中國古代编鐘和半音音階的起源（英文）

Ancient Chinese Bells and the Origin of the Chromatic Scale

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。

In recent decades Chinese archaeologists have unearthed ancient musical instruments whose implications for music theory reach well beyond ancient China.Tuned sets of bronze bells that still sound their original pitches are now known as far back as the eleventh century BCE.Most remarkable and most informative is a fifth century set found in the tomb of Marquis Yi of Zeng(d.433 BCE).Its sixty-five bells—a total of 2,500 kilograms of bronze—play a five-octave pentatonic scale that begins two octaves below middle C.A three-octave stretch within that compass is fully chromatic.The bells are inscribed at their strike points with the names of the pitches they sound and with longer texts describing transpositions from one pentatonic tonality to another.Nineteen further instruments—drums,winds,zithers,and a set of forty-one chime stones—were found alongside the bells.The chime stones,twelve per octave,are numbered from1 to 41 in pitch order.Beginning on the first G# above middle C,they supply just under three and a half octaves of the chromatic scale.Like the bells,they are inscribed with their pitches and with transposing inscriptions written by theorists who understood the chromatic scale as equivalent to all possible transpositions of the anhemitonic pentatonic scale.On the evidence of these and earlier finds,the present paper argues that in China the chromatic scale was constructed and instruments were tuned to it long before theorists learned how to calculate musical scales.The existence of a non-mathematical route to the chromatic scale has implications for our understanding of the scale in the West as well as in China.