Shi'er lü

Shi'er lü (; ) is a standardized gamut of twelve notes used in ancient Chinese music.Joseph C.Y. Chen (1996). Early Chinese Work in Natural Science: A Re-examination of the Physics of Motion, Acoustics, Astronomy and Scientific Thoughts, p. 96. . It is also known, rather misleadingly, as the Chinese chromatic scale; it was only one kind of chromatic scale used in ancient Chinese music. The uses the same intervals as the Pythagorean scale, based on 3:2 ratios (8:9, 16:27, 64:81, etc.). The gamut or its subsets were used for tuning and are preserved in bells and pipes.Chen (1996), p.97.

Unlike the Western chromatic scale, the was not used as a scale in its own right; it is rather a set of fundamental notes on which other scales were constructed.Needham, Joseph (1962/2004). Science and Civilization in China, Vol. IV: Physics and Physical Technology, p.170-171. .

The first reference to "standardization of bells and pitch" dates back to around 600 BCE, while the first description of the generation of pitches dates back to around 240 CE.

Note names Traditional Chinese Simplified Chinese Pinyin English Ratio Audio tonic/unison 1 : 1 semitone 37 : 211 major second 32 : 23 minor third 39 : 214 major third 34 : 26 perfect fourth 311 : 217 tritone 36 : 29 perfect fifth 3 : 2 minor sixth 38 : 212 major sixth 33 : 24 minor seventh 310 : 215 major seventh 35 : 27 There were 12 notes in total, which fall within the scope of one octave. Note that the shí'èr lǜ-based mathematical method used by the ancient Chinese could never produce a true octave, as the next higher frequency in the series of frequencies produced by the Chinese shí'èr lǜ system would be higher than 880 hertz.

See the article by Chen Ying-shi. by (Yi zhong ti-xi, liang ge xi-tong by Chen Ying-shi of the Shanghai Conservatory), Musicology in China, 2002, Issue 4, ，2002，

Shi'er lü

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