Who is Zhu Zaiyu 朱载堉 (1536–1611), and why is he important in the field of pre-modern music theory? Zhu was a prince, official, musician, mathematician, and astronomer of the Ming dynasty (1368–1644). Apart from his unusual life story (e.g., Peng 2019, pp. 89–111), he is best known in (global) music history for his early discoveries in the development of equal temperament (e.g., Cho 2003). Zhu Zaiyu came up with a highly interesting solution to the mathematical problem of how to divide an octaveFootnote 1 into twelve equally distributed semitones,Footnote 2 namely—to put it in terms of our modern definition of ‘equal temperament’—that all twelve tones should have the same “distance” from their respective neighboring tones.Footnote 3 Since Zhu’s calculation method represents not only a revolutionary break with the tradition, but also a true innovation in the history of Chinese music theory in this regard (Peng 2019, p. 49), one might say that his approach to equal temperament represents the “final climax of [pre-modern Chinese] acoustic and musical theory” (Needham and Robinson 1962, p. 128, insertion BP), paralleling or even preceding the discovery of equal temperament in Europe (Needham and Robinson 1962; Kuttner 1975; Dai 1985).

Zhu explained his ideas in Lüxue Xinshuo 律呂新說 (New Treatise on the Doctrine of the Laws of Tuning), the introduction to which dates to the year 1584. It later became a two-volume section of the 19-volume (in the 1606-edition) Yuelü Quanshu 樂律全書 (Comprehensive Writings on the Laws of Music)—like other related works by Zhu: Lülü Jingyi 律呂精義 (The Essential Meaning of Musical Tuning, six volumes, introduction printed in 1596) and Suanxue Xinshuo 算學新說 (New Treatise on the Doctrine of Calculation, one volume, printed in 1603). The original edition of Yuelü Quanshu began in 1595 and was completed in 1606 (Zhu 1606; Zhu 1787–1795; see also Peng 2019, pp. 8, 113, 286). Zhu Zaiyu’s achievements in music theory were nothing short of groundbreaking (Dai 1986).

It is a kind of “irony” of Chinese cultural history that, as historical events unfolded, Zhu’s research was denied the profound impact it could have had on the development of music in China. This was due to political reasons, namely the fall of the Ming dynasty (1368–1644) and the rejection of the ideas of the Ming prince under the Qing (1644–1911/12). Another reason was the general conservatism, or rather backwardness with regard to innovative ideas also in the field of music theory during this last imperial dynasty (Peng 2019, pp. 62–63). Although at least one scholar during the Qing dynasty seems to have recognized the value of Zhu’s work (64–65), it was not until the twentieth century as well as under the influence and initially also in the direct context of Western scholarship in EuropeFootnote 4 that Chinese researchers started to become interested in Zhu Zaiyu’s works again (72–77, 82–88). In his homeland, Zhu’s theories had been rejected or received little attention (in theory and practice) until the early 1950s (Yang 1952).

It was a much earlier Western discourse on some of Zhu’s music-theoretical approaches that paved the way for Western and, on this basis, much later for Chinese scholars again to reinvestigate the ideas of Zhu Zaiyu: Since the end of the seventeenth century, a few European Jesuit missionaries to China had shown an interest in Chinese court music. They had played the role of scientists at the Chinese court of the Qing, and one of them, actually the last surviving Jesuit missionary to China at the time, discovered that Zhu’s theories were of extraordinary value: To this day, it is recognized in Chinese and Western discourse that the French Jesuit missionary Joseph-Marie Amiot (1718–1793) was the first scholar to make Zhu Zaiyu and aspects of his music theory known in Europe. From the late eighteenth century to the 1920s, and then again from the 1960s until the 1980s, Zhu Zaiyu and his theories became the object of Western scholarly attention in the field of Chinese music—which, of course, represented a very specialized niche of academic research.

In this sense, the research question, or rather the underlying knowledge interest of this article, can be formulated as follows: What is the basic historical trajectory of Zhu Zaiyu’s reception in French, German, and Anglophone contexts? The present article can be understood as a kind of groundwork regarding the question of the reception history of Zhu’s music-theoretical thoughts in the West. The scope of the investigation is limited to the most important stages and Western scholars. The history of the modern reception by Chinese scholars is not covered here and will be treated in another (complementary) research publication. Aspects of popular or non-academic discourses that mention Zhu Zaiyu in the West, for example in popular journals or newspapers, will not be addressed here.

I begin this investigation with a brief discussion on “Joseph-Marie Amiot, his Reception of Zhu Zaiyu’s work, and related commentaries by Pierre-Joseph Roussier from the late 1770s.” The second section is entitled “Zhu Zaiyu’s music-theoretical thoughts were mentioned and briefly discussed in German scholarship from the 1780s to the 1920s” and provides the basic elements and characteristics of this discourse. The third section complements the second one, namely in view of the “Consolidation and improvement of the reception of Zhu Zaiyu’s music theory in the Anglophone world from the 1940s to around 1980.” Finally, “Conclusion and outlook” offers a critical reflection on the history of the Western reception of Zhu’s theory and a further outlook on how to proceed further in possible contexts of future research.

Joseph-Marie Amiot, his reception of Zhu Zaiyu’s work, and related commentaries by Pierre-Joseph Roussier from the late 1770s

The eighteenth century was a time when Chinese art and craftsmanship were in great demand in Europe (e.g., Wang 2021). It fueled entire industries in China (e.g., Kroes 2007). Some of the Jesuit missionaries in China were eager to send information about Chinese music back to Europe for further study by European scholars. Joseph-Marie Amiot was not the first to mention Chinese music in the remarkable historical campaign of these scholars to spread Chinese knowledge and culture to the West. It is generally assumed that Claude-François Ménestrier (1631–1705) was the first to raise the subject of Chinese music in this context in 1681. In the first half of the eighteenth century, there were others who paid attention to Chinese music theory and practice: Joseph de Prémare (1666–1736), Jean-Baqtiste Du Halde (1674–1743), and Karel Slavíček (1678–1735).

Due to the lack of any recording technology, it was of course impossible to preserve any audio material directly. And because of the great distances involved and still technologically unadvanced mobility of the time, it was not possible to send musicians and their original instruments to Europe for a concert performance. The early (Jesuit) musicologists in China were only able to provide their summaries on aspects of Chinese music theory (in the form of letters), or translated books on aspects of Chinese music, scores, paintings, and some musical instruments to Europe. However, even though their interpretations of Chinese music are riddled with errors from today’s point of view, these early pioneers showed a strong interest in the musical arts of China and thus laid important foundations or provided starting points for later Western scholarship in this direction.Footnote 5

Amiot’s Mémoire sur la musique des Chinois, tant anciens que modernes, published in 1779 and again in 1780 (as a second edition in the sixth volume of the Mémoires concernant l ̓histoire, les sciences, les arts, les mœrs, les usages &c. des Chinois, par les missionnaires de Pekin), was the first comprehensive, systematic, and detailed introduction to Chinese music in a Western language (Amiot 1779, 1780).

A few decades earlier, Amiot had translated the Chinese musicologist Li Guangdi’s 李光地 (1642–1718) Guyue Jingzhuan 古樂經傳 (Classics of Ancient Music) into French. The manuscript, now considered lost (Picard et Amiot 2023, p. 2), was then sent to France in 1754.Footnote 6 Amiot’s initial motivation was to clarify the misconceptions of other French scholars about Chinese music at the time and to convey the correct information about it (Chen 2013, pp. 42–89). It is important to note that this translation of the Guyue Jingzhuan 古樂經傳 has often been confused with Amiot’s much later Mémoire sur la musique des Chinois, which builds on the theory of Zhu Zaiyu. Also in 1754, or shortly thereafter, Amiot had sent a second manuscript discussing the contemporary system of Chinese music. It is entitled De la Musique Moderne des Chinois. It was rediscovered at the end of the twentieth century and is now available in electronic form and in the form of a critical edition (Amiot [1754 or later]; Picard et Amiot 2023).

The work in question here, Mémoire sur la musique des Chinois, consists of two parts. In the first part, Amiot provides a rather sketchy and incomplete history of Chinese music, including a classification of the eight types of Chinese musical instruments. In the section on silk-stringed instruments, he presents in particular Zhu Zaiyu’s theories on the guqin 古琴, a kind of ancient Chinese zither.Footnote 7 He also attempts to compare Chinese instruments with those of other civilizations. For Amiot, the Chinese instruments, which differ from European forms, are evidence of the long history of Chinese music and its parallel cultural evolution with Western music.

In the second part, Amiot attempts to systematize the vast and complex system of music theory in Chinese music. It should be noted, however, that although Amiot played the cembalo and flute, he does not seem to have been well versed in the intricacies of music theory. The text shows that he had great difficulty in expressing the profound and complex terminology of Chinese music theory—which was completely alien to European scholars at the time—accurately in his contemporary French. Another possibility is that Amiot wanted to preserve as much as possible the original perspective of the conceptual system of Chinese music theory by avoiding the use of Western musical concepts and their superimposition on the original conceptual system.

However, even if this possibility is true, the ambiguity resulting from Amiot’s difficult way of writing has caused misunderstandings in the subsequent reception. In particular, Amiot missed the central aspect of Zhu Zaiyu’s attempt, namely (1) his development of a twelve-tone system based on the equal temperament and (2) his establishment of a completely new method of calculation that breaks with the traditional method of calculating the length of the pitch pipes of all twelve tones. The older method, which Zhu breaks with, is called the ‘law of adding or subtracting a third’ (sanfen sunyifa 三分損益法) (Peng 2019, p. 179). Zhu considered it imprecise (pp. 49, 180).

In the second section of Amiot’s work we also find some additional notes by the French music theorist Pierre-Joseph Roussier (1716–1792). He had reviewed and edited Amiot’s manuscript. Although Amiot knew that Roussier did not knew Chinese and was a proponent of the idea that ancient Egyptian musical tradition preceded that of China and was also the origin of all music theory, Amiot personally asked Roussier to proofread the book: Aside from his conviction of Egyptian origins, Roussier was a great admirer of Chinese civilization (Godwin 1995, p. 31), and he knew of the ‘law of adding or subtracting a third’ (sanfen sunyifa 三分損益法) in China, which both scholars identified with ‘la Progression Triple’ that Roussier had earlier identified as a core mathematical principle for deriving the diatonic scale.Footnote 8 It was Roussier’s “obsession […] to prove the validity of the triple progression for both ancient and modern music” (p. 32). It is also a kind of “irony” in the history of the reception of Zhu’s ideas on equal temperament that Amiot, who was unaware of Zhu Zaiyu’s intention to create an equal temperament tone system, invited an editor who was the greatest fan of the triple progression and who propagated “the evils of equal temperament” (p. 31).

Amiot’s decision to include Roussier is also indicative of his involvement in the contemporary European debate on the origins of music. Amiot had unexpectedly received Roussier’s new book, Mémoire sur la musique des anciens, which had been sent to him from France to Beijing in 1774 (Picard et Amiot 2023, p. 6). In this book, Roussier proposed, from a Pythagorean point of view, that music must have originated in ancient Egypt and Greece (Peng 2019, p. 67). Amiot, on the other hand, based on his knowledge of Chinese music, then proposed that the earliest origins of music should be sought in China, that the Chinese system of twelve tones in an octave had been invented even earlier than in ancient Egypt or Greece, and that it was possible that Greek music had been influenced by Chinese music theory.

One must assume that Amiot wanted Roussier to review and edit Mémoire sur la musique des Chinois not only because of their shared passion for the idea of the ‘triple progression,’ but also to convince him to accept his arguments for an ancient origin of music theory in China (Chen 2013, p. 96).

The music-theoretical aspects of Amiot’s treatise are mainly based on a selection of content from Zhu Zaiyu’s Yuelu Quanshu 樂律全書 (Comprehensive Writings on the Laws of Music), but he omits the most important part of this 19-volume work: the mathematical method by which Zhu Zaiyu calculated the equal temperament. Amiot did not understand the underlying algorithm that Zhu had provided in his work. Instead, he simply listed Zhu’s calculations, that is, the various data of pitch pipes to produce the respective tones, as an improvement of the older calculation method. Although Roussier’s comments did not directly refer to Zhu Zaiyu’s original idea of equal temperament in terms of his understanding of his xinfa milü 新法密率 (‘new law of precise division’),Footnote 9 he saw through Zhu’s calculations that the resulting semitones lead to an equal temperament (Amiot 1780, p. 153). It should be noted that it was Roussier, not Amiot, who at least dimly realized that Zhu’s original theory of milü 密率 (‘precise division’) was directed at the problem of creating an equal temperament.

However, Roussier was generally not fond of the idea of equal temperament in music, and his other annotations and his criticism of what he read through the lens of Amiot’s already misleading assumptions created additional misunderstandings in the subsequent history of the reception of Zhu’s ideas in the West:

Although Roussier seems to have realized that Zhu was implying a theory of equal temperament, he pieced together a series of implausible “explanations” to refute Zhu’s (originally plausible!) theory of milü 密率, while trying to relate to Amiot’s misleading statements: That is to say that while Amiot himself had not realized that Zhu’s theory implied equal temperament, and, based on his own views, had misinterpreted (in a rather accommodating way) the nature of the twelve pitch pipes and also the method of calculating the length of each pitch pipe, which Zhu had conceptualized as the twelve semitones of an equal temperament (Amiot 1780, pp. 85–88, 120), Roussier did not help to clarify the matter either—nor do his further comments correspond to Zhu’s original (and plausible) views (Peng 2019, pp. 70–71).

One can speculate that Roussier’s “hunch” of an equal temperament system, that he might have suspected from the materials provided by Amiot—that is, a system which he rejected—combined with Amiot’s erroneous assumption that Zhu merely wanted to modify Roussier’s “sanctified” triple progression approach, confused the commentator Roussier and also caused him to take a rather disapproving stance. According to the correct observation by Albert von Thimus (1806–1878), Amiot had claimed that Zhu, in pointing out the inadequacy of calculating musical ratios using the traditional progressions of the twofold and threefold, had considered another method of the ancients (Thimus 1868, p. 311), who “might have used another progression to supplement and correct the triple progression” (Amiot quoted in Thimus 1868, p. 311, tr. BP).

This statement aroused to a high degree the annoyance of Roussier, who raved to the point of eccentricity about the exclusive justification of the triple progression. He expressed his displeasure in long notes on pages 92, 116, and 117 of Amiot’s book, which he had edited. (Thimus 1868, p. 311, n.**, tr. BP)

In addition to the (misleading) introduction of aspects of Zhu’s music theory and elements of the thought of the aforementioned Li Guangdi, Amiot’s original handwritten materials had also contained some information on Chinese musical performances that found their way into the printed Mémoire sur la musique des Chinois, such as the score of the “Chuxian Yuezhang—Sihuang Xianzu 初獻樂章—思皇先祖” (“First Offer Musical Segment—Thinking of the Ancestral Emperor Huang”) from Zhu Zaiyu’s Lüxue Xinshuo 律呂新說 (New Treatise on the Doctrine of the Laws of Tuning), and there are also illustrations of musical dances during rituals (see also Wu 2008).

Zhu Zaiyu’s music-theoretical thoughts were mentioned and briefly discussed in German scholarship from the 1780’s to the 1920’s

According to the information available to the author, the first mention of Zhu Zaiyu in contemporary German-speaking countries dates back to 1784. Johann Nikolaus Forkel (1749–1818) was one of the founders of German music historiography. During his time as head of the music department of the University of Göttingen, he published the Musikalischer Almanach für Deutschland auf das Jahr 1784 (Musical Almanac for Germany of the Year 1784), a collection of the most important and up-to-date musical knowledge of his time and cultural environment. In this 1784 edition, Forkel published a chapter “Von der Musik der Chineser [sic]” (“On the Music of the Chinese”) based on Amiot’s work (Forkel 1784, pp. 233–274). Forkel himself did not do much research on Chinese music, so the content of this text is merely a kind of summary of the main points of Amiot’s treatise.

Forke especially emphasizes the influence of Zhu Zaiyu on Chinese music:

Finally, Prince Zaiyu appeared. With the support of all the skillful people in his kingdom, he restored music to its former glory. He also restored the ancient music to its original form. He introduced the 36 pipes arranged in chromatic order in three heights, namely bass, alto, and soprano. He believed that he was the one who had mastered the true musical sound of ancient music (Forkel 1784, p. 245, tr. BP).

After Forkel’s opening, the subject of Zhu Zaiyu and Chinese music remained largely silent in the German-speaking world for more than 40 years. During this period, we find only a few minor articles mentioning Chinese music with passing references to Zhu Zaiyu.

The topic was revived by the article “Chinesische Musik” (“Chinese Music”), written by the musicologist Gottfried Wilhelm Fink (1783–1846, University of Leipzig). It was published in 1826 in his work Allgemeine Enzyklopädie der Wissenschaften und Künste in alphabetischer Folge (General Encyclopedia of Sciences and Arts in Alphabetical Order). Fink’s interpretation of Amiot is very precise and detailed. He not only explains the content of Amiot’s work, but also tries to render Amiot’s often rather vague and ambiguous descriptions into German as clearly and precisely as possible (Fink 1826).

The interest in Zhu Zaiyu among German scholars reached its peak a few decades later, namely in the 1860s. With the widespread acceptance of anthropological research methods in the Humboldtian educational system, a stronger interest in non-European traditional music had developed. However, during this period scholars generally treated traditional Chinese music as an ancient but simple and archaic musical tradition, which was a misleading perspective. They associated it with ancient Egyptian and Greek music, and a number of theoretical comparisons were developed.

This approach was in itself inappropriate. After all, ancient Egyptian and Greek music were “dead” historical musical cultures that existed only in the realm of theoretical research. The ancient music of Egypt or Hellas was no longer performed or practiced; it was not part of a real contemporary musical culture. At that time, traditional Chinese music was still a living musical culture to a considerable extent, and it had undergone a complex historical development. Moreover, Egyptian and Greek music can be regarded as the historical foundations of later music-historical developments in the European history of music. Chinese music had developed independently of Western music and its historical foundations and the basic music-theoretical discourses that were involved in this process.

Scholars of the time, who had limited information and were unable to read Chinese sources, often overlooked the historical development of Chinese music and its relationship to contemporary Chinese music theory and interpretation. In analogy to Hegel’s famous verdict in the history of philosophy, Chinese music was treated as an allegedly static music-historical phenomenon. This has led to many misunderstandings.

Although the name ‘Zhu Zaiyu’ appeared frequently in various treatises, the texts of these scholars were still mostly based on Amiot’s vague descriptions and sometimes misleading interpretation of Zhu, on Roussier’s speculative and disapproving annotations, and the previous references in the German language (which were also based on Amiot). This inevitably led to many misinterpretations, and the discourse did not really get going or come to fruition. In particular, the often merely phonetic transliteration of technical terms from the original Chinese in Amiot’s work was a major obstacle to an adequate understanding of Zhu’s thought by later generations.

August Wilhelm Ambros (1819–1876), a leading music critic of his time who was also a composer, wrote a three-volume work on the history of music. In the first volume, Geschichte der Musik: Die ersten Anfänge der Tonkunst; Die Musik der antiken Welt (History of Music: The First Beginnings of the Art of Sound; The Music of the Ancient World, 1862), Ambros considers Chinese music to be a historical musical culture similar to that of ancient Greece (Ambros 1862, p. 20). Again, Chinese music culture is misrepresented as historyless. Ambros erroneously believed that only pentatonic, that is, five-tone scales existed in ancient China, and that it was only thanks to Zhu Zaiyu that a seven-tone scale was finally introduced in the seventeenth century.

This is a misunderstanding resulting from Amiot’s presentation. The classical work Guoyu 國語, written around the fifth or fourth century BCE, already mentions a twelve-tone system. Although nothing is known about the idea of equal temperament at this early stage, it is known that it was the reservoir not only for five-tone systems but also for seven-tone systems. These can be traced to the text of the Huainanzi 淮南子 (c. 139 BCE). Such seven-tone systems (as well as the pentatonic systems) could also be transposed along the twelve-tone cycle, the tones of which were thought of in analogy to the twelve months of the calendar or the twelve double hours of the day (Peng 2019, p. 75, n. 209, n. 210, etc.).

From today’s perspective, another problem in the reception of Chinese music theory in German musicology was that the concept of musical scales of tones (“ascending” or “descending,” that is, sequences of tones going “up” or “down” in successive “steps”) in the sense of ancient Greek and modern Western music theory did not exist. Among other reasons, which I have described in more detail in Peng (2019), this is why I use the terms ‘five-tone system’ or ‘seven-tone system’ instead of ‘scale’ here. In their original Chinese context, these tone systems were seen as analogous to closed circles instead of scales or “ladders” or “steps” (see also Peng 2019, pp. 239–242). Ambros was unaware of this, and his theory overlooks and ignores the original Chinese framework and these differences, and in some ways, and unintentionally, leads to a Eurocentric appropriation of the Chinese materials.

A respected historian of his time, Ambros’s presentation somewhat misdirected the subsequent discourse of German scholars. Among these was Hermann von Helmholtz (1821–1894), who was undoubtedly the most influential figure in the dissemination Zhu Zaiyu’s story during this period. One of the most renowned physicists of his time, he wrote an influential work on acoustics, Die Lehre von den Tonempfindungen als physiologische Grundlage für die Theorie der Musik (The Doctrine of Sound Sensations as a Physiological Basis for the Theory of Music, 1863), while teaching at the University of Heidelberg. In the chapter “Die Tonalität der homophonen Musik” (“The Tonality of Homophonic Music”), he refers to the pentatonic scale in Chinese music, and it is unfortunate that Helmholtz was also misled into regarding Zhu Zaiyu as the originator of the seven-tone “scale” (or rather the seven-tone system, as mentioned above), and that he believed it to be based on a kind of mean-tone temperament (in which adjacent tones are not exactly the same distance apart), rather than the equal temperament that Zhu Zaiyu had introduced in his day.

Helmholtz writes:

Among the Chinese, a prince named Tsay-yu is said to have introduced the [heptatonic, that is, the seven-tone scale] in the face of strong opposition from conservative musicians, and also the division of the octave into twelve semitones; the transpositions of the scales were found by these intelligent and skillful people, but the melodies recorded by travelers are mostly of the five-tone scale. (Helmholtz 1863, p. 397, tr. and insertion BP)

This narrative is consistent with that of the other German scholars who preceded Helmholtz in this matter. As mentioned, the twelve-tone system can be traced back to Chinese antiquity.

Helmholtz’s book became very well known in academic circles and was quickly translated into several languages. It circulated in Europe and America within a few years. Although his work contained only a few remarks on Chinese music and Zhu Zaiyu, and only borrowed from earlier scholars in this regard, Zhu Zaiyu became widely known as a representative of Chinese music and attracted the attention of many scholars. The problem here was the misattribution of innovativeness in the sense of an alleged introduction of the twelve-tone system and the seven-tone system by Zhu, while Zhu’s true innovative achievement, that is, his realization of an equal temperament tuning system and his completely new calculation method in this regard, was overlooked.

An example of the strong influence of Helmholtz’s Zhu Zaiyu reception is the book Die Kunstmusik in ihrem Principe, ihrer Entwicklung und ihrer Consequenz (Art Music with regard to its Principle, its Development and its Implications, 1882). It was written as a dissertation by the music theorist and composer Anton Krisper (1858–1914), who was a close friend of the composer Gustav Mahler (1860–1911). In this book, Krisper attempts to classify Chinese music, represented for him by Zhu Zaiyu (Krisper 1882, pp. 38–42), as “simple music” (einfache Musik) (1882, p. 35) which, in his view, and together with ancient Greek music as well as the “simple,” that is, homophonic, music of many other peoples, was to be understood from an allegedly more developed perspective of the contemporary European “chord music” (Akkordmusik) (1882, pp. 97–98) and as being theoretically compatible with it.

In his analysis, Krisper follows Helmholtz’s argument that all ancient music that he discusses in the sections of his work—be it Chinese, ancient Greek, Indian, or Persian/Arabic music—is based on a very similar theoretical foundation, namely the circle of intervals of fifths (1882, pp. 37–40). In Krisper’s view, all the (allegedly) “simple” non-European music is perceived as a preliminary stage that can be absorbed into the European music-cultural complex. Krisper is unaware of the aforementioned differences in the theoretical understanding of music in China and Europe. After Krisper, his student Hugo Riemann (1849–1919), the famous music historian and theoretician, also referred to Krisper’s views in his Katechismus der Musikgeschichte (Catechism of the History of Music, 1909) (Riemann 1909, pp. 68–70).

Guido Adler (1855–1941), one of the founders of Viennese musicology, also refers to Chinese music and to Zhu Zaiyu in his Handbuch der Musikgeschichte (Handbook of the History of Music, 1924). Based on his music-anthropological studies, he places Chinese music in the contemporary cultural category of the “primitive peoples” of East Asia. He incorrectly identifies Zhu Zaiyu’s birth date as before the birth of Christ and falsely declares Zhu Zaiyu to be the founder of ancient Chinese music (Adler 1924, p. 13). With Adler, the German discourse on Zhu Zaiyu came to an end—which, of course, also has to be seen in the context of the decline of classical Chinese music at that time:

When the fabulous performers of the imperial court disbanded and became inactive in 1911 after the abdication of the last dynasty, it took less than fifteen years for a superb tradition of various performing arts to disappear. According to those still alive who witnessed these court offerings before 1911, there is really no comparison possible between the prevailing standards then and today, even considering the famous and internationally acclaimed Peking Opera Company of the 1950’s and 1960’s. (Kuttner 1973b, p. 69)

Finally, I would like to direct the attention to the German philosopher and private scholar Albert von Thimus (1806–1878), who took note not only of ancient Chinese musical thought and various sources in this regard, but also of Zhu Zaiyu in particular. Thimus stands out somehow, and he was not connected with the rest of the German Zhu Zaiyu discourse of the nineteenth century.

In his two-volume opus magnus Die harmonikale Symbolik des Alterthums (The Harmonic Symbolism of Antiquity, 1868), Thimus refers to Zhu Zaiyu’s theory as a kind of representative of Chinese harmony theory (Thimus 1868, pp. 306, 311). More than other scholars, he focuses on the connection between Zhu Zaiyu’s music-theoretical thoughts, their general contexts in Chinese music and its historical theoretical foundations, and Chinese philosophy, numerology, and occultism—namely, as the basic material for his comprehensive approach and argument that various (in his view crucial) ancient civilizations had all developed systematic theories of cosmic harmony in different but comparable or even compatible ways. He appears to be incredibly well-informed for an academic outsider, and he even seems to have worked with original sources as well. From a discourse-historical perspective, Albert von Thimus also correctly describes the aforementioned reason for Roussier’s refutation of Zhu’s approach, namely in the context of the (misleading) interpretation or presentation by Amiot (p. 311).

In addition to the scholarly discourse, references to Zhu Zaiyu were also made in various dictionaries, popular science articles, and even tabloids during this period. These merely drew from the above-mentioned academic discussions and do not fall within the scope of the present investigation.

Consolidation and improvement of the reception of Zhu Zaiyu’s music theory in the Anglophone world from the 1940s to about 1980

Between the 1940s and the 1980s, two Western scholars made notable contributions to the field of modern Zhu Zaiyu studies. One was the British educator and musicologist Kenneth G. Robinson (b.1917, year of death unknown). He wrote the first Western monograph on Zhu Zaiyu’s theory, and he was the first Western scholar since Amiot to study Zhu Zaiyu’s ideas directly from the original Chinese publications (Bao and Wang 2008). The other researcher is the Jewish-German-American musicologist, music archeologist, and anthropologist Fritz A. Kuttner (1903–1991), who, after being forced to flee from the Nazis in 1939 (e.g., Kuttner 1989, p. 9; Messmer 2012, p. 193), had lived in exile in Shanghai. He also played a role in the modern Chinese music history during the ten years of his stay and before finally emigrating to the United States in 1949.

What distinguishes these scholars from the earlier German-language discourse, which had come to a standstill during the 1920s, is that they broke away from Amiot’s influence and were the first to conduct independent research based on Chinese sources. They became the first Western researchers to overcome Amiot’s and Roussier’s misinterpretations, namely the misleading idea that Zhu Zaiyu’s system of calculation and tuning merely represented a continuation of the ancient method of the ‘law of adding or subtracting a third’ (sanfen sunyifa 三分損益法), or that it implies some kind of mean-tone temperament, etc. They discovered the truly innovative aspects of Zhu’s music theory in its historical context.

Robinson received his doctorate from Oxford University in 1948. The original title of his dissertation is A Critical Study of Ju Dzai-yü’s Account of the System of the Lü-lü or Twelve Musical Tubes in Ancient China (Robinson 1948). In 1980, it was finally published in Germany in a modified form and under the title A Critical Study of Chu Tsai-yü’s Contribution to the Theory of Equal Temperament in Chinese Music (Robinson 1980). Robinson’s most important publication is the chapter on “Sound (Acoustics),” which was published as a special contribution to the physics subsection of Joseph Needham’s multi-volume work Science and Civilisation in China in 1962 (Needham and Robinson 1962, pp. 126–228). Robinson also co-authored an entry in the Dictionary of Ming Biography, 1368–1644 with Chaoying Fang (1908–1985), a well-known American historian of the Ming and Qing dynasties. Here, both authors outline Zhu Zaiyu’s life, writings, and theories (Robinson and Fang 1976, pp. 367–371).

Needham and Robinson also refer to comparative studies of ancient Chinese music and Pythagorean theory by Kuttner (Needham and Robinson 1962, p. 176, n. b; see also Kuttner 1959), who praised Needham and Robinson’s work (Kuttner 1965b). Needham and Robinson had followed Kuttner’s work since the late 1950s and drew on Kuttner’s unpublished work and his collection of research materials to write their chapter (Needham and Robinson 1962, pp. 126, 382; see also Peng 2019, p. 80).Footnote 10 In 1975, Kuttner published a research paper on Zhu Zaiyu, “Prince Chu Tsai-yü’s Life and Work: A Re-Evaluation of his Contribution to Equal Temperament Theory.” According to Kuttner’s own account, this work had already been completed in 1968. In addition to describing Zhu Zaiyu’s life and presenting his three major works on equal temperament theory (see further above), Kuttner criticizes Robinson’s assumption that Western music theorists received the idea of equal temperament from Zhu Zaiyu. In addition to this, Kuttner wrote the entry “Chu Tsai-yü” for the 1973 edition of the German music dictionary Musik in der Geschichte und Gegenwart (Kuttner 1973a, pp. 1481–1483).

While Robinson was able to work with Chinese-language sources and collaborated with Joseph Needham, who counts as one of the most important sinologists of his time, Kuttner was not very much integrated into sinological circles of his time. On the other hand, Kuttner was the only important Western Zhu Zaiyu scholar after Amiot who had personally visited China and even spent many years there. But he had lived there as a refugee and was not a trained sinologist. Because of the circumstances of his stay, Kuttner had given up studying Chinese after a few years, and for the rest of his career, he relied on native speakers as translators for his research (Kuttner 1989, p. 9). Thus, although he was one of the first scholars after Amiot to work with the original sources and even had some first-hand experience of (the deteriorating) pre-modern Chinese music culture back then,Footnote 11 he was not in a position to interpret the related ancient and pre-modern textual sources by himself.

As concerns my controversial reputation in sinological studies, the views and reactions of my learned colleagues about me reach from the absurdest negative to equally exaggerated admiration. There were several scholars whose “admiration for Kuttner’s amazing achievements” went far beyond the degree that could still be called reasonable. In between were quite a few respectful recognitions of successful publications or lectures. (Kuttner 1989, p. 10)

Kuttner paved the way for an important methodological or hermeneutic step, namely in the sense that he emphasized the difference between Western and Chinese music cultures, rather than subsuming the latter under an allegedly more advanced Western framework. This is also the reason why he stressed the importance of studying the theoretical basis of pre-modern Chinese music theory, because

[…] the Westerner is unable to find a direct, naive and absolute approach to Chinese music. His approach is necessarily impaired by habitual association with Western music, by the permanent urge to compare Oriental music with his much-loved Western experience. (Kuttner quoted in Messmer 2007, p. 405)

Indeed, learning to differentiate on a theoretical level means the first step in obtaining the key to pre-modern Chinese musical culture and to understand its manifestations in their own right and context.

Conclusion and outlook

Looking at the contents of the Western Zhu studies mentioned above, we can see that Zhu Zaiyu was regarded as a representative figure or even as an authority in Chinese music theory since the transmission of music-theoretical elements in the eighteenth century and throughout the entire period under review. While Zhu Zaiyu was largely unrecognized in China during the Qing Dynasty, he was accepted and recognized by many Western scholars since the nineteenth century. In the first half of the twentieth century, Zhu Zaiyu and his theories were even given qualifiers such as ‘well known’ and ‘famous’ in the West. However, despite such a high “popularity rate,” the many misconceptions and blind spots in these historical studies cannot be ignored:

First, there was a lack of competent translations and interpretations of Zhu Zaiyu’s original texts. After Amiot and until Robinson’s collaboration with Needham, that is to say, for more than 150 years, no Western scholar had the opportunity to study the original works of Zhu Zaiyu. Western musicologists had to rely on the limited and vague descriptions and even misconceptions handed down by Amiot. They often had to guess at Zhu Zaiyu’s own theoretical thinking. Many misunderstandings of Amiot’s narrative and the unfamiliarity with Chinese music and language did not allow for more than superficial and misinformed short accounts, or even nothing more than short mentions of Zhu Zaiyu. The results were, of course, neither groundbreaking nor praiseworthy.

Second, the cultural background of Chinese music was not studied in depth. Especially in the earlier German-speaking discourse, Chinese music was often categorized in a simplistic and Eurocentric fashion as ancient, or rather simple “ethnic music.” One often gets the impression that Chinese music was placed far behind European art music in the “evolutionary civilization ranking.” In this perspective, only a few—barely understood—elements of Chinese music were mentioned, while the backgrounds of the entire theoretical system, historical developments, and cultural contexts of Chinese music were ignored. On this “basis,” we find comparisons with supposedly similar, but in fact fundamentally different concepts and theories of other historical musical cultures of ancient civilizations, such as elements developed from Pythagorean or Neo-Pythagorean backgrounds. However, even basic music-theoretical concepts such as ‘interval’ or ‘pitch,’ cannot simply be projected onto the pre-modern context of Chinese music theory, because these categories were not used in the original contexts (Peng 2019, pp. 21–28). Under these circumstances, although Zhu Zaiyu was chosen to represent Chinese music as a whole, this meant that he had become a kind of substitute symbol for an allegedly simple and backward “typically Chinese music,” while his truly innovative theory of music was overlooked. It did not even come into focus.

The scattered nature of the discourse and the very few names mentioned in this investigation also signal the fact that, to date, no large and consistent circle of scholars really devoting themselves in detail to Zhu Zaiyu’s important and very extensive work has emerged.Footnote 12 There was also a lack of adequate communication and exchange with Chinese scholars. Even experts such as Kenneth G. Robinson and Fritz A. Kuttner, who overcame most of the aforementioned fallacies in the earlier discourse, were only “soloists.” As a result, the study of Zhu did not make much progress and partly even shrank in proportion during the 200 years after Amiot’s rather comprehensive, “high-profile” pioneering introduction of elements of Zhu Zaiyu’s views.

Zhu Zaiyu’s musicological terminology is inherently difficult and complex. In fact, understanding the original Chinese text, with its very unusual and specialized terminology, must present an almost insurmountable lifelong obstacle for most musicology scholars who are not native Chinese speakers. Even Western sinologists may have great difficulty in “deciphering” such a large amount of complex source material in the context of very specialized meanings.

Therefore, in order to initiate a broader and deeper international discourse on Zhu Zaiyu's music theory, more Chinese music scholars are required to translate and annotate more of the original texts.Footnote 13 It should be noted, however, that even native speakers will then also have to face the problem of having to avoid the direct application of the concepts and logic of Western music theory in the context of such translations. It is important to place Zhu Zaiyu’s theory in the historical context of Chinese music and to interpret it systematically within the conceptual framework of its time and place. Modern Chinese musicology has largely adopted the concepts and perspectives of Western music theory. One has to understand that these cannot and should not simply be applied to the analysis of Zhu’s theory. Any attempt at translation must be preceded by critical reflection. Finally, in a second step, special comparative concepts also have to be developed, that is, as analytical tools to distinguish between the Western and traditional Chinese foundations of music and music theory from an overarching perspective. The topic offers a vast landscape of future research opportunities. As a further preparation in this direction, an analysis of the Chinese history of the reception of Zhu Zaiyu in academic scholarship must be carried out. This will be the task of a planned follow-up publication by the present author.