I define music by the based on musical criteria. Not on passports of lines on maps. If there is such a thing as Chinese music then it is music that fits within the culture of music, defined on the grounds of musical technical criteria, that developed in China.
I don't think that using a Chinese melody in western music turns the music into Chinese music.
But your terms are just so frustratingly vague. What is "western music?" Is Rachmaninoff "western music?" What about Russian composers that were writing music before the fashionable influx of central European culture. And since when are all nations stuck with just "musical technical criteria" that developed in their culture? Bartok, in his study of folk musics, found that the folk music of the world that thrived was the music that had the most influence from
foreign cultures. The folk music that was stagnant, and not developed, was the music in nations isolated from the world. Is a composer like Chen Yi, born and raised in China, who plays the Chinese folk instruments, but writes music in idioms we traditionally think of as, to use your term, "western," no longer a Chinese composer? Does she no longer write Chinese music? The term "Chinese music" is obviously meaningful only as far as it tells you, a Chinese person wrote this music. Just like noone can hear the works of Prokofiev, Scriabin, Medtner, Rachmaninoff, Gubaidulina, Schnittke, Shostakovich, Stravinsky, and then say exactly what "russian" music is, besides the fact that a Russian wrote it.
Walter Ramsey