'12 pitches'; Mandarin pronunciation: [ʂɻ̩˧˥ aɚ˥˧ ly˥˩]) is a standardized gamut of twelve notes used in ancient Chinese music.
The shi'er lü 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.
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 that never jump more than three available notes, and never jump two twice in a row. (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.
A comparative table of Eastern and Western notes of chromatic scale, from a book published in
Kyoto
in 1909. This table shows that the pitch of the first note
Huang Zhong
(
黃鐘
;
huáng zhōng
) is equivalent to D in Western classical music, while it was A in
Ming era
.
