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Shi'er lü

Shi'er lü is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Shi'er lü rather than just read about it. In short: Shi'er lü (Chinese: 十二律; pinyin: shí'èr lǜ; Wade–Giles: shih2-êrh4 lü4; lit. '12 pitches'; Mandarin pronunciation: [ʂɻ̩˧˥ aɚ˥˧ ly˥˩]) is a standardized gamut of twelve notes used in ancient Chinese music. It is also known, rather misleadingly, as the Chinese chromatic scale; it was only one kind of chromatic scale used in ancient Chinese music.

Shi'er lü — main illustration
Shi'er lü — illustration

Key takeaways

  • Shi'er lü belongs to science; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Shi'er lü to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Shi'er lü from memory before moving on to harder problems.

Reference excerpt

Shi'er lü (Chinese: 十二律; pinyin: shí'èr lǜ; Wade–Giles: shih2-êrh4 lü4; lit. '12 pitches'; Mandarin pronunciation: [ʂɻ̩˧˥ aɚ˥˧ ly˥˩]) is a standardized gamut of twelve notes used in ancient Chinese music. 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 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. Unlike the Western chromatic scale, the shi'er lü was not used as a scale in its own right; it is rather a set of fundamental notes on which other scales were constructed. 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

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.

See also Chinese musicology

Further reading Reinisch, Richard (?). Chinesische Klassische Musik, p. 30. Books On Demand. ISBN 978-3-8423-4502-7.

Sources

External links Graham Pont. "Philosophy and Science of Music in Ancient Greece: The Predecessors of Pythagoras and their Contribution", Nexus Network Journal.

Illustrations

Shi'er lü: 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.
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.

Worked examples

Example 1 — a first encounter with Shi'er lü

Start with the simplest possible case. Write down what Shi'er lü claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Shi'er lü before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Shi'er lü ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Shi'er lü

In research
Shi'er lü appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Shi'er lü in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Shi'er lü is common in secondary-school and first-year university syllabi. It links to neighbouring topics 3-limit tuning and intervals, Chromaticism, Music of China, so understanding it makes those chapters shorter.
In everyday life
Look for Shi'er lü outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study Shi'er lü in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Shi'er lü means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Shi'er lü out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Shi'er lü in simple terms?

Shi'er lü (Chinese: 十二律; pinyin: shí'èr lǜ; Wade–Giles: shih2-êrh4 lü4; lit. '12 pitches'; Mandarin pronunciation: [ʂɻ̩˧˥ aɚ˥˧ ly˥˩]) is a standardized gamut of twelve notes used in ancient Chinese music. It is also known, rather misleadingly, as the Chinese chromatic scale; it was only one kind of…

Why does Shi'er lü matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Shi'er lü?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Shi'er lü.

Tags

  • 3-limit tuning and intervals
  • Chromaticism
  • Music of China
  • Musical scales

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