hi, i'm not a historian but i saw the question and felt compelled to answer. there is a cd of music composed by teodorico pedrini (1671-1746), a jesuit at the chinese court, whose liner notes deal with this very subject which is interesting to me as an inhabitant of a lesser frontier (chile).

essentially, european music flourished at the court of the fourth qing emperor, kangxi, the longest serving (1661-1722) and most cosmopolitan of the emperors. he commissioned not only the first proper study of chinese music, but also of european music as transmitted by jesuit priests who had arrived earlier and were a mainstay at the court. these priests composed, performed and taught european music, as well as performed their duties as missionaries, and served as cultural liaison to europe which, it has to be said, was a long way off and difficult. the first real exposure and study of chinese music, and likewise the first real european influence at the court, was through these missionaries:

The first trace of European music in China dates back to the beginning of the seventeenth century. In 1601, Matteo Ricci, the first Jesuit priest to arrive in Peking brought with him a spinet, which caused sensation at court, and, for centuries, was preserved as a relic along with the clocks and other objects that had accompanied him. Of course, music was for him above all a means of demonstrating the superiority of the Catholic religion. He would sing edifying tunes, often with texts which he translated into Chinese. In Peking, in 1608, he even published an anthology entitled "Eight airs with accompaniment on the European organ", which met with incredible success: new editions appeared, one after another, until the nineteenth century. The music has apparently been lost, but the Chinese words still exist.

by the end of the 17th century european music was well-known in china:

(...) Father Verbiest wrote in 1680: "We have built a caillon in one of the church towers and in the other we have had an organ set up, built with tin pipes, according to the rules of music. All may visit it, and I do not think it has its equal for grandeur in the whole of the Orient. These two works of art, which we owe to the skill and ingenuity of Father Pereira, a very able musician, are quite perfect. It is unbelievable how these two instruments draw the crowds to our church." And, in 1710, Matteo Ripa reported: "The Emperor claimed to be an excellent musician and an even better mathematician. (...) Where music was concerned, he was totally ignorant, but on both these subjects he had good taste. And as for harpsichord and spinets—he had an instrument in almost every one of his apartments—he did not play them, but he had them played to his wives, as he did not himself possess that art."

These accounts, amongst many others, show how, in the space of a hundred years, European music and musicians had acquired an important position at the court of the Emperor Kangxi. "In the year 1679, the Emperor summoned Father Grimaldi and Father Pereira to the Palace to play a harpsichord and an organ which they had once presented to him. He appreciated European melodies and apparently took pleasure in listening to them. He then commanded his musicians to play a Chinese tune on one of their instrments, and he played himself with much grace." (Du Halde, Descripton of the Chinese Empire). The Portuguese Jesuit Tomás Pereira died in 1708, leaving unfinished an important treatise on European music, which had been commissioned by the Emperor as a complement to a definitive treatise on Chinese music. Earlier, he had taught European music a the court, where eunuchs had been trained to sing Catholic music, in the image of the castratti in Italy.

a detail that may be lost reading these quotes is that european penetration of china was by no means straightforward, and was limited to these missionaries who themselves were subject to the whims of chance. father pedrini for example took several years to arrive (with a detour in chile and peru, of all places), and upon reaching the philippines took another detour in macau fraught with difficulty, which delayed his entry to china. eventually he did and served at the court of emeperor kangxi, who later died and left him at the whim of less kind rulers (who jailed him at one point) although he managed to live the rest of his life in china.

the jesuit priests communicated with europe through letters which are remakably well-preserved and rich in detail. the liner notes, referring to these "Lettres édifiantes et curieuses" (edifying and curious letters, jesuit chronicles describing the life of missionaries in china), discusses the musical cross-pollination of the priests in contact with chinese music:

These chronicles also contain many references to Europeans playing Chinese music, generally before the Emperor. We have tried hard to imagine how the missionaries—who were fascinated by Chinese music and culture, yet at the same time anxious to prove the superiority of the European art (and therefore of the Christian religion) may have performed these scores. Most of these tunes come from a very curious manuscript by Père Amiot of the Society of Jesus, who lived in Peking from 1750 until his death in 1793. In this manuscript, he attempted to provide a synthesis of the Chinese and European systems of musical notation, by writing the Chinese characters on the European stave.

the cd i have mentioned has several pieces by père amiot (1718-1793) which i believe are this very synthesis mentioned above. they are tinged with delicate oriental expression, a sample of which can be found here

later in the text there is a discussion of of the double role played by these jesuit missionaries and musicians:

We know from eyewitness accounts that missionaries in China (Jesuits or Lazarists) performed both European and Chinese music before emperors of the Manchu dynasty. (...) European instruments (violin, cello, flute, harpsichord) had been imported by the missionaries, whose strategy was to convert China to Christianity, starting from the top. They did this, first of all, by demonstrating their status as experts and thus gaining access to the court; they then aimed to prove the superiority of the West, of Christendom, and therefore—syllogism—of Chistianity, in the realms of science, astrononomy, cartography, measurement, and music, the study of which belonged to the field of scholarship in both civilisations. Acoustics, instrument-making, notation and performance were all a part of this strategy of integration, competition and persuasion. Within that context, playing Chinese music, and playing it well, was a question of politeness and diplomacy; if necessary, it also enabled the priests to show their outstanding talents. There thus grew up a subtle interplay between the ideas of charming their hosts, filling them with wonder and amazing or impressing them.^1

the posts below will give more depth to the above quotes.

^1 jean-christophe frisch, liner notes to the cd "teodorico pedrini: concert baroque à la cité interdite", éditions audivis astrée E 8609, 1996