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中國考古學家在近幾十年發掘出來的古代樂器對音樂理論的啓示遠遠超出了古代中國的範圍。現知仍能奏出原始音高的編鐃可以早至公元前十一世紀,而最不同凡響、最富含信息的是公元前五世紀的曾侯乙墓所出的編鐘(下葬年代爲公元前433年)。它由65件樂鐘組成,用銅量達到2500公斤,所奏五聲音階從中央C音下的第二個八度開始跨越五個八度音程。在這一音域中的三個連續八度具有完整的半音音階。在這些鐘的敲擊點鑄有它們的音名和描述如何從一種五聲調式移到另一種五聲調式的長篇銘文。和編鐘一起出土的還有鼓、管樂器、弦樂器和一套原有41件的編磐等另外19種樂器。編磬按照音高順序從1號編到41號,每個八度音程有12件。從中央C音之上的#G開始它們剛好提供了三個半八度音程的半音音階。編磐和編鐘一樣有關於它們的音名和移調的銘文,而寫作這些銘文的樂理學家將半音音階視爲無半音五聲音階所有移調產生音高的順次排列。根據此墓及時代更早的發現,本文認爲在中國半音音階的形成和以此調音的樂器的產生,均遠早於樂理學家對如何計算音階的掌握。這一不用數學方法而得到半音音階途徑的存在,對於我們理解中西方的音階均有啓發意義。
The revelations of ancient Chinese musical instruments excavated by Chinese archaeologists in recent decades have far exceeded the scope of ancient China. Known to still be able to play the original pitch can be edited as early as the eleventh century BC, and the most extraordinary, the most informative is the bells of the fifth century BC Zeng Hou cemetery (buried for the BC 433 years). It consists of 65 pieces of music clock, with a capacity of 2,500 kilograms of copper, playing a pentatonic scale spanning five octaves from the second octave under center C. Three consecutive octaves in this range have a complete chromatic scale. The beatings at these bells are cast with their names and long inscriptions describing how to move from one pentahydraat to another pentatonic. There were also 19 drums, wind instruments, stringed instruments and a set of original 41 pieces of braid unearthed together with chimes. Arrangements are numbered from 1 to 41 in pitch order, with 12 for each octave. From the # G above the central C, they just provide half-notes of three and a half octaves. Plagiarism and chimes have inscriptions about their names and transposons, and the philosopher who writes these inscriptions treats the chromatic scales as a sequence of pitch-free pitch shifts for all transpositions. According to this tomb and the earlier discovery of the times, this paper argues that the formation of chromatic scales in China and the production of instruments tuned by them are much earlier than that of the philosophers on how to calculate the scales. The existence of the semitone steps without mathematical methods is instructive for us to understand the scale of China and the West.