What are the differences between heptatonic scales used in China and in other cultures? Here we introduce three levels in the Chinese scale system: Yun (均), Gong (宫), Diao (调), and try to illustrate the Chinese scale derivation process called “three Gong in the same Yun (同均三宫 Tong Yun San Gong)”, a theory first proposed by Chinese musicologist Huang Xiangpeng in the 1980s and widely accepted since then.
Step 0
The first step is to get familiar with twelve pitch names in the Chinese music system. The table below lists them and their matching pitch in the Western notation system in the order of perfect fifths. Here the first one Huang Zhong (黄钟) is mapped to C. The mapping is not fixed and has varied over time.
| Chinese pitch names | 黄钟 | 林钟 | 太簇 | 南吕 | 姑洗 | 应钟 | 蕤宾 | 大吕 | 夷则 | 夹钟 | 无射 | 仲吕 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Western pitch names | C | G | D | A | E | B | F# | C# | G# | D# | A# | E# |
Step 1
According to this table, we could choose a sequence of seven notes as a Yun (均) collection, for example, Huang Zhong (黄钟 C) to Rui Bin (蕤宾 F#) as Huang Zhong Yun (黄钟均). This will be used to yield scales in the next steps. Twelve Yun (均) collections can be generated in total.
Step 2
The Gong (宫) note is the most important note in each scale. In practice, it is the root note of the major-third chord. Looking closely at the Yun collection from Huang Zhong (黄钟 C) to Rui Bin (蕤宾 F#), we find three Gong: C in C-D-E, D in D-E-F#, and G in G-A-B. This is the origin of the three Gong in the same Yun concept (同均三宫 Tong Yun San Gong).
Step 3
Using each Gong as a starting note, we can have three sequences in the scalar order. These are three basic heptatonic Diao (调) that represent three different types of heptatonic Diao in one Yun collection: Zheng Sheng Diao using C as the Gong (C宫正声调), Su Yue Diao using D as the Gong (D宫俗乐调), and Xia Zhi Diao using G as the Gong (G宫下徴调).
| C宫正声调 Zheng Sheng Diao using C as the Gong |
宫 | 商 | 角 | 中 | 徴 | 羽 | 变宫 |
|---|---|---|---|---|---|---|---|
| Chinese pitch names | 黄钟 | 太簇 | 姑洗 | 蕤宾 | 林钟 | 南吕 | 应钟 |
| Western pitch names | C | D |
E | F# | G | A | B |
| D宫俗乐调 Su Yue Diao D using D as the Gong |
宫 | 商 | 角 | 和 | 徴 | 羽 | 闰 |
|---|---|---|---|---|---|---|---|
| Chinese pitch names | 太簇 | 姑洗 | 蕤宾 | 林钟 | 南吕 | 应钟 | 黄钟 |
| Western pitch names | D | E | F# | G | A | B | C |
| G宫下徴调 Xia Zhi Diao using G as the Gong |
宫 | 商 | 角 | 和 | 徴 | 羽 | 变宫 |
|---|---|---|---|---|---|---|---|
| Chinese pitch names | 林钟 | 南吕 | 应钟 | 黄钟 | 太簇 | 姑洗 | 蕤宾 |
| Western pitch names | G | A | B | C | D | E | F# |
There are nine distinct scale degree names: 宫 (Gong), 商 (Shang), 角 (Jue), 和 (He), 中 (Zhong), 徴 (Zhi), 羽 (Yu), 闰 (Run), and 变宫 (Bian Gong). This is why people often say Chinese music has nine sounds (九声 Jiu Sheng). In the following table, the nine degrees are listed as if they are all in the sequence of C as the Gong:
| Scale degree | 宫 | 商 | 角 | 和 | 中 | 徴 | 羽 | 闰 | 变宫 |
|---|---|---|---|---|---|---|---|---|---|
| If C as the Gong | C | D | E | F | F# | G | A | A# | B |
| Interval distance | M2 | M2 | m2 | m2 | m2 | M2 | m2 | m2 | m2 |
In these nine scale degrees, five of them are more important: 宫 (Gong), 商(Shang), 角 (Jue), 徴 (Zhi), and 羽 (Yu). If C is written as the 宫 (Gong), it is the most familiar pentatonic scale C D E G A. 和 (He), 中 (Zhong), 闰 (Run), and 变宫 (Bian Gong) are four auxiliary tones, only used to build heptatonic Diao. Thus, Huang describes the relationship between heptatonic and pentatonic Diao in China as follows: five tones as the core, seven tones as the background (以五声为骨干，七声为背景).
Step 4
So far we have only looked at the Diao that start from the Gong. At this stage, we will consider transposition. Starting from the three basic heptatonic Diao derived in step 3, we can rotate a note in one Diao so that non Gong notes can become the first note of the Diao. Notice that only the five main tones (宫, 商, 角, 徴, and 羽) can be the first note. Below is an example of the Zheng Sheng Diao using C as the Gong (C宫正声调) itself and four Diao derived from it. All of them are the Zheng Sheng Diao (正声调) and using C as the Gong, but they differ by their initial notes.
| Scale degree names/Diao names |
宫 | 商 | 角 | 中 | 徴 | 羽 | 变宫 | 宫 | 商 | 角 | 中 | 徴 | 羽 | 变宫 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| C宫正声调 Zheng Sheng Diao using C Gong as the initial | C | D | E | F# | G | A | B | |||||||
| D商正声调 Zheng Sheng Diao using D Shang as the initial | D | E | F# | G | A | B | C | |||||||
| E角正声调 Zheng Sheng Diao using E Jue as the initial | E | F# | G | A | B | C | B | |||||||
| G徴正声调 Gong Zheng Sheng Diao using G Zhi as the initial | G | A | B | C | B | E | F# | |||||||
| A羽正声调 Gong Zheng Sheng Diao using A Yu as the initial | A | B | C | B | E | F# | G |
The resulting Diao and derivation process is similar to the way medieval church modes are derived.
Conclusion
From these five steps, Huang concludes that theoretically there are 180 heptatonic Diao. The calculation is: 12 Yun collections * 3 Gong in each Yun * 5 Diao (one starts from Gong and four transposed ones) = 180. One interesting fact is that there are “duplicate” Diao in these large set. For example, D商正声调 (Zheng Sheng Diao using D Shang as the initial) (D E F# G A B C) is the same as D宫俗乐调 (Su Yue Diao using D Gong as the initial) (D E F# G A B C). Both are identical in pitch, but differ in the names of scales and degrees. This may suggest differences in the function of each scale and degree in Chinese music.
Acknowledgements
This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program under grant agreement No 760081 – PMSB. We thank Claude Latour for supporting this research through the Latour Chair in Digital Musicology.
References
Huang, X. P. (1986). Zhongguo chuantong yindiao de shuli luoji wenti [Mathematical Logic in the Tone-relation of Traditional Chinese Music], Zhongguo yinyuexue, 1986(3), 9-27, 8, 143.
Huang, X. P. (1990). Chuantong shi yitiao heliu [Tradition is a River], Beijing: Renmin yinyue chubanshe.