch pipes are thus produced. The following diagram illustrates the comparable lengths of these pipes. 1. Huang-chung 2. (pien-huang). ta-lu 4. tai-tisu 81. Do ) ---- ~ _-- ~ -- _- _ ~~ ~- ~~- ~ ( Re 5. (pien-tai) 6. chia-chung 7. ku-si ~_ - ~ - _ ~ _ - - ( ) Mi 8. (pien-ku) 9 chung-lu 10. ju i-ping 11.ling-chung 1 2.(pien-ling) 13. i-tse 14. nan-lu 15. (pien-nan) 16. u-y i 1 ring-chung ~--] ::: I ( ) Fa Sol ( 53.27) 50, La ( ) Si 18. (p en yi~~~~~~~~~~~~] (piens-ying) ( 42.09)

73 68 As shown in this diagram the six altered tones are inserted among the original twelve pitches, thus completing the procedure of transposition. However, Han Cha-Chou ( ) -- a powerful minister -- criticized this system as being falsely founded and, therefore, prevented it from being implemented. It is this present author's opinion that any theory can only be validated when it is substantiated by practice. From ancient time, the structure of Chinese music is based on the pentatonic scale. Some instruments [it is true,] are constructed to allow realization of heptatonic scales, such as flute (dyi), panpipe (sheng, ), hsiao and lute (pi-pa). However, [the most classical of instruments] zithers (chin, se, and cheng,) are structured to produce the traditional pattern [of pentatonic scale].

74 Section X: Chu Tsai-Yu's Twelve Equal-Tempered Lu Chu Tsai-Yu, a contemporary of Emperor Moo Chung ), was born in the fifteenth year of Chai-Ching ( ) of the reign of the Emperor Ming Shih Chung, A.D. 1536), and was an uncle of Emperor Shen Chung ( ). His father, prince Hou-Huan (. If I, ) (a brother of emperor) was a scholar [in the science] of lu-lu series. He is from a family of learned men and, therefore, he inherited and pursued scholarly tradition. His scholarly writings include Lu- ft Hsueh-Hsin-Shuo ( ( A, A New Account of the Science of the 1 If ~it Lu Theory), Lu-Lu-Ching-I (, The Essence of the Standardized E, A Discourse Lu On the Lu Series), Lu-Lu--Cheng-Lun = and Yueh-Lu-Chuan-Shu ( 4, Collected Works On Music and The Lu Theory) etc. There are four major aspects regarding [his system of] lu: 1. It did not follow the measurement system of Wang Mang (' 4-). 2. It did not subscribe to the classical theories (i.e. Han Dynasty) of Liu Hsin ) and Pan Ku ( i ). 3. It did not employ the process of san-fen-sun-i for the tone generation beyond the eighth tone [in the tonal series]. 69

75 70 4. It did not accept the length of Huang-chung [pipe] as being nine tsun. Due to the fact that he was advocating a theory which apparently renounced the traditional system, his system was not accepted by his contemporaries. During the later reigns of Emperors Kang Hsi ( ) and Yung Cheng (4,1_ ), decrees were issued to refute [Chu Tsai-Yu's] system. However, both Chinese and western scholars of recent years have come to recognize the importance of his theory. In particular, the recent scholarship expresses profound admiration of Chu's extraordinary invention formulated some four hundred years ago. This author, however, is of the opinion that his revolutionary lu system was affected by the importation of western scholarship. The following will provide support to this view. 1. Hsu Kuang-Chi ( ) (alias Chih-Kuang ( V ), died during the reign of Emperor Chung Cheng ), was a scribe in the court of Emperor Ming Shen. It is known that, with his position as a court scribe, he studied western scholarship. 2. In the eighth year of Wan-Lee ( \.) of the Emperor Ming Shen Chung (A.D. 1580), an Italian priest, Matteo Ricol, arrived at Kung-Chou province (-} ) to undertake missionary work and, from there, he went to Pei-Ching (3{ ). As he was knowledgeable in Chinese and western scholarships, as well as in astronomy, geography and medical sciences, he was

76 71 given important tasks in the court of Emperor Shen Chung. During this period, court ministers such as Hsu Kiang-Chi and Lee Chih-Tsao (t) frequent company [of father Ricol]. enjoyed the (cf. Tsu-Hei,, a dictionary). 3. In the twenty-fourth year of Wan-Lee A.D. 1596), Chu Tsai-Yu proposed the reform of lu's system. This is sixteen years after Mattero Ricol's arrival in China. 4. Rome has been the center of the Catholic Church since the ancient times. And the music of the Roman church has been held in high esteem for many generations. Morever, the music of the Roman church originated in Greek music and the Greek musical system is based on the system of "seven [ecclesiastical] modes" which resembles ancient Chinese modal system kung mode, sung mode, etc. Therefore, recent western scholars recognize the existence of a close tie betwen the two when they discuss the ancient Chinese and Greek musical cultures. This is particularly evident in the fact that the Pythagorean numerical system of tone generation in the sixth century, B.C. is identical to the ancient Chinese musical process of san-fen-sun-i. The modal system of the Roman church music originally contained eight modes which became the source of western music. During the sixteenth century,

77 72 the western modal system adopted four additional modes, and the total number of modes became twelve. are grouped into authentic and plagal modes). (These (cf. The Concise History of Western Music by Wang Kuang-Chi). In light of the above historical events and the sequence of their chronology, and particularly the fact that Chu Tsai-Yu's revolutionary theory of tonal system was formulated at the end of this period, the above hypothesis as the possible source for the formulation of his tonal theory [as being affected by western tonal science] may not be altogether improbable. In addition, the coming of Italians into China can be traced as far back as Marco Polo (A.D ). It is recorded that Marco Polo arrived in China in 1275, and Emperor Shih Tsu of the Yuan Dynasty (( Cj ) inquired him on matters concerning culture, and subsequently conferred upon him an offical rank. Marco Polo served in the Chinese government for about twenty years before returning to Italy. During the Genoa War, he enlisted in the military service and was later imprisoned as a war criminal. During his two-year jail term, his narrations of his travel encounters were recorded by an inmate. This is now the famous Travels of Marco Polo (Tong-Fang-Chien-Wen-Chi, n L ) (Lit. Record of Eastern Sights and Tales). This took place three hundred years before Matteo Ricol arrived in China, when the cross current between the Chinese and western cultures was already in ferment. During the age of Chia Ching (.) of the Ming Dynasty, Ao-Mang ), the neighboring island of Kung-Tong province ), was leased to Portuguese as a commerical port which, in turn,

78 73 increased the pace of cultural contact between East and West. Emperor Shen-Chung of the Ming Dynasty greatly admired Matteo Ricol's scholarship, and government ministers took pleasure in obtaining Matteo Ricol's company; as the saying goes "The prosperity of the lower echelon is dependent on his acquaintance with the upper echelon." (" ) Therefore, studying of western scholarship became fashionable in this period. Chu Tsai-Yu was born during this period, and was well versed in traditional theory of lu. It is [therefore] probable that he compared the theories on tonal generation of Chinese and the western cultures, and that [although] both employed the process of san-fen-sun-i, [he realized] that the ancient Chinese system of tonal generation of successive and circular kung (i.e. cycle of fifth method) is improper, and that the length of the fundamental pitch needed revision. Huang-chung Therefore, since he did not subscribe to the legend of the length to be nine tsun, it follows that the did not embrace the established theory by the Han Dynasty scholarship or it's measurement system. It can be said, therefore, that Chu Tsai-Yu's revolutionary theory of lu is not only formulated as a convenient system for accomodating [problems of] transposition, but also an attempt to unify the Chinese and western tonal systems. The importation of western culture [into China] must have had a tremendous influence on [Chu Tsai-Yu's revolutionary] idea. Chu Tsai-Yu's theory of twelve equal-tempered lu is admired by many recent [western] scholars, and Chinese [scholarship] obtains a considerable degree of self esteem. In view of such an accepted opinion

79 74 [regarding Chu Tsai-Yu's contribution], this author would not dare take exception by presenting opposing view points. The historical events presented here are intended simply for the purpose of providing the background of western scholarship during the time of Chu Tsai-Yu's formulation of his theory.6 It has been referred to in a preceding paragraph (see page 70) that Chu Tsai-Yu had pointed out in his book it it I Lu-Lu-Ching-I the essential errors in the process of generating lu pitches during ancient eras. Chu Tsai-Yu adopted the measurement for the Huang-chung pipe as one chih (one foot) of hen-shu-chih (lit. "horizontal-grain chih; exact meaning or unit of measurement unclear). (One hen-shu-chih is equal to Huang Ti's chun-shu-chih which is divided into nine tsun, therefore, the length of both chih-s are the same). [The measurement system via hen-shu-chih is] based on the decimal system. This calculation is according to that recorded in Chou-Li Record of the Rites of the Chou Dynasty),, that "In using [a round] table as a basis for measurement [calculation], a square [could be drawn] inside it, and rounding [the four corner points of the square will, in turn, produce a] circle. It further states that the diameter of the circle and the hypotenuse of the square are the same length. That is, finding the hypotenuse of a square will give the diameter of the circle. The basis for measurement is the length of Huang-chung pitch, which is equal to one chih of the measurement system." 6 The original paragraph is greatly condensed here merely to convey the essence of the declaimer made by the author.

80 75 t! [Chu Tsai-Yu's] process of lu generation is as follow: "...giving the square root of one chih to be the ratio of the Huang-chung pitch. The east-west side [i.e. the base of the right triangle with in the circle] of ten tsun becomes the base (RJ ); multiplying itself thus giving one hundred [square] tsun becomes square base (1J4 ). The south-north side [i.e. the higher of the right triangle within the circle] of ten tsun is altitude (fl); multiplying by itself thus giving one hundred tsun becomes square altitude ((4. The exact number of the hypotenuse which is the diameter of the circle [containing the right triangle] is the square root of the sum of the base and altitude squares, which is , which, in turn, is the ratio of [the pitch] an octave below jui-ping pitch." The diagram below illustrates this [principle of calculation], with corresponding mathematical formula. north wst The length of the pitch an octave below the jui-ping pitch is: = chih.

81 76 That is, with the length of Huang-chung pitch pipe being one chih, the pitch an octave below jui-ping pitch as calculated according to the above formula will be chih. The process of producing the length of other pitch pipes is described in the same treatise as follow: ".. The ratio of the pitch an octave below jui-ping, multiplied by ten gives tsun; this number being first square-rooted then divided by ten, thus gives which is the length of a pitch an octave below nan-lu. This number is multiplied by base number of ten and again by altitude number of ten, thus giving the cube number of tsun; this number being first cubic-rooted then divided by ten, gives chun. This number being the ratio of the pitch an octave below ying-chung. This can be expressed as the following mathematical formulae: x = chih (to produce the length of a pitch an octave below nan-lu pitch from jui-ping) x 10 x 10 = 10 = chih (to produce the length of a pitch an octave below ying- 'I chung pitch from nan-lu) 7 The number is incorrect -- 1 instead of 4 is recorded in This may be due to mistaken recording during transcription where the sounds for 10 (shih) and 4 (shih) are similar.

82 77 '1 Therefore, the process of Chu Tsai-Yu's lu generation is: from the Huang-chung to arrive at a pitch an octave below jui-ping pitch; ft from jui-ping to arrive at a pitch an octave below nan-lu; from a lower 1' octave of nan-lu pitch to arriving at a pitch an octave below yingchung. This process does not comply with the theory of the number Huang-chung pitch being nine tsun, or with the process of san-fen-sun-i, and therefore does not result in generating tones beyond the eighth tone [i.e. beyond the octave gamut]. The following should be noted: In the ancient process of producing lu, the "half length" of Huangchung pitch does not exactly equal to the octave equivalent of Huangchung (that is, the octave equivalent of Huang-chung is lower than the [supposed Huang-chung] pitch [produced via san-fen-sun-i; i.e. C being lower than B#]. However, the pipe length of Chu Tsai-Yu's Huang-chung pitch is exactly half the length of that an octave low Huang-chung; the length of the pitch an octave above Huang-chung is exactly half the length of the fundamental Huang-chung pitch. What, then, is the reason [for this discrepancy between the two processes]? It is due to the fact that the inside diameters of each of these pipes are not the same size. Lu-Lu-Cheng-I lists the length of Chu's lu-pipe as below: (see next page)

83 78 Pitch Name Pipe Length (unit is by Chia-Chih) Higher Octave Within the Proper Lower Octave fen fen fen Huang-chung I, ta-lu tai-tisu chia-chung ku-si chung-lu jui-ping ling-chung i-tse If nan-lu wu- i ying-chung Note: Chia-chih is based on decimal system, one chih is equal to ten tsun; one tsun is equal to ten fen.

84 79 By examining the above table, it is apparent that any one lupipe has a corresponding [lower octave] equivalent which length is exactly twice its length, and also has a corresponding [higher octave] equivalent which length is exactly half its length. This relation is not limited to Huang-chung pitch. According to the principles of physics, if the length of aircolumn is to increase or decrease proportionately with the frequency of sound wave, then, the inside diameter of the tube should also change. That is, with pipes of the same length, the smaller the size of inside diameter the higher the pitch; the bigger the size of inside diameter the lower the pitch. Therefore, merely reducing the pipe-length by half will not produce a pitch an octave higher. [It is apparent that] Chu Tsai-Yu was aware of [this principle] and, therefore, he stated that, "...[for example,] taking two identical Huang-chung pipes of either bamboo or wood, and cutting one pipe into [exact] halves, and blow the half-length pipe and the full-length pipe together. Tones from these two pipes will not be concordant, as can be easily experimented. Or, taking [for example] two identical ta-lu pitch pipes of the same circumferences with that of the Huang-chung pipes; and cutting one of the pipes into two [exact] halves, and play them; they will not produce a harmonious sound. Although the higher-octave pitch of ta-lu will sound concordant with Huang-chung, [the interval] causes a slight difference (i.e. degree of discordance). Therefore, it becomes evident that the pitch of the half-length lu will be a semitone lower than the [octave equivalent of the] full-length lu [of the same diameter]."

85 80 The full-length "lu" as referred to in the above statement implies the standardized lu [in the "obligatory" register of the twelve lu- 8 lu]. Chu Tsai-Yu did not attempt to correct the ratios of lu-pipe lengths; instead, he amended the problem [in tone generation] by reducing the inside diameters of successive lu pipes. Regarding the calculative process of length vs. inside diameter [of successive lu pipes], he states that, "...The length of the middle-register Huang-chung pitch is set as one chih. Multiplies it by 1,000,000Y000, then divides by 10,594,463,094, arriving at [the length of] fen, is the ta-lu (pipe). The inside diameter of the middle-register Huang-chung pitch is set as fen. Multiping by 1,000,000,000, then dividing by 1,029,302,236, thus arrives at fen, the inside diameter of the ta-lu (pipe). The following mathematical formulae illustrate this process: (the unit of calculation is fen). 100.(fen) x 1,000,000,000 = fen -- 1,059,463,094 (thus obtaining the length of the middleregister ta-lu pipe) 1,000,000,000_ x 1,00,000,006= fen (thus obtaining the inside 1,029,302,236-- diameter of the middleregister ta-lu pipe) 8 The remainder of this sentence is omitted, as it merely repeats the preceding sentence.

86 81 The ratio of used by Chu Tsai-Yu in obtaining the [successive] pipe length is from 12 J7; the ratio of in reducing the inside diameter is from 242. The basis for using the square root of 2 is that Chu Tsai-Yu regarded the length of the pitch pipe an octave below Huang-chung as being two feet of hsia-chih ( ), and applied this as the basic standard in producing lu. [In addition,] in order to establish the relationship between the frequency and the air-column of pipes where ratio [between them] is constant [that is, each successive pipe length is decreased by the ratio of ], and thus in order to arrive at equal-distant pitch series, twelfth-root (12U) of the pipe length is used. Likewise, in applying the twenty-fourth root of two ( 2 4 T) to produce the ratio for inside diameters, Chu Tsai-Yu decreased the surface-diameter of successive pipes by the ratio of , which is obtained by the square root of , the length ratio. Since Chu Tsai-Yu began with the pipe an octave below Huang-chung in calculating the ratio of decreasing diameter size of successive pipes, any two adjacent pipes will have [the identical ratio of] surface diameter. A contemporary musicologist, professor Pen-Li Chuang ( ) proved the correctness of this process, using the following mathematical formulae: "Taking Chu Tsai-Yu's two adjacent lu-pipes and designating their surface diameter as A 1, and A 2 ; and their inside diameters as D 1, and D 2, and the ratio of these two inside diameters as K 1 ; therefore,

87 82 A D= D A 2-2 ADD 1 1 (1 Al 2D = D )K K = D22 Therefore, the ratio of surface-diameter of Chu Tsai-Yu's two adjacent lu pipe is, A 1 _2 2 A 2 = K = ( ) = A2 (cf. Pen-Li Chang's Study of Chinese Tonal System) In his book Lu-Lu-Ching-I, Chu Tsai-Yu also pointed out the process of calculating the ratio of lu pipe's outside diameter. It may be said that, since the ancient pitch pipes were made from bamboo, it is not difficult to obtain the length of these pipes; however, [proper size of] the inside diameter of these pipes needed [to produce specific pitches] could not be easily determined. If the inside diameter were obtained to meet the [acoustical] requirement, the additional need to obtain the outside diameter will only further complicate the matter. This is particularly so, since the thickness of outside diameter [i.e. the thickness of bamboo tube] affects only the timbre of tone and not the pitch level. That is, the thickness of pipe may affect the pipe opening, it changes little the length of air column of the pipe. Therefore, the process of calculating lu pipe's outer diameter could be discarded. (The process of calculating

88 83 the outer diameter is given below merely to illustrate the formula.) is to Lu-Lu-Ching-I records the method of calculating the outer diameter as following: "That two openings of the pipe can be drawn as circles, with inside and outside circumference. The outside circle encloses the square the side of which equals the diameter of the inside circle. The hypotenuse of the square equals the diameter of the outer circle... The circumference [of the outer circle] being 40 tsun, containing the square size of nine tsun (side), and with [the known] sides [of right triangle] the hypotenuse may be obtained; likewise the diameter, as well as the circle size, can also be obtained." Professor Chuang Pen-Li, in subscribing to this principle, proposes the following drawing: below is a brief comment. A D

89 84 A, B, C, D, are four points forming a square, with nine tsun in each side. AB is the altitude; BC is the base. From these two sides the hypotenuse AC can be obtained as AB 2 + BC 2 = This is [also] the diameter of the outer circle. The ratio between outer and inner diameters is ft = This is what Chu Tsai-Yu required as outer diameter of "the middle register" pitch, equivalent to the inner diameter of the pitch an octave lower. That is, the outer diameter of the higher octave pitch coincides with the inner diameter of the middle register pitch. The [listing of the] length, the inner and outer diameters of Chu Tsai-Yu's pipes [has] been attested by acoustical experiments made by Professor Pen-Li Chang, giving as comparison the original measurement by chia-chih and the current metric measurement system. This is shown as below: (see next page)

90 85 Pipe Length Inner Diameter 'Outer Diameter Pitch Name t a Chi fh'h cm. Ch-n ih cm. Chen-ih cm. Huang-chun ta-l tai-tisu chia-chung > ku-si chung-lu o jui-ping ling-chung i-tse nan-lu Wu-y ying-chung uang-c ung ta-lu tai-tisu chia-chung o ku-si a chung-lu S Jii-ping ling-chung i-t s e nan-lu wu-yi ying-chung Huang-chun ta-lu tai-tisu chia-chung Co ku-si chung-lu jui- in ling-chung i-t s e A nan-lu wu-y ying-chung

91 86 With regard to Chu Tsai-Yu's theory of twelve well-tempered lu-s, Professor Chuang Pen-Li had made a detailed examination, and asserted that [Chua Tsai-Yu's calculation] is best applied to strings; when applied to pipes, however, the theory requires revision in terms of inner diameter. (cf. Chuang Pen-Li, Study of Chinese Tonal System.) Chu Tsai-Yu called the instrument which he used to examine lu as chun-chuen ( 1 ).9 According to his Lu-Hueh-Hsin-Shuo, this instrument is made of [wood from] paupownia, and is shaped like a chin or se (zither). (The head., yueh, and the tail W _yin, are on the upper board of chin and support seven strings. The yueh is located at chin's head, the yin is put at chin's tail; "head," "shoulder," and "tail" are so named relative to the positions of different width on the chin's board.) The [sides of the] body are straight from head to tail, and there are two holes on the bottom of chin. The strings are not supported by bridges, thus it is unlike se, and therefore named chun-chuen. The instrument is approximately fifty-five tsun. The width of chuen's head and tail is eight tsun. The diameter of the bottom two holes is three tsun. [For an acoustical experiment,] a pitch-pipe can be placed inside the instrument, whereby the string stretched from the head to the hole could be measured against the Huang-chung pitch (pipe). The strings of chuen are of two types: the first and middle strings 9. The original text of this paragraph contains a great deal of detailed descriptions of the instrument. The translation only conveys the essential information, leaving out redundant portions.

92 87 are single string; all the remainder are double strings. Alongside the outer (the thickest) strings are marked with measurement divisions. Each [of the eleven] portions from head to tail is divided into nine, measured in terms of base-nine (9 x 9 x 9). On the other side, along the thinnest string, are also measurement markings which, in contrast, are divided in terms of decimal (i.e. base-ten, 10 x 10 x 10). On these measurement markings, red color is used to identify the old lu-s (length), where no frets are positioned, while gold is used to identify the new lu-s which are also marked with frets. The lu names are also inscribed along the gold-colored side. The use of stringed instrument such as chuen occurred several times during the history of lu, such as four tong-s of the Emperor Liang Wu, Wang Pu's lu-chuen, etc. However, the drawing provided in Chu Tsai-Yu's book is noteworthy in its detailed depiction, whereby readers of later age could obtain a fairly accurate idea of this acoustical instrument. 10 Using a lute (pi-pa) with the semitone frets, with string length of 71 cm., the pitch measurement (the principle of Chu Tsai-Yu's chuen) can be shown as follows: (See next page) 10. This paragraph is greatly condensed from the original text. Also, the following paragraph is omitted, as it reiterates information already given previously.

93 88 The 1st shiang (d ; fret) position is located at =66.99 cm point The 2nd shiang The 3rd shiang The 4th shiang The 5th shiang The 6th shiang The 1st ping (,, fret) = = = = = =47.42 cm point cm point cm point cm point cm point cm point etc..... The following drawing shows the profile of the commonly used sixfret pi-pa (with additional eighteen-position markings), in order to illustrate the above measurement positions. (see next page)

94 89 -_yueh-shan first ping first fret (s 2nd shiang 3rd shiang 4th shiang 5th shiang 6th shiang I C e0 N -) If it d"" continuing through the 31st ping Base - Chu Tsai-Yu's twelve well-tempered lu-s, [after all,] did have a practical application. [That is,] Chu Tsai-Yu's system began to be adopted three-hundred years after his death (in ca. A.D. 1937), due primarily to the Central Broadcast Station's advocating his system of

95 90 tuning. Although Chu Tsai-Yu's theory was formulated toward the end of Ming Dynasty, it was relegated to the position of an appendant information in the Historical Hall of the Ming Dynasty. Two hundreds and sixty-eight years after the Ming Dynasty, during the Chin Dynasty, Emperor Kang Hsi, Yung Cheng, and Chien Long ( ) decreed to refute [Chu Tsai-Yu's] theory, declaring it to be not worthy of further discussion. (The following paragraph is deleted.) it At any rate, Chu Tsai-Yu's theory of twelve well-tempered lu-s is of particular historical note. That is, in the annal of acoustical theories leading toward eventual formulation of equal-tempered tonal system, Chu's posit must be regarded as the earliest, predating those of Marin Mersenne (1636), Andreas Werckmeister (1691) and J. G. Neihard (1706) by fifty to one hundred years. Also to be noted is an earlier attempt [inthe history of Chinese theory of tone generation] toward the equalization of tones within an octave; Her- Cherng-Tian's proposal of twelve equal-division tone system preceded Chu Tsai-Yu's by ca 1,000 years (cf. section III of this chapter). (The two paragraphs in the original text have been condensed into one.) The following table shows the comparison between the tone system of Chu Tsai-Yu and Her Cherng-Tian.

96 91 Chu Tsai-Yu Her Cherng-Tian Pitch Name The Different The Different Length Length Between Length Length Between Two Adjacent Two Adjacent Pitches Pitches Huang-chun t4g-lu94.38 tai-tosu chia-chung ku-si chung-1u ui-ping _ing-chung i-tse nan-lu wu-i ying-chun octave higher of Huang-chung -L1_I

97 92 In the above table, the length of Her Cherng-Tian's [Huang-chung tube has been altered to become the same as that of Chu Tsai-Yu; lengths of subsequent tubes have also been changed proportionately]. For the listing of Her Cherng-Tian's tube length, see Section III of this chapter. In examining the above table, it can be observed that Her Cherng- Tian's lu system which predates Chu Tsai-Yu's by one thousand years closely approximates the equal-tempered tone system. If this ancient twelve "unequally tempered" tone system was found to be not entirely suitable for transposition, the ancients must have realized it, as each succeeding generation advocated revision of that lu system. However, in this endeavor, [the ancient often relied on the Classical sources for] determining the Huang-chung pitch and calculating the pitch (ratio) number -- the process which was further complicated by conflicting opinions on measurement, such as the choice between hen-shu or chungshu in obtaining the "middle distance" of hsieh-shu (k ). In addition, the theory of lu system was to take into account considerations such as the theory of yin-yang dualism (, male and female), the five elements (i f, metal, wood, water, fire and earth), the five human relationships (...0-, between sovereign and subjects, father and sons, husband and wife, among brothers, and among friends), the five constant virtues (1, benevolence, righteousness, propriety, knowledge and faith), the question of either exhaling or inhaling, the matter of air-column, etc. and, as the result, making scale tones -- the primary important element in music -- a matter of secondary concern.

98 93 [It should be noted that] the fact that the tones in the pentatonic scale -- kung, shang, chueh, chih, yu -- were easily accomodated in the process of san-fen-sun-i in the remote ancient, and the fact that ratio 9r was recognized by chance, does not [support the thesis that] the lu ratio was established [before the existence of musical tones]. In fact, the lu, which can be accurately derived from the process of san-fensun-i, is limited to five tones. If all additional lu-s were to meet the requisites of equal-tempered scale, they must be generated by the other, modified process of calculation. If such a new process can not be derived, the [additional tones] can be [accurately] produced. Therefore, further theories were continued to be proposed after that of Her Cherng-Tian, and [in this tradition] Chu Tsai-Yu's theory was likewise not immediately accepted by his contemporaries. In addition to the above [as regarding the equal-tempered scale of Chu Tsai-Yu not being adopted], this author wishes to represent the following points of consideration [as possible reasons]. 1. Since the ancient time, the ritual music-making belonged to imperial court. That is, treatises record the ritual music as courtly function in events such as ceremonies of rite, morning assemblies and official receptions etc. Therefore, the song texts were of primary importance, followed by emphasis on correct manners of musical recitation. The role of instruments in the ritual music, then, is to supply "harmony" to such textual recitation and providing rhythmic

99 94 support to [ritual] dance and, therefore, the intonation [of instrument] may not have been of primary importance. However, although the object of lu is [the tuning of] instrument, at best, the lu system was nothing more than to establish the [correct] register for the Huangchung pitch. Morever, although there were pitched instruments used in ancient ritual music, such as zither, hsiao, chiang, sheng, hsun, the main instruments for pitch reference were the bells and ching. It is already a difficult task to bring these various instruments into perfect accord one with another, leave alone the question of [establishing] an absolute pitch standard. This may be the reason why the lu system had not always been recongnized as the most important element in music. 2. The melody of Chinese music, especially the ritual music, consists mainly of five tones -- kung, shang, chueh, chih, and yu, without resorting to other two altered lu (i.e. pien-kung and pienchih), much less the other five altered lu-s. What, then, is the reason for the existence of complete twelve chromatically pitched bell-, lithophone- and pipe-sets? This is for the purpose of transposition [of ritual melodies]. As to the fact that no equal-tempered lu instruments

100 95 were previously invented to accomodate transposition, there is yet another reason. Because the main function of instruments was mainly to be in "harmony" [i.e. in perfect unison] with the [singing of ritual] song, and is not like today's usage of instruments as an accompaniment. Also, although bells and ching-s are percussion instruments, they are also melodic instruments in that they are pitched [and capable of producing various tones], and, additionally, in the hands of skilled players, [slight] alteration could be made on the tones on these bells and lithophones by striking at different positions. Pitches on wind instruments can also be altered by change of embouchure and relying on player's ears; likewise, pitches on stringed instruments such as zithers can be easily adjusted. As the [text of] ritual music is sung syllabically and the music flows in slow, quadruple meter [musicians were able to adjust slight differences in intonation of instruments]. Morever, the position of court musicians was a family inheritance as was the custom [whereby performance technique was transmitted via intimate traditions, learned more by rote]. Therefore lu theory system played an even less important role.

101 96 3. I have observed the drawings of suspended [percussion] instruments contained in The Rites of The Chou Dynasty (Chou Li). The drawings depict sets of twelve bells and lithophones as used in Royal Court. In addition, there are twelve individually hung bells as well as chime-stones, all pitched. This author doubts if they were all played at the same time [i.e. in performance of ritual melody]. According to the;historical chronilesy;the twelve-month year was established during the Chou Dynasty, and, as is believed,.each month has a specially designated lu. Therefore, as there are twelve hanging idiophones, each lu is used only in a particular month. It may be inferred [from the fact that these idiophones were individually hung] that the ancient people already realized that lu-s which were arrived from the process of san-fen-sun-i were not totally concordant [one with another] for performing transposed music. When ritual music is transposed, certain idiophones were designated as "silent bells" as their pitches could not accurately accomodate transposition of music. As mentioned, ritual music essentially employs only five tones, and,

102 97 therefore, seven other bells (tones)would not be needed if transposition did not take place [during a given performance]. Furthermore, in ritual occasions, musicians were often contented with only the sounding of particular ceremorial Introit bell. 4. The system of lu was established by the ritual needs and orders of the ruling court, and theories of lu were added in each succeeding dynasty, making it even more complex, creating a dychotomy between theory (of lu) and practice [of performing musicians and instrument markers]. This [speculative] theoretical pursuit can be seen even in Chu Tsai-Yu's tone system in which he calculated to the twenty-fifth decimal point. What he had accomplished -- in obtaining small difference of pitch frequencies of several small bamboo pipes -- over four hundreds years ago received little appreciation from the court or the people. In the shadow of foreigner's intrusion into Chinese society, any proposal submitted to the court reflecting foreign influence would only be looked upon with suspicion. Therefore, it is easily understood that Chu Tsai-Yu's system was denounced in the succeeding dynasties.

103 I Section XI: Emperor Kang Hsi's Yueh-lu In the Chin Dynasty, a northern tribe called Nu-Chen (Ad[ P I, part of Manchurian Emperor) invaded China. As the culture of Nu-Chen is inferior to that of China, this new regime held the Chinese cultural and educational heritage in high esteem, and adopted the old system of the preceding dynasty of Ming. The first emperor of the new dynasty, a mere tender youth when ascended to the throne, spent much of his ten-year reign in pacifying the nation and did not accomplish much in terms of cultural system. It was not until seventy years later, in the fifty-second year of Kang Hsi reign, that the ritual music was reestablished and [a new system] was decreed in the fiftyfourth year of Kang Hsi. Since then and until as late as August of 1968, this ritual music system continued for some three hundreds years. Modern historians maintain that the second emperor Hsuan Yeh was an enlightened ruler. During his some sixty years' reign, he led the [development and condification of] political and military system, and his ability and scholarship are regarded as equal to that of Emperor Wing Chung of the Han Dynasty ( ). With the strong military force and widened territory, next only to the Yuan Dynasty (7r9{) particularly at the beginning of the Chin Dynasty, the ruling regime was able to enlighten the 98

104 99 the political and civil administrations and thus maintained the imperial rule for two hundred sixty-eight years. Among notable cultural achievements are: the editing of an encyclopedic work Kang Hsi Dictionary ( ), the great anthological Collection of Pictures and Books ())), and gathering of all retired scholars in a great meeting ( assemble all the literary master works. ) which purpose it was to It is also said that [the Emperor Hsuan Yeh] himself was a tirelesss student and excelled in mathematics. It was his effect to reestablish the lu system, and himself wrote, among other, two important works, Lu-Lu-Ching-I ) and Lu-Lu-Tsuan-Yao (4). I' Kang Hsi, in establishing the lu system, first used the chih measurement but, after several experiments, adopted the hen-shu-chih ) as a standard measurement. Hen-shu-chih is the same as chia-chih ( ), also resembles the nine-inch-base (kr4 ) Huang- Ti-chih ( )). One chia-chih of Chin Dynasty is equal to eight tsun and one fen of the yin-chao-chih (4z,, the standard foot adopted by the Ministry of Public Works during the Ming and Chin Dynasties), while the kuo-lu-chih (j, the old lu's measurement) of the nine tsun Huang-chung pitch.is equal to 7.29 tsun of the yinchao-chih system. The length of the pipe thus determined, the inside diameter of the Huang-chung bamboo pitch pipe was set as 1200 grains. This system, according to the Lu-Lu-Ching-I, is described as follow:

105 100 "... chung-shu and hen-shu was used as the measurement to determine the length of Huang-chung pipe, as compared with the [making of] modern pipe instruments. The Huangchung pitch as established by hen-shu-chih can be represented with the pitch produced on hsiao (flute), stopped on the kung-chih hole (.L. L), or on dyi (kun-dyi, flute) on the shih-chih hole ( to the modern pitch of F.) (The pitch corresponds On the other hand, the Huangchung pitch as established by chung-shu-chih can be represented with the pitch produced on hsiao stopped between yi ( ) and song-chih (J. ) holes, or on dyi between kung-chih ( T.. ) and fan-chih (J ) holes." According to Musical Chronicle of The Sui Dynasty (Sui-Shu Yin-Yueh-Chih, f ), lu theorists of various generations, from the Chou to the Liang Dynasty of the Five Dynasties (7 _ used as many as fifteen calculation of lu pitch. different [measurement] systems in the Since then, the lu measurement system met numerous revisions, thus causing enormous difficulty in the investigation,, If of the lu-lu theory. Essentially, [the determination of size of the chung-shu and hen-shu-chih-s as the measurement units] is a primary step [toward accurate study of the history of lu], where, a slight mistake can result in great errors in the end. For example, a small discrepancy in measuring a lu-pipe of "three tsun circumference" will

106 101 cause a considerable difference in the pipe's pitch register. The chih of the Chin Dynasty closely approximates the "ancient chih" (i.e. hen-shu-chih -- the "chia-chih" or the nine-base, eight-one fen of the "Huang-Ti-chih"). Regarding the comparison of the "modern chih-s" ( ( ) (i.e. chung-shu-chih -- the "chu-kung-chih" (1.,.. ) of the Ming Dynasty, also resembles the "chu-chih" ( ) as used by craftsmen and the yin-chao-chih as established by the Ministry of Public Works in the Chin Dynasty with the above ancient chih, Ta-Chin-Whei-Dien (k ) gives the following: Modern chim (yin-chao-chin) (chung-shu chih) I Imown Ancient chim (chia chih) (hen-shu chin) The Huang-chung pitch's length of the Chin Dynasty is nine tsun of the ancient-chih, equivalent to 7.29 tsun of yin-chao [i.e. modern] chih. [The nine-base hen-shu-chih of Huang-Ti, equivalent

107 . 102 to 8.1 tsun of chia-chih, is also equal to 7.29 tsun of yin-chaochih.] (The "nine-base" hen-shu-chih -- Huang-Ti-chih -- contains ten tsun, with each tsun divided into nine fen.) On hsiao and dyi as representing the Huang-chung pitch pipe of ancient hen-shu-chih of nine tsun, equivalent to 7.29 tsun of yin-chao-chih, will produce the following pitches: (kun dyi) C) G F E D C B - -AN-= = - = = - -AM Pw M IM -- J=-- ww I 4 ) A I5 voth o ey~ (tong-hsiao) C yi-chih hole B A G F kung-chih hole E (hanging hole) sand-chih hole

108 103 The preceding illustrations demonstrate the pitches produced on hsiao stopped at kung-chih hole and dyi at shih-chih hole. Those are equivalent to modern western pitch of F [as a possible representation of the Huang-chung pitch]. However, using chung-shu-chih, equivalent to nine tsun of yin-chao-chih as the length of Huang-chung pitch pipe, the Huang-chung pitch will lie between yin-chih and song-chih holes on hsiao, or between kung-chih and fan-chih holes on dyi, and is approximately equal to C#. Emperor Kang Hsi of the Chin Dynasty adopted the ancient nine tsun hen-shu-chih for measuring the lu-pipe and, therefore, the Huangchung pitch is equivalent to the modern western F. The above-mentioned pipe instruments -- kun dyi and tong-hsiao -- are still employed today. Stopping all the holes of kun dyi, also called "hsiao-kungdyi," produces the pitch A. This A is the fundamental or finalis of the sol mode or hsiaokung-diao (/K\L j ) [akin to the anhemitonic mixolydian mode], relative to the [western] D-major scale [as might be shown as in the following example]. ~~Sol Ik do rye i t8?)

109 104 Stopping all the holes of tong-hsiao produces D which is a fifth lower [than the A tone] on kun-dyi. This will explain the fact that [between these two instruments], although the finger positions differ, the same pitch series are produced. [The preceding drawings showing the finger positions and their relative pitches on these two instruments should serve to illustrate this principle.] 1 1 Note: The above description is based on the contemporary kun flute. It is to be noted, however, that the fundamental tone of the ritual music in the ancient time is a semitone lower than the modern flute and, therefore, the ancient Huang-chung pitch should be E instead of F. According to various statementsin Ching-Ting-Ta-Chin-Whei-Dien's Document of the Chin Dynasty Imperial Ceremonies, A.D. 1818), the lu system during the Kang Hsi reign was still based on the process of san-fen-sun-i in producing the lengths of lu pipes. The diameter of every lu pipe is 2.74 fen. The following table gives all the lu pipes' lengths: (see next page) 11. This is in substitution for the pargraph omitted.

110 105 Length of Pitch Pipe Pitch Name Pitch Within Lower Octave The Proper Higher Octave Gamut Huang-chung ta-lu tai-tisu chia-chung ku-si chung-lu jui-ping ling-chung i-tse f, nan-lu wu-yi ying-chung

111 106 The unit in the above measurement is fen. It is to be noted that lengths of pipes whose pitches are an octave apart are in 1:2 ratio. [It is easily seen that] such [instrument sets will] not produce the twelve equal-tempered lu system. [Morever,] the traditional pipe instruments such as kun-dyi and tong-hsiao are illustrated with their holes placed equal distance one from the other. Therefore, these instruments were to be used in the transposition of ritual music, and players must rely on the special embouchure and fingering techniques. Such skill is one which not everyone is capable of mastering and, therefore, [in order to facilitate the performance], the traditional Chinese music is often played in G (ching-kung-diao, 6$ ) and D mode (hsiao-kung-diao). With recent creation of new instruments such as pan-pipe, plucked string instrument with semitone frets, a new type of flute with eleven holes, and the bowed stringed instruments which resemble their western counterparts, i.e. cello and double bass, the problem of transposition ceased to exist. It might even be said that contemporary Chinese music has adopted the western musical system. However, up to the present, the traditional Chinese music appears to employ only four modes: C, D, F, and G. Other modes, such as A, B, and E etc., are found only in the regional music. This [continued adherence to a limited modal possibilities] may be seen as a lingering effect of the Chin Dynasty music system. The fact that the tonal system of the Chin Dynasty is different

112 107 from the twelve equal-tempered system may be open to criticism. However, from the other perspective, it is precisely because of this difference in tonal system that a character peculiar to the modern Chinese music can be appreciated. For example, the hsi-pi (Nt, name of a popular tune in Peking opera) of pi-huang, a kind of Chinese opera) or the yueh music western ears] would sound out of tune. ) contains pitches which [to However, if these pieces were to be performed with "accurate" pitches, they would certainly lose their innate musical flavor and distinct characters. This may be regarded as one of the reasons why Chinese music has not completely been westernized. It has been all through the history that the object of the ruling court in establishing a music system was [for the performance of] ritual music. And treatises on tonal system such as Lu-Lu-Cheng-I often use the finger-hole names on hsiao and dyi to express the Huang-chung pitch. As hsiao and dyi are popular instruments among common people, [the reason for using these instruments in referring to Huang-chung pitch] might be to provide a means for easier acceptance by the populace. Morever, hsaio and dyi are capable of producing seven tones, and it is an impossibility for them to accomodate twelve I' lu-s. Illustration No. 38 in Ta-Chin-Whei-Dien gives illustrations of wind instruments such as tong-hsiao, dyi, ching, sheng, and hsun etc. -- all of which are shown with two different types -- "ku-si" and "chung-lu". The interval of tonal pattern between ku-si and chunglu is a semitone and, therefore, when combined, all twelve lu-s are

113 108 represented. Ku-si, the instrument with higher pitch series, was used in the yang month, while chung-lu was used in the yin month; that is, each of them is used on the different occasions. Although, there is the twelve lu-s system, in practice music still employs only seven tones. If ritual music is said to not employ the two altered tones, the music is essentially based on the five-tone scale pattern. The only difference is that the music performed in the yin months is a semitone higher than that in the yang months. WY The lu system has remained virtually unchanged since Emperor Kang Hsi of the Chin Dynasty revised it. In 1968, the Department of Culture of the Ministry of Education led a reform in the Confucian rituals. However, changes were brought about only in the ceremony, costumes, and the order of music; the musical system was not affected. Such a revised Confucius ritual music has been performed only at the Confucius Temple in Taipei city. However, the instruments were also tuned according to the western tonal system. The result, alas, is a performance of Chinese music in western style. The western influences, as can be detected in not only the subsequent arrival of equal-tempered tonal system formulated by Chu Tsai-Yu, the choice of the main wind instruments which are tuned a perfect fifth apart, but also the revision of notational system during the Kang Hsi era reflecting the concept of the western staff notation etc., brought the final demise of the ancient san-fen-sun-i method of tonal generation. On the other hand, as recent scholarship has

114 109 documented, there is not a significant difference between the tonal system of Kang Hsi era and the ancient Chou of ca. two millennia, B.C This is a condensation of the following four paragraphs; the abbreviation is done as these paragraphs provide little new or relevant material.

115 CHAPTER III SOME OBSERVATIONS ON THE HISTORY OF TONE GENERATION It has been observed that, over a millennium in Chinese ancient history, each generation produced a tonal system relying on a different measurement system, resulting in the fundamental tone Huang-chung which differs slightly from other system. Recently, Yang Yin-Liu produced a lu pipe through investigation of historical treatises, and has made a comparison of different fundamental Huang-chung pitches of various tone systems. From his work, Collected Essays On The History of Chinese Music ( ), is the following table: Dynasty Classification of Huang-chung Pitch Ratio Modern pitch Name Chou Late Chou Dynasty lu system F + Han Liu Hsin's lu system G1- Tsai Yong's bronze yueh E + little flute) lu Wei Tu Kwei's lu system #Fog- Shyun Hsu's lu system of the Jin G1- asty Dynasty 110

116 111 2 F I North- South Dynasty Song, Chi, Liang, and Chen Dynasties ll systems Emperor Liang Wu's lu G system Late-Wei, east-wei, and North D1+ Chin Dynasties lu systems Pre-North Chou lu system E + Late North Chou Dynasty lu system #F 1 1/ Early Kai-Huang era's lu system F Sui 111 Wan Po-Tsang's sui-chih lu ( IK( E + in the 15th year of Kai-Huang Ta-yueh lu system G - f1 Chen Kuan's lu system #F Popular music lu system A + Tang Chin- Shang lu system(407.7 G - "If 1 Wei Yen-Ling's lu system F + The fundamental tone of new musical scale of ritual music (ancient lu Cl- system)

117 Late Wang Pu's lu system G Chou Early Song Dynasty lu system (Wang Pu's lu system) G1- Emperor Tai;-;Chu, Chien-Teh's #F1 her-hsien lu ((1? 4 ) F.- Lee Chao's lu system in the Emperor Jen Chung Song 3' Practical lu system in the F1- Emperor Jen Chung 'I Old lu system in the Emperor F1 Jen Chung 3 Juan Yi and Hu Yuans' lu system in the Huang You year of Emperor Jen Chung 359.3#F Early Song Dynasty and late A 1 "yen-boo" lu system ( ) Early Song Dynasty to the Hsi- 1 Ning year of Emperor Shen Chung's F + "chiao-fan" lu system ( ) The Hsi-Ning Year of Emperor Shen Chung's Yang jei and Li chis' lu systems F'- a I ji

118 The Hsi-Ning year of Emperor Shen Chung's "chiao-fan" lu system F1+ Fang Chen's lu system in the D - Yuan You year of Emperor Jen Chung Song The fundamental tone of new scale of new scale of chiao-fan in the E + Yuan You year of Emperor Jen Chung Wei Han-Chin's lu system in the Chung Ning year of Emperor Hui D + Chung Liu Ping's lu system in the Ta Kuan and Cheng Her years of #D+ Emperor Hui Chung Tien Wei's lu system in the Hsuan her year of Emperor D 1 Hui Chung Yen-yueh's lu system after the Cheng her year of #D 1 Emperor Hui Chung Ta-yueh lu system ( ) in the Cheng Her year of Em eror Kao Chung D1+ Ching Yuan Ya-yueh's lu system Ming D +

119 114 Ming The fundamental tone onew scale 1 of tai-chung-dyi ( ) in A + the Ming Dynasty Chu Tsai-Yu's lu system #Dl+ Chin Kang Hsi's lu system F - In examining the above table, it can be observed that the Huang-chung pitch established for the ya-yueh in each generation lies in the register between D 1 to #Fl. Since it is said that the fundamental pitch approximated the register of human voice, and [the range of] human voice can be assumed to have remained [virtually the same throughout history], therefore, the ratio of the fundamental pitch could not have changed considerably. Additionally, [such limitation of human vocal register] is expressed by way of musical instruments and for notation of music. One additional consideration is that the courtly music emphasized plainness and solemnity [thus within the middle register]. To this day, there are still many eastern and western scholars investigating the register of Huang-chung pitch. However, most of these are based on the [tone system of] Chu Tsai-Yu of the Ming Dynasty or Kang Hsi's lu system in the Chin Dynasty. The notable ones are:

120 Hisao Tanabe ( \) a contemporary Japanese musicologist, used the nine tsun of the ancient chih as the length for Huang-chung pipe, with the opening diameter of 3.38 fen. This pitch is equal to the western pitch El. (vibration is 327 Hz) 2. Professor Eric von Hornbostel of German examined all the Chinese chronical treatises and determined that [the original music system of] the south-east Asia, Indonesia, and south America were derived from Chinese lu pipe system. He further stated that the length of Huang-chung pipe is 23 cm., producing the pitch OF1. However, Wang Kuang-Chi made further investigation and determined the fundamental pitch to be Fl. 3. M. Victor Mahillon, a president of the Royal Museum of Instruments of Belgium, produced Huang-chung pitch pipe and another pipes, one an octave higher and the other an octave lower, based on the measurement system of Chu Tsai-Yu's lu pipes. These pitches are equal to El, E2, and E3 4. Maurice Courant, a French scholar, in his book A Study of The History of Chinese Ritual Music (Y' ), gave Huang-chung pitch as El.

121 J. A. von Aalst, a Dutch scholar, in his book Chinese Music, stated that, in the eighteenth century, Chinese Huang-chung pitch was F. Additionally, he gave the standard frequency of Chinese Huangchung pitch as Hz, which is almost equal to D. Morever, he gave instruments yu-lou (' 0 ), sheng and dyi as examples for having the fundamental tone of D. 6. Professor Chuang Pen-Li examined all the ancient and modern treatises and also, in researching the ancient measurement of chih, used [the size of] ancient coins as basis for determining the measurement to produce lu pipes. According to his book A Study of Chinese Lu System ( he stated that the frequency of Huangchung pitch is 325 Hz which is almost equal to E1' Although these scholars offer different pitch standards for Huang-chung pitch, recent music theorists are in general identify Huang-chung pitch to be equivalent to C. This, however, is designated only to give a convenient system for comparison, because the fundamental tone of western music system is C. It may be said that various theories of tone system and their development are attempts at resolving the problem of melodic transposition. In this sense, the theory of tone generation can be seen as the earliest

122 117 and, at the same time, the primary and continuous concern in the entire history of Chinese music. Basically, theoretical process of ancient Chinese tone generation system is similar to the Pythagorean system, and both systems are related to the concept of ethos of music and numerical symbolism. Their purpose is to make music a means of representing the harmony between heaven and earth. The generative system in the calculation of Chinese tonal system is the application of the "Pythagorean method" which is based on the cycle of fifths. It should be recognized, however, that ancient Chinese employment of this system predates that in ancient Greek culture by at least several centuries. There have been a number of studies, particularly during the last decade, investigating the possible cultural and musical crossrelations bwteeen ancient Greece and ancient China, among them are those by F. Kuttner, and E. McClain.13 (See bibliography) This, while most intriguing and undoubtedly a worthy subject for comparative historical-musicological research, is beyond the scope of the present study. Suffice it to say, however, that a relation of tonal systems in the ancient civilized worlds of East and West did exist and perhaps as 13. Notable studies by these two inyestigators are the following: "A Musicological Interpretation of Twelve Lu-s in China's Traditional Tone System" (Ethnomusicology IX/l, 1965),"The Yell Bell of China and the Endless Search" (Music Educator's Journal, LIX/8, 1973), and "The Development of the Concept of Music in China's Early History" (Asian Music, 1/2, 1969), by Fritz Kuttner, and "Pythagorean Paper Holding: A Study in Tuning and Temperament" (The Mathematics Teacher, LXLLL/3, 1970), The Myth of Invariance: The origin of The Gods (New York: Nicolas Hays Ltd., 1976), and "Plato's Musical Cosmology" (Main Currents in Modern Thoughts, XXX/1, 1973), by Ernest McClain.

123 118 a much more intimate one than one is prone to realize. And if music is indeed a universal language, this common approach to the tonal system -- the adherence to the "san-fen-sun-i" principle -- may be regarded as one primary reason in producing that quality of universality in music, East and West.

124 APPENDIX Facsimile of Huang Ti-Pei's Perspectives of Chinese Music, Chapter III, SE.ction 1-11 (pp ) 119

125 120 u. it 0 - K' -jala..c A- '!k 51k,..79* 4, ti AIL,.. A T - t E k o 5 k A,. - t 4TJ,, 1 E! 4ry l3 T1- r sar,4o -iit -At O - A Q -- m-4 " TP X )sa A O _ M - 4 (4) ' p.9 oggfy&kiprm '15 i.- =c - i( TT% (51)

126 121 sta o 4-% 9% - A -Ir+. > A A > 0T -~ spt ar ' i e w s > * ie ti A r 0 > Tv* 4k aa r r k,4-lt T 4- i k+.4 0 A+ ktnr 0 +, > 1.LT, -..,0= t -&oj- A*v r-e N -i 5 5 t 55 >_ie(ao 5M U K4 Tj o itt& Ar MA *R A.og- W * A+++ A ( 52 )

127 (1+ )=60x 4 0 1x2 _111 A -)t A PA, - t - 4je~~ j% ~1~ ~M# a t (53)

128 123 T A) 0~~ kt~ ( Do Re Mi Sol La Do IRe Fa *-.-. m,i rf t L - } T g E T t- -+-fit. -: y -A a y A TC. (54 )

129 124 1 T 1 0O 01LYT5 0 t -s -.4 -jk'a - - lia d- s r --- e I _ M f I 4. Tr i t/ w*1t so- e0 (55 )

130 125 t A ( ~s4a U r r -, - ~ - -R * t -. k-, Al 3r, 4k jjt = ,AT*&.. ~ i*0eit M-4.f~t.4* - ip".ih. i mtog % 31 a - - a _ L -Tt P' Af ie T4 4A j qerg 7 TWT C r-.t ' y " ' - ''x - r t- -W r1 E- i-, + -4-'A t ~ 8' { ' rr 3Yt:& i..- 5&tJ, F -4 A--.L T ~ - it 1, A t ua, C. (56)

131 126 -A o10 (4- ' N2 IEAJAp +=A - 4T't o. A 4' # 'it. j~j~~fj0 ~-~r~1 ~-u-a om4 A% S AL.-. f-... r d T -4&+ 4 - A- '7 jo r & CA * & q -ll-. k- t -Z; El t: ~ -) A, -., ag a 2 u (57)

132 127 vfpt U T ~r*akt4l + i = t f4 i == =8.02 r r ==5, == 7.15 it = E-6 = 638 k = = = = f11= ==9.00 Vu4L ~- LtAL~ ~r 7g r!f*u j (58 )

133 - 128 I - - I I 2 I I 51: E3 * it-i &) 51 'I 8.42 jit 8.49 'ci 4,~ ~. ~t t*.. 1k r 4Lt 1 I 'a 4; Fr 7.58 it 4 7,11 t ~4:v~ -~5%: tt ~ i :3 ~ t Fr 54f6.01 'Zi% 5.62 Si.70 it 5.33 W5% : 5.36 S oo 4, i (+I -j 51 (x -4)t 38 (,1. -4) ('. -i) ll _ - 32 (.. - 4) 38 <- 4) 29 (.I -4i) 34 --t) 25 (' " I bmmm o [ I ri ot I k A 0 (59 )

134 o A- &N o 1 &. 0 Ir4 it r4k. ' :t *7 It-o L-LFrA1 4LT. L.. NI 3K K M Ast rr C rr -k,o ' -- TA. -F 3 T >4.E A w1 f -i4 '$ (60 )

135 Lw& O -K *0 : M( -7- '4% - 0 }.+ - r > T - - r a y 'T T.i- s A 'fjr ' ajk t o A 4. 4K' - 4 -j% 'T o Ta 4 4. A &J:--o J y*e J&, -J,- 4. '- TO N- TA 5 ir 44 (MANC o M 7T fa J As" -XWX 4- o "_ I694 ~djit krt is -4-ifAiE-WW tae - Mt5- (61)

136 131 k 8 i 9T r % J~ K 4Sot) D - I -- o x % 4 3 ;-4 I- TD A p T. $ t',. -- Ar -b 41 -.? 4q r AIL z- xt AA -A m i 6L41A-U 0 l A * _ 7 4-2f4,. in r,, 6 < 7C (62 )

137 132 XJ.J-2 vu R4%A 9 W AR~ T )00L~ yr, ". TT( 44%,AAA A 4A A W s PI< A A> All -<7 r0 na Ni A11-T6 4Mt 05 r 4- P- I.4mr T e 7 4$ "# t -k 44-0 (63 )

138 (- 5 F L 1 t i t, 41 Fr 0 tr aer IK y &$74 f i h C W"31- -OT ES 140, loo i+ ( 'o f75o2-4-.) Frj rut i1 A eit W * i. a S TLr A... >\j r..i. t-,$g (64)

139 % k ir ('% i A -IM 5 AA 0 A (4dZ. 3$ A A IL ~2.6 ~- ~ ~~zzi'2.5 I ~ICE. ' T 12.3 A ( 65 )

140 135.g. K g -t -- ii >$ 7~A~. II $ It r o & e Ar+=-A- 'A T T4*-AT4 D y s? +0434A v j9+j -& -YiF4, T r-* ~MNT 9 - X,.>ssg garr -J. 0 - ' T*,- LPI r'te " T o t 7o1&,s -4-. ' p-l + o&t4r1 'Ai*> fta%, ~ ~ ~ T~ jl A. I & x o.. ~-r ,- C.t L I/CTs- R < Ts...5. & fib- A k 0j 1-_/ A Ms :t ' rat T.T s ' (66)

141 ' 136 o fr Ng7 0 L 5k 4A.I 2 ji *1(C H JS W!(CHOL 4 - SON) K-.4 ~ % IEHRE VOM SCHALL -- t N &k $ ' >Q r * pad 44s0-14-&7k 4981em 0 p j g 4 ' G, A9 ' P 2 A45'Fkt fl 2 N rbit&- A k If.- % -- a 0 )-* & -l=440 A, A 0 5 -A.k o<dcc-4. n i471 L A0.IKJrGRAMM -N-(VIOLIN A $t rr 6,870 k t- 0 9 E x R2* L D (67 )

142 137 LAr( i& o,f~ii - r 1: x - A C & 2/( t id-w1 4 E- A t<4ln.s~&~~i -t- rt -N 1 l TE it - L 1 ' ' 5A Tti % J r 4 -i * G * - - A 1g, * o Ji.R - j (68)

143 138 T -6-4 : =-- f 0 Y- o * fs, 4 g r@e.t (4+3 4T. ) A o ) 4 4v - p 7 t '644- ) > -k{ o -t4 s I 4--. a' -f - 0 y ~ ~ ~ it o 'q AL-&3-~- --t --*(-r 3 o t 0 t- -t - - 4oI- 9it o4- -- o 9 (63-3)i7& T =9 (63-6)+7= ' (63-21) 7 = 6.O O -t IJ r. - <it- )4T (63--33)+7 = 4284 t " (69 )

144 139 4~kL~ I 4~;&T T 4 ( -t 63+7 =9.00 t=9.004 i 5 (63-3)=7 = (63-6) 7 =8.14 '8.O 0 (63-9) ,7.49 (63-12: 7 =7.28 > 'it 5.1 ' (63-15)7 = (63-18&7 = ' (6 3-21)+7=6.00 = (6 3-24)7 = J, (63-27)+7 = j-(63-30>7 = (63-33) _ (6-3 =.8 -,. (63-36)7 = ~& 3J;- ~~ 4 k. k rt T t0 % O A-7r,-,-"., gxt ( 70 )

145 ( 140 e F Tr ec _.U * - / e t & rem % o 'A sk 4K6 -I X 4 :n o JC~Ji 74 M.it%> w *C l T t - DN I. T v i 0 A -Tye O A A* 7 1 / ' C -E*# (71)

146 141 ft " la 4.. -Z, I*-,. 4t- HT ) -: 0 > 959- ) T * L" I0 Ti A~ ~ * I T > At. - gt %y,~ 'i 454: 54, 5t :.1 ' '. T '\, /3 MT- 9 4 irr 4o 17 A - l 1 - > it i aa F ~~L-1~' Jj4 J1. o Z..- t5 ( rf-i T -- )( 1% ( T '\1 r % 99 i 9's r t: i.. k 1 j.' T ry 0 t K = - T o s (72)

147 142 - " Y - of t r 4Lit '.- C +. - > o - I A ' ' A -T. 4. ~ ~ ~ &i ~ r rt 1 ta-i47 '(.00i 47 J i f 4f $ 51 i 4 A.i- + T,.Ad. 'k 3L oark& >. i A - 'IT 0 &14 j T - ' I & t 7-0, * n14ti~t1. T-( o 44 it) T o o- ra r ( 73 )

148 143 I I g l -; il i g> q.., '-g - - 4(f-6:g o -,09TE <0rb - -- l - I L ti K T I. T AT o e g-- $...- I~t it..[. J4 E,.. l (. 4 J.. 4 i(~~ ( ( > 0r-- -A4~.- 9- i-( ~, ( ( )-Tf (f 0g4 =- r r = g or-3 1 s.i 4~ 4,. -i9.00a 9.00' s "; il ( M. or - t j t $ity A 4k1-7 >7.-- Tt 4 t o. Ej Re So.l Sol La Re if.~ ~ ~~ it j.1... (27 R~~~~~~4 eto 0 o 5 ~l ~ $; ( 74 )

149 144 9A o 3 :i T = T ( ' )L )! o 0- t w o 4-7 >' t Ar-i 0 4,5* o wta jrm * " a _-I-.HHRNBOSTE L ( 75 )

150 A TI$ T TT 'k"& Tp >f? I;*--,.- IL %.J o L r -. qy-... o Ap Al v', - &J5teA.ISTORY OF KO EAN M4CM -$. r ir ''T i F ar *afd* AAEP KP *ou(a HISTORY OF KOREAN MUS IC) 7 l $ rr'd 4 <, :& 5t-*= - -L4V : S A AC 6 6$$ k 4 : h G #F F E #D D #C C Ao ArX * -- - ( 76 )

151 EI04 -A-N.t * 4 4.1*\ * 0r1 TJr, * ',,. ",(,-te -. fr ' )t B. -A& - -R it0 TXoMA 'M 'N -- i* (77)

152 147 * M -- J-54r...zi * > &. $o---ri p o4 5 d.'.ffr.- - I, 3 N2.454S 4 t CA -.a- *- 7%ro.a a&,$,rr T i N si* >---0 Jjlk 0 -F ug t -- *9- T " X,A.t..t A r 5: ( ~D-o) w4 3 o ( % Z 7 ' *'g ---- ' > i 0 (78 )

153 148 "---_-.. ( r Do Re Mi Sol La - - Ap ) (-Sit. ) 1..- (La() Do) -*g-. I r (#Fa ) +... >T (M i )5 (so, ) fo t /~s \ --- ( -jk- a..- s i T Er (~4Fa.S1 S0 )m -, * F~t aka ~LAJT6PI" firqra,.11! - 4) 0 IPA - g... 5 o $ ;fo r.)~ x(1+3)=79-91 w -1. A- -i379.91x3(1- T3)4s < (L = 54) 3. (4 i53.27x (1 + )= x( s5 9 <-.E y=48) 5. JT t 47.3sx(1+ 3)=63.13 All < «(. i 64 1 < -= ( # x (1-3.)=42.09 (79)

154 'r -++- n N-bT I- t - J i ( CT: i aar * 4xr& 9 SIt :it i BI,F, I I -K j.w - - (1 7 jr 1B I I I I B B BI B B B B B BI 1 B T4A& Br=.$4gi g B B -~i (80)

155 ) ~k... ~ 4 r 81. Do. c ~ - - ~- - ~~ Re I. 4 ( ) Mi cx: tl o6.v 13.~ E rJT 15. ( ) t 18. t -~~~~ :: :..: S-: ( ) Fa Sol ( 53.27) 50, La ( 47.35) S i ( 42.09) % Ti FN g pk-t o oi 0. -T y i :.A Br4 i7g?,.. ( 81).

156 151 if.aait*.it-1 0 N & 1 i i14%>* ~A~ W it00a,\,4#1 gao o & ' - J { tas 1 f :.1 s.t u t- -*- ' - ~-..P., Fr (82 )

157 152 p1 U 9 - \+ tj( Ax+ G1636~~ 4 - T Ot - o. o cj E'. r.- ri R " XA &!~o i.trp' 34. -za~ t.i4o kt -> 'yami N &t ~r +i 040 PAA - ()- _.- w 5-JM. IN 9 %1%0 AL - J f- i t- r. *, ;T '$- t''i - ~ r * rr 'I 4 o ~ ~ ~ ~ A.k -L kaaa,-1-l r ~ a- Ai A yr - :a 0 o" p. x & > rt-v *4%# -4i-r-r % (83)

158 153 =-) + '*-- '' ( MATTEO RICOL) ' -_ f i Z:-.( g L) ). 941T4-, - - t - o, 5}9-6 ) '. i42#--; I..4 4 F 0r'T 41 r m ti +- na 4-,-I -W--7 -t- C 18-Tr &t' 7 ilii- f 40 g-- -,- (PYTHAGORAS)..rg--oiip ' L3 T 1-~s'>i~ +-- $ T YTAGOA )- F (84 )

159 154 { - 4 T- -TC ( MARCO- POLO o T 75& fi. - 'off>7' ) o A i-y o L A It C (GENOA _- - J'.... RJA-.ir t- -M-' -4 ~-%pr41 ili gg o 4 p' A ll o. I'* - o~~~~~~~~~4 -Pal A, TM 44 *t W&T- 4 - Pret# -k ALk.to o L' -ot 4T- it7p, f.r o y.- <jq " 4 - '7 T /j 7 ''r A A J-' j T-44it 4 1% t r I, k A ~ ~ ~ ~ - A -%> -tka.il3 T 4 - AW.TA I~7 %ONA e a 4!k Wts.+ I k 1 l DA1I- fft / -; 0Fi I L A~ *W45sr4:rrA&-- t.;sm rll < "A94A 4.%#16 %.A% m ~l f %rk a E4 ;5, *. Z., 14-sk>1 #k- P' 17 ( 85 )

160 i 155 loo 0 TH i it*jtlu% t o * T$OrLyat a A fr a.;t -- A.f{---5A%- 1*A<. o 'ot ) - Vo - - ti - ' p 9+ : 9- - A 4- as.$,, J+ ) T r 4-.jo * 7j.-.?r 7 l 10 f10 + = pff so 8 f*& 1T1A.414 **# ( 86 )

161 ^ta + - * Am - - t A=-o ~~'A"r - V,*JM i' & >1 - g X 10.: ) $ e a T.*" i54 A4 i o892071i xi 0 X ] ) K Z r" r -o>;\ &T& 1-1 %.{-}{, i T -5.-,,.TN i '- C." ) - ( >-41 *.t - 0-, S. A!I E 41;- > iti - y *,: *.. 5:g WL,4- O PIAT j ;s 0a nm-a (87)

162 C ' is k A It f6 f , it (i.. Ac & 'ATi E i ' T *T-*. 1. T f 1, 17 '---- j ( I * T- i t C T ( T q.e i * i ) ---Tq-> -- ' '7 ( t ) (88)

163 158 TT 0 o -4 r, Al 6 "5- nq Fo (- 0, s-" -o R ) X 1,000,000, ,463, ( *) (, J X 1,000,000, , 302, ; - (89)

164 159 A j L.059rT, t r 1 rt o - ~ 1 -A. I 52. TE..L t J t[ PAt2 2 > )&K- A& r'- f I o- IL2 2 Tt. it + t T. f I R-7 X118&--g%1% 1 il -- ; k,i i rt JFrA T il& =-4115 A, ' t Tit T.. A A2 A J1 5x 4AT D i "D2 *Ni.& KK>! Al1= 1A2==42- Al D12 D1 22 A DDi 2 = 2 -KK A 2 D-2 D 2 A i _ 2 2 A K - ( ) = A 2 5 (90)

165 160.-.' T' A li 6 i~ = JL81j i i ry; > it att... i T -ic I A*' El i & E % > F 31; T- I ' PA W -41->, i *r o91 * No T O N l# '7 EP#i toi i 7~~~~~~~. 4 -[$g&>k%& Y-( -1-% -M o *----- ] A & g} $ ) O' km I e > -T.-.. { -J- m A D ABCD44 I ' 4VAM-Jo AB8,.b, BC~r"*6) 0* %-y7'aac&. A 4A C2 =9f ~ A j 1 5,. 4-. L )j 5 ~rfy= B 7 9 *> C o.. %. f4 5 0., 3k 7 =.. Y - - L pt&-.i; (91)

166 JL if- X Nv m 70 ' c T 4 L Ti - -x L(I-.t , S *, ' # M At f it AL * #i * i y it $ I j { 7 f W T A t ,804 1' f#, A4' ( 92)