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PitchIntervalScaleChinese Pentatonic ModesBianzhongBianqingYunluo

This page is the deep dive behind the bianzhong entry.

That page answered *what it is*: almond cross-section · two tones per bell · twelve lü · 3,755 inscribed characters. This page answers three harder questions:

⚠️ Why can one bell give two tones? Why can two tones per bell add up to a whole tuning system? And how do we know any of this? Start with the thing most easily called a miracle — the two-tone bell. The sources state the mechanism plainly: strike the centre face, and the vibration carries four longitudinal nodal lines exactly at the side faces — so you hear only the "centre tone"; strike a side face, and the nodal lines move to the centre — so you hear only the "side tone." The two paths can be taken separately or together (struck together, they make harmony). ⭐⭐ Rule ㉙: the two-tone bell is not a miracle, it is engineering — shape, material and grinding, all three required. The almond ("tile-pair") section is the shape; the copper–tin–lead recipe is the material; "cast first, grind after" is the craft. Together they made possible, in the sources' own words, "a fairly complete scale from no great number of bells."

⭐ The protagonist here is the Zeng Hou Yi bianzhong — excavated in 1978 at Suizhou, Hubei; the largest, heaviest, most complete and most imposing set ever found. (Unless noted, all numbers and examples below refer to it.)

One bell, two tones

This figure is the foundation of the page. Unpacked, it is three source sentences:

1. Two sets of natural frequencies. Strike the centre and the bell vibrates in one set; strike a side and it vibrates in another. 2. Nodal lines hold a tone down. "Striking the centre face, the vibration carries four longitudinal nodal lines exactly at the side faces — the main sound heard is the centre tone, and the side tone is suppressed"; the reverse holds for the other strike. 3. They do not interfere. The two "can be struck separately or together, without interfering" — the sources call it a strange physical phenomenon; the museum puts it better: struck together, "they form a pleasing harmony."

⚠️ All of it rests on one shape: the almond section ("like two tiles closed together"). Let the section become round or oval and "only one pitch is produced" — in the sources' words, "when bells later became circular, the two-tone bell disappeared." A side effect: this structure also keeps the bianzhong from "ringing on" like a Western round bell — its sound stops in time, and that is why it can play melodies.

Twelve lü: a system built from pairs

Two tones per bell is only the beginning — the real project is the scale. Why should each bell give a pair a third apart? The answer is plain in the sources: "the advantage of the two-tone bell is that a fairly complete scale can be built from no great number of bells."

编钟属体鸣乐器（有固定音高）。曾侯乙编钟以姑洗律为标准设计（现代乐理即按 C 调），中心音域十二个半音齐备、可以旋宫转调；此处以现代十二个半音 C4–B4 示意（十二律的传统名称为黄钟 · 大吕 · 太簇 · 夹钟 · 姑洗 · 仲吕 · 蕤宾 · 林钟 · 夷则 · 南吕 · 无射 · 应钟）。各套编钟的实际音高不同，本图不代表所有编钟。记谱即实音。

Twelve semitones, none missing — the precondition for xuangong zhuandiao: shifting the tonic and playing in another key. And how was that verified? The sources give one example checkable term by term:

⭐ The strangest thing in that table: the bell is inscribed with its note names, and the measurements agree. This was not lucky beauty — it was designed, tested and labelled. On precision, one more set of figures: among the 33 youzhong (shaft bells) there are 22 pairs of duplicate tones; over half of the pairs differ by under 15 cents, the rest by about 20 — "within the tolerance of modern musicians."

The size of one set

What kind of object holds this many precise tones? The file card of this one:

⭐ That last row deserves a pause: one of the 65 is not a band member but a gift — a diplomatic document mixed into a musical instrument. (The whole assembly is called a "ritual-and-music treasure": instrument, ritual object, display of power and craft at once. The tomb also held chime stones, a drum, se, sheng, xiao, chi… making the full "xuanxuan" array — bells and stones hung on three sides — a whole band.)

The owner's manual written on the bells

If one thread proves "not an accident," it is the inscriptions:

• 3,755 characters across bells, frame and hooks (mostly gold-inlaid): serial numbers, records, pitch labels and tuning theory.
• ⭐ Every bell labels its own notes: pitch inscriptions are written in the Guxi mode (roughly C), marking the scale-degree or note name each strike point produces — where to strike, and what will sound, is written on the bell itself.
• ⭐ 28 lü-names and 66 scale-degree names — most of them unknown to any surviving text.
• ⭐ A multi-state conversion table: the inscriptions record correspondences between the lü-names of Zeng and of Chu, Jin, Qi, Shen, Zhou… The same pitch had different names in different states, and the bells give the exchange rates. Example: middle group 3, bell 5 is inscribed "shouzhong zhi gong", noting that "shouzhong" is Chu's name for huangzhong.

⭐ Hence the scholarly verdict: these inscriptions are "an imperishable classic of ancient tuning theory." Instrument and literature are, here, the same object.

Cast and ground: how the pitch is fixed

The craft chain, without hedging:

• Cast. Lost-wax and sectional moulds, bronze welding, inlay: one yong bell's mould used 126 mould and core pieces (middle group 3, bell 1, after Hua Jueming and colleagues). The recipe is acoustically relevant: measured 12.49–14.46% tin, 1–3% lead — the lead "checks the transmission of sound without harming the timbre."
• Grind. "After casting, the natural pitch is higher than the target; the smiths ground specific areas of the inner wall thinner to lower the pitch… tuning can only subtract, never add — grind too far and the bell is scrap." The most sensitive area is the "sound ridge" opposite the side face; the walls keep the traces: ridges, grooves, channels — "the tuning marks left by the ancient craftsmen."
• ⭐ The same philosophy as the chime stones: grinding cannot be undone (rule ⑨: material decides the route and its reversibility). The difference: stone versus bronze — and bronze can be re-melted. Only, re-melting erases every grind.

⭐ One more thread: the scholar Feng Guangsheng divides the two-tone technique into three stages — "natural two-tone" (it happens), "cast two-tone" (it is intended), and "cast-and-tuned two-tone" (it is precisely adjusted) — and places Zeng Hou Yi at the peak of the third stage, "almost at the limit of the technique." Two-tone bells have an evolutionary road from accident to design; this set stands at its end.

The Kao Gong Ji: a casting code two thousand years old

Antiquity left a technical document — the "Fushi makes bells" section of the *Kao Gong Ji*:

• It names everything. Rim edges, mouth, striking face, bands, crown, shaft… every part of a bell has a name, including the tuning groove (sui).
• It states the principle. "Thickness sets the vibration; from it come clear and muddy tones" — with bounds: too thick sounds like stone, too thin scatters.
• It gives proportions. "A bell large and short: its sound hurried, heard briefly; a bell small and long: its sound easy, heard far" — ⚠️ note: this is about duration and carrying, not pitch.
• It even specifies the tuning groove: take one sixth of the thickness as its depth, rounded.
• And it sets the alloy. "Six recipes of metal: one part tin to six, for bells and cauldrons" — the first entry in the world's oldest surviving alloy code. (Readings of the "six recipes" differ; the measured tin content of these bells, 12–15%, is the same order.)

⭐ Read the Kao Gong Ji and the bells side by side: one is a written standard, the other a physical object. The text says how it should be done; the bells show it was done.

How we know

None of this page is copied from old books — it was measured:

⭐ And before this set surfaced, one sentence passed for common knowledge: "it was once thought in the West that China only acquired a concept of relative pitch late in the Warring States period, under Western influence." The inscriptions and measurements made that claim "collapse of itself" — because the systematic pitch names and lü correspondences prove that both absolute and relative pitch concepts existed before the Warring States. One instrument rewrote a discipline's verdict.

Common misconceptions

• "Chinese bells are like Western bells: one tone each." ⚠️ Backwards — two tones each; it was round bells that "produce only one pitch," and with them the two-tone bell disappeared.
• "The two-tone effect was a lucky accident." ⚠️ There is a documented evolution from natural to intended to precisely tuned; this set was made, not found.
• "Ancient instruments were out of tune." ⚠️ Measured: over half of 22 duplicate pairs within 15 cents — inside a modern musician's tolerance.
• "The inscriptions are records and decoration." ⚠️ Their core is pitch labels and tuning theory: each bell labels its two notes, and the set carries a conversion table across Zeng, Chu, Jin, Qi, Shen, Zhou.
• "Grinding a little more is harmless." ⚠️ Tuning only subtracts — over-grind, and the bell is scrap.
• "It sounds good because it rings on." ⚠️ The opposite: the almond section stops the sound — and that is the physical precondition for playing melody.

Timbre, and how to hear it

The listening task is simple: hear one bell's two tones.

Three cues:

1. Two tones, one bell. Centre first, side second — one instrument, two notes a third apart; and they can sound together (harmony) without fighting. 2. The metal's ring is held. Compared with a Western round bell, the attack is clear and the tail short — not a flaw, but the precondition for melody. 3. Layers, colours. The upper niu bells are bright and clear, the middle yong bells round, the great lower bells deep — a whole register of characters inside one set.

The family

⭐ The last column is the point: from two tones to one runs a line of functional choice — bells wanted melody (so: two tones, hung in sets); round bells wanted volume and solemnity (so: made circular, melody abandoned). One bronze technology, two posts.

Next

Percussion stands at seventeen. One remains:

Not another instrument — an assembly. Put the bangu, the big gong, the cymbals, the small gong and the clappers back at their posts: how does a percussion band organise a whole opera? Who cues the tunes, the metres, the gestures, the freeze?

Percussion in Chinese opera. :::

Sources

• ⭐⭐ 振动机制：「敲击正鼓部时，钟体以一组固有频率振动，发出『正鼓音』；敲击侧鼓部时，以另一组固有频率振动，发出『侧鼓音』」；「敲击钟的正鼓部位，钟腔形成的振模有四条纵向节线正好位于侧鼓部位，这时听到的主要是正鼓音，侧鼓音受到了抑制；反之，节线在正鼓部位，就只能听到侧鼓音」；「正鼓与侧鼓可以单独击发，也可以同时击发，且互不干扰」依计量专题资料与曾侯乙编钟研究资料
• ⭐ 每钟两音与和声：「每件钟均有呈三度音程的两个乐音，可以分别击发而互不干扰，亦可同时击发构成悦耳的和声」；「仅少数大型甬钟的侧鼓音不甚明显之外，绝大多数钟均能在正鼓部和侧鼓部，分别击奏出呈三度音程、且与标音相符的两个乐音」依博物馆与考古资料
• ⭐ 圆钟对照：「横截面为椭圆形的钟，就只能产生一个音频，所以后期的钟演变为圆形时，双音钟也就消失不见」；「这种结构使编钟不像西方圆钟那样会出现余音袅袅的现象」（另有资料称其截面为「筒瓦形」：共鸣箱像两片瓦盖在一起）依科普与乐器资料
• ⭐⭐ 实测一例：「以中层 3 组第 5 号钟为例：正鼓部标音『羽』，实测频率 427.7 Hz（相当于现代 A4 音）；侧鼓部标音『宫』，实测频率 516 Hz（相当于现代 C5 音）；两音相差 88.3 Hz，恰为小三度音程，与『羽-宫』的音程关系完全吻合」依计量专题资料
• ⭐ 测音精度：「33 件甬钟有 22 组重复音，将它们分别比较，半数以上重复音的音分差仅在 15 音分之内，其余的重复音则多在 20 音分之内，其音分差在现代音乐家的音准宽容度之内」；「历经 2400 余年埋藏，出土后多数编钟仍能奏响，音准几乎未发生漂移」依曾侯乙编钟研究资料与计量专题资料
• ⭐⭐ 调音工艺：「编钟铸成后，自然音高于目标音高，工匠通过在钟体内壁特定区域打磨减薄来降低音高，直至精确达到目标频率。调音只能做减法不能做加法 —— 一旦打磨过度便无法挽回，一件编钟即报废。钟体内壁可见大量打磨和刮削痕迹」；「相对侧鼓部有一条『音脊』……受到不同程度的磨砺，甚至出现了『音槽』……以加厚和减薄并用的办法调节钟的双音」（音乐考古学家冯光生的研究）；「钟体内壁上有凸起的音塬和凹陷的音隧，这些都是古代工匠们留下的调音 · 调律痕迹」依计量专题 · 研究资料与博物馆资料
• ⭐⭐ 铭文：「钟笋 · 钟钩 · 钟体共有铭文 3755 字，内容有编号 · 铭记 · 标音及乐律」；「（标音铭文）依姑洗均（C 调）记写着各钟所发乐音的阶名或音名」；「钟铭所见律名 28 个 · 阶名 66 个，绝大多数都是前所未知的新材料」；「记述了曾国与楚 · 晋 · 齐 · 申 · 周等国的律名对应关系」；「中层 3 组 5 号钟铭文标注『兽钟之宫』，并注明『兽钟』即楚国对『黄钟』的称呼 —— 这是一份完整的先秦律制换算表」依博物馆 · 考古与计量资料
• ⭐ 规模：「钟架呈曲尺形，架长 748 · 宽 335 · 高 273 厘米；由 6 个佩剑武士形铜柱和 8 根圆柱承托；钟架及挂钩等构件达 246 个，可以拆装」；「共 65 件：上层 3 组钮钟 19 件、中层 3 组甬钟 33 件（短枚 · 无枚 · 长枚三式）、下层 2 组大型长枚甬钟 12 件，另有镈钟 1 件」；「最大者通高 153.4 厘米 · 重 203.6 千克；最小者通高 20.4 厘米 · 重 2.4 千克；钟体总重 2567 公斤，加钟架（含挂钩）铜质部分合计 4421.48 千克」；「镈钟通高 92.5 厘米 · 重 134.8 千克，铭文记载楚惠王在位第 56 年（前 433 年）为祭奠曾侯乙而铸」；「出土时尚有 6 件丁字形彩绘木槌与 2 根彩绘木棒」依文物与博物馆资料
• ⭐ 同墓乐队：「同墓乐器成编：编钟 · 编磬 · 建鼓 · 瑟 7 件 · 笙 4 件 · 箫 2 件 · 篪 2 件 · 小鼓 2 件……构成诸侯宴食祭祀时完整的『轩悬』（三面悬挂钟磬）场面」依考古资料
• ⭐⭐ 音律体系：「音域跨五个半八度（仅比现代钢琴少一个八度），中心音域十二个半音齐备，一钟双音、七声音阶，可以旋宫转调」；「以姑洗律为标准设计制作，以现代乐理讲即按 C 调调制 —— 说明春秋战国之际，我国已存在绝对音高和相对音高的概念」依光明日报 · 博物馆与研究资料
• ⭐ 铸造与合金：「用浑铸 · 分铸 · 铜焊 · 铸镶 · 错金 · 磨砺等工艺制作」；「（甬钟）用分范合铸；据华觉明等学者研究，一件甬钟的铸型须用范 · 芯共 126 块组成（以中层第三组第一钟为例）」；「复合陶范铸造技术 · 铅锡为模料的熔模法 · 钟壁厚度设计 · 鼓部钟腔内的音脊设置 · 热处理技术，加上『合瓦形』结构，使铸件产生双音区」；「含锡量 12.49%–14.46%、含铅 1%–3%；编钟含铅既能阻止钟声传递，又不至于影响编钟音色」依冶金研究与报刊资料
• ⭐⭐ 《考工记》：「凫氏为钟，两栾谓之铣，铣间谓之于，于上谓之鼓，鼓上谓之钲，钲上谓之舞，舞上谓之甬，甬上谓之衡……于上之攠谓之隧」（钟的各部名称）；「薄厚之所震动，清浊之所由出」；「钟已厚则石，已薄则播」（太厚则声闷，太薄则声散）；「钟大而短，则其声疾而短闻；钟小而长，则其声舒而远闻」；「为遂，六分其厚，以其一为之深而圜之」（隧的做法）；「金有六齐：六分其金而锡居一，谓之钟鼎之齐」（钟鼎的合金配方；各家对『六齐』的解读不完全一致）依《周礼 · 考工记》
• ⭐⭐ 认识史：「音乐考古学家冯光生对『一钟双音』现象做了研究……将其发展分为『原生双音』『铸生双音』『铸调双音』三个阶段，分别属于自然存在 · 有意获取 · 精确调制；他认为曾侯乙编钟的双音技术属第三阶段的巅峰时期，几乎达到技术的极限」；「以前西方有人认为，中国直到战国晚期受西方影响才有了相对音高的概念，这一说法不攻自破」；「1978 年 8 月 1 日，历史上第一场曾侯乙编钟原件演奏音乐会举行」；「1979 年起 7 家单位联合研究，1984 年 7 月复制成功」依研究资料与媒体报道
• 「编钟属于八音中的金」依通行资料

Used for fact-checking only; all prose is original.