# Shí-èr-lǜ

Shí-èr-lǜ on C.

Shí-èr-lǜ (Chinese: 十二律, [ʂɚ̌.âɚ lŷ], 12 pitches) (twelve-pitch scale) was a standardized gamut of twelve notes.[1] Also known, rather misleadingly, as the Chinese chromatic scale, it was one kind of chromatic scale used in ancient Chinese music. The Chinese scale uses the same intervals as the Pythagorean scale, based on 2:3 ratios (8:9, 16:27, 64:81, etc.). The gamut or its subsets were used for tuning and are preserved in bells and pipes.[2]

Unlike the Western chromatic scale, the shí-èr-lǜ was not used as a scale in its own right; it is rather a set of fundamental notes on which other scales were constructed.[3]

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.[3]

## Note names

There were 12 notes in total, which fall within the scope of one octave. Note that the 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 system would be higher than 880 hertz.

How the scales are produced. Start with a fundamental frequency. (440 hertz is used here.) Apply the ratios to make the first column. Copy the second and all further elements in this column to the respective heads of the other eleven columns. Apply the ratios to make the second through the twelfth columns. So doing produces 144 frequencies (with some duplications). From each column five different selections of non-adjacent frequencies can be made. (See the colored blocks at the far left.) So each column can produce five different pentatonic scales, and with all the columns involved there are 60 pentatonic scales available to musicians.

See the article by Chen Ying-shi.[4]