''Shí-èr-lǜ'' (, , ''12 pitches'') (twelve-pitch scale) was a standardized

gamut In color reproduction, including computer graphics and photography, the gamut, or color gamut , is a certain ''complete subset'' of colors. The most common usage refers to the subset of colors which can be accurately represented in a given circ ...

of twelve notes. Also known, rather misleadingly, as the Chinese chromatic scale, it was one kind of

chromatic scale The chromatic scale (or twelve-tone scale) is a set of twelve pitches (more completely, pitch classes) used in tonal music, with notes separated by the interval of a semitone. Chromatic instruments, such as the piano, are made to produce the ...

used in ancient Chinese music. The Chinese scale 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 Pipe(s), PIPE(S) or piping may refer to: Objects * Pipe (fluid conveyance), a hollow cylinder following certain dimension rules ** Piping, the use of pipes in industry * Smoking pipe ** Tobacco pipe * Half-pipe and quarter pipe, semi-circul ...

. Unlike the Western

, the shí-èr-lǜ was not used as a

scale Scale or scales may refer to: Mathematics * Scale (descriptive set theory), an object defined on a set of points * Scale (ratio), the ratio of a linear dimension of a model to the corresponding dimension of the original * Scale factor, a number ...

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

* 黃鐘 (黄钟) - Huáng Zhōng - tonic/

unison In music, unison is two or more musical parts that sound either the same pitch or pitches separated by intervals of one or more octaves, usually at the same time. ''Rhythmic unison'' is another term for homorhythm. Definition Unison or pe ...

- 1 : 1 - * 大呂 (大吕) - Dà Lǚ -

semitone A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically. It is defined as the interval between two adjacent no ...

- 3⁷ : 2¹¹ - * 太簇 - Tài Cù -

major second In Western music theory, a major second (sometimes also called whole tone or a whole step) is a second spanning two semitones (). A second is a musical interval encompassing two adjacent staff positions (see Interval number for more deta ...

- 3² : 2³ - * 夾鐘 (夹钟) - Jiá Zhōng -

minor third In music theory, a minor third is a musical interval that encompasses three half steps, or semitones. Staff notation represents the minor third as encompassing three staff positions (see: interval number). The minor third is one of two com ...

- 3⁹ : 2¹⁴ - * 姑洗 - Gū Xiǎn -

major third In classical music, a third is a musical interval encompassing three staff positions (see Interval number for more details), and the major third () is a third spanning four semitones. Forte, Allen (1979). ''Tonal Harmony in Concept and P ...

- 3⁴ : 2⁶ - * 仲呂 (中吕) - Zhòng Lǚ -

perfect fourth A fourth is a musical interval encompassing four staff positions in the music notation of Western culture, and a perfect fourth () is the fourth spanning five semitones (half steps, or half tones). For example, the ascending interval from C to th ...

- 3¹¹ : 2¹⁷ - * 蕤賓 (蕤宾) - Ruí Bīn -

tritone In music theory, the tritone is defined as a musical interval composed of three adjacent whole tones (six semitones). For instance, the interval from F up to the B above it (in short, F–B) is a tritone as it can be decomposed into the three ad ...

- 3⁶ : 2⁹ - * 林鐘 (林钟) - Lín Zhōng -

perfect fifth In music theory, a perfect fifth is the musical interval corresponding to a pair of pitches with a frequency ratio of 3:2, or very nearly so. In classical music from Western culture, a fifth is the interval from the first to the last of five ...

- 3 : 2 - * 夷則 (夷则) - Yí Zé -

minor sixth In Western classical music, a minor sixth is a musical interval encompassing six staff positions (see Interval number for more details), and is one of two commonly occurring sixths (the other one being the major sixth). It is qualified as ''min ...

- 3⁸ : 2¹² - * 南呂 (南吕) - Nán Lǚ -

major sixth In music from Western culture, a sixth is a musical interval encompassing six note letter names or staff positions (see Interval number for more details), and the major sixth is one of two commonly occurring sixths. It is qualified as ''major' ...

- 3³ : 2⁴ - * 無射 (无射) - Wú Yì -

minor seventh In music theory, a minor seventh is one of two musical intervals that span seven staff positions. It is ''minor'' because it is the smaller of the two sevenths, spanning ten semitones. The major seventh spans eleven. For example, the interval fro ...

- 3¹⁰ : 2¹⁵ - * 應鐘 (应钟) - Yìng Zhōng -

major seventh In music from Western culture, a seventh is a musical interval encompassing seven staff positions (see Interval number for more details), and the major seventh is one of two commonly occurring sevenths. It is qualified as ''major'' because it is ...

- 3⁵ : 2⁷ - There were 12 notes in total, which fall within the scope of one

octave In music, an octave ( la, octavus: eighth) or perfect octave (sometimes called the diapason) is the interval between one musical pitch and another with double its frequency. The octave relationship is a natural phenomenon that has been refer ...

. 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. Chinese Music Gamut & Scales

See the article by Chen Ying-shi.一种体系两个系统 by 陈应时 (Yi zhong ti-xi, liang ge xi-tong by Chen Ying-shi of the Shanghai Conservatory), ''Musicology in China,'' 2002, Issue 4, 中国音乐学，2002，第四期

Sources

External links

*Graham Pont
"Philosophy and Science of Music in Ancient Greece: The Predecessors of Pythagoras and their Contribution"
''Nexus Network Journal''. {{DEFAULTSORT:Shi-Er-Lu 3-limit tuning and intervals Chinese music Chromaticism Musical scales

Note names

See also

Further reading

Sources

External links