📚 Year 12 Cambridge Music: Formula & Theorem Quick Reference | 剑桥12年级音乐公式定理速查手册
This quick-reference guide distills the essential theoretical rules of the Cambridge Year 12 Music syllabus into clear, formula-like statements. Mastering these 'formulas' and 'theorems' provides a solid foundation for score analysis, aural skills, composition, and understanding musical styles across the Western classical tradition and selected world music.
本速查手册将剑桥12年级音乐课程大纲中的核心理论规则提炼为清晰的公式化表达。掌握这些“公式”与“定理”将为总谱分析、听觉技能、作曲以及理解西方古典传统与部分世界音乐风格奠定坚实基础。
1. Interval Calculation Formulas | 音程计算公式
Number of semitones + interval quality = interval name. Count the letter names first to determine the numeric size (e.g., C–E is a 3rd), then count the semitones to identify the quality (major, minor, perfect, augmented, diminished).
半音数量 + 音程质量 = 音程名称。先数字母名确定度数（如C–E为三度），再数半音数量来确定质量（大、小、纯、增、减）。
- Perfect Unison: 0 semitones | 纯一度：0半音
- Minor 2nd: 1 semitone; Major 2nd: 2 semitones | 小二度：1半音；大二度：2半音
- Minor 3rd: 3 semitones; Major 3rd: 4 semitones | 小三度：3半音；大三度：4半音
- Perfect 4th: 5 semitones | 纯四度：5半音
- Augmented 4th / Diminished 5th (tritone): 6 semitones | 增四度/减五度（三全音）：6半音
- Perfect 5th: 7 semitones | 纯五度：7半音
- Minor 6th: 8 semitones; Major 6th: 9 semitones | 小六度：8半音；大六度：9半音
- Minor 7th: 10 semitones; Major 7th: 11 semitones | 小七度：10半音；大七度：11半音
- Perfect Octave: 12 semitones | 纯八度：12半音
2. Chord Construction Theorems | 和弦构成定理
Triad theorem: riad = Major 3rd + Perfect 5th (or M3 + m3 on top). Minor triad = Minor 3rd + Perfect 5th.
三和弦定理：根音 + 三音 + 五音。质量由根音上方的叠加音程决定。大三和弦 = 大三度 + 纯五度（或大三度上叠小三度）。小三和弦 = 小三度 + 纯五度。
Major: Root → +4 semitones (M3) → +3 semitones (m3) → 5th
大三和弦：根音 → +4半音（大三度）→ +3半音（小三度）→ 五音
Minor: Root → +3 semitones (m3) → +4 semitones (M3) → 5th
小三和弦：根音 → +3半音（小三度）→ +4半音（大三度）→ 五音
Seventh chord formula: + minor 7th (M3, P5, m7). Diminished 7th = Diminished triad + diminished 7th (m3, d5, d7).
七和弦公式：根音 + 三音 + 五音 + 七音。属七和弦 = 大三和弦 + 小七度（大三度、纯五度、小七度）。减七和弦 = 减三和弦 + 减七度（小三度、减五度、减七度）。
3. Cadence Formulas | 终止式公式
Perfect cadence (V–I): Dominant to tonic. Both chords in root position, with the tonic in the soprano at the final chord for a perfect authentic cadence.
正格终止（V–I）：属和弦到主和弦。两和弦皆为原位，结尾和弦女高音声部为主音则为完满正格终止。
Plagal cadence (IV–I): Subdominant to tonic. Often called the 'Amen' cadence.
变格终止（IV–I）：下属和弦到主和弦。常称“阿门终止”。
Imperfect cadence (I/ii/IV – V): Ends on the dominant, sounding unfinished.
半终止（I/ii/IV – V）：结束在属和弦上，听感未完结。
Interrupted cadence (V–vi): Dominant to submediant. A deceptive resolution; the expected tonic is replaced by vi.
阻碍终止（V–vi）：属和弦到下中和弦。装饰性解决，预期的主和弦被vi替代。
4. Circle of Fifths & Key Signature Formulas | 五度圈与调号公式
Sharp key formula: For major keys, the last sharp in the key signature is the leading note (7th degree). The tonic is a semitone above the last sharp. Order of sharps: F♯ C♯ G♯ D♯ A♯ E♯ B♯.
升号调公式：对于大调，调号中最后一个升号是导音（第VII级）。主音在最后一个升号上方半音。升号顺序：F♯ C♯ G♯ D♯ A♯ E♯ B♯。
Flat key formula: For major keys, the second-to-last flat is the tonic. The key signature with one flat is F major. Order of flats: B♭ E♭ A♭ D♭ G♭ C♭ F♭.
降号调公式：对于大调，倒数第二个降号就是主音。一个降号是F大调。降号顺序：B♭ E♭ A♭ D♭ G♭ C♭ F♭。
Relative minor theorem: The relative minor of a major key starts on the 6th degree (or a minor 3rd below the tonic). It shares the same key signature.
关系小调定理：大调的关系小调开始于其第VI级音上（或主音下方小三度）。两者共享相同的调号。
5. Rhythm & Time Signature Formulas | 节奏与拍号公式
Simple time: e, 3 = triple, 4 = quadruple. Bottom number indicates beat unit: 4 = crotchet, 8 = quaver.
单拍子：每拍分为两个均等部分。上方数字表示拍数：2为二拍子，3为三拍子，4为四拍子。下方数字表示拍子单位：4为四分音符，8为八分音符。
Compound time: is a multiple of 3 (6,9,12). Beat unit is a dotted note: 6/8 = two dotted crotchet beats.
复拍子：每拍分为三个均等部分。上方数字为3的倍数（6、9、12）。拍子单位是附点音符：6/8 = 两个附点四分音符拍。
Dotted rhythm formula: al duration. Double dotted = 1.75 × original. Triplets fit three notes in the time of two.
附点节奏公式：附点音符 = 原时值 × 1.5。双附点 = 原时值 × 1.75。三连音在两者时值内弹奏3个音。
6. Melodic Writing Rules | 旋律写作规则
Stepwise motion principle: A well-written melody moves predominantly by step (2nds). Leaps (3rd or larger) should be balanced by stepwise motion in the opposite direction.
级进原则：好听的旋律以级进（二度）为主。跳进（三度及以上）应通过反方向的级进来平衡。
Melodic contour theorem: An arch-shaped melody often has one clear high point (climax) approached and left by step. Avoid augmented intervals and leaps of a 7th in vocal melodies.
旋律轮廓定理：拱形旋律通常有一个清晰的高潮点，并以级进方式到达和离开。声乐旋律中避免增音程和七度跳进。
Non‑harmonic tones formulas: Passing note (stepwise between two chord tones), neighbour note (step away and back), appoggiatura (leap, then step), suspension (tied, then resolve down by step).
和弦外音公式：经过音（两和弦音之间的级进），辅助音（离开并返回的级进），倚音（跳进后级进解决），延留音（连线保持后下行级进解决）。
7. Harmonic Progression Theorems | 和声进行定理
Functional harmony cycle: I – IV – vii° – iii – vi – ii – V – I. Chords progress forward (left to right) or to any chord directly to the right; retrogressive motion is less common.
功能性循环：I – IV – vii° – iii – vi – ii – V – I。和弦向前行进（从左到右）或直接进行到右边的和弦；逆行较少见。
Voice leading golden rules: Common tone retention, smooth stepwise movement in inner voices, avoid parallel 5ths and octaves, leading note resolves up to tonic.
声部进行黄金法则：共同音保持，内声部平稳级进，避免平行五、八度，导音上行解决到主音。
First inversion principle: I⁶ and V⁶ create variety; ii⁶ often precedes V; the bass line becomes more melodic. Diminished triads are often used in first inversion.
第一转位原则：I⁶与V⁶增加多样性；ii⁶常前置于V；低音线条更富旋律性。减三和弦常用第一转位。
8. Texture & Structural Formulas | 织体与结构公式
Texture theorem: Monophony (single melodic line), Homophony (melody plus chordal accompaniment), Polyphony (two or more independent melodic lines). A composition can shift between textures.
织体定理：单声部（单一旋律线），主调织体（旋律加和弦伴奏），复调织体（两条或以上独立旋律线）。作品可在织体间切换。
Musical form quick reference: Binary (AB), Ternary (ABA), Rondo (ABACA), Theme and Variations, Sonata form (Exposition – Development – Recapitulation), Fugue (exposition of subject and answer in tonic/dominant).
曲式速查：二部曲式（AB），三部曲式（ABA），回旋曲式（ABACA），主题与变奏，奏鸣曲式（呈示部 – 发展部 – 再现部），赋格曲（主题与答题在主/属调上的呈示）。
9. Expression & Tempo Marking Key | 表情与速度标记速查
Tempo formulas (metronome values): Largo ≈ 40–60 BPM, Adagio ≈ 66–76, Andante ≈ 76–108, Moderato ≈ 108–120, Allegro ≈ 120–168, Presto ≈ 168–200.
速度公式（节拍器数值）：广板约40–60 BPM，柔板约66–76，行板约76–108，中板约108–120，快板约120–168，急板约168–200。
Dynamic symbols: pp (very soft), p (soft), mp (moderately soft), mf (moderately loud), f (loud), ff (very loud). Crescendo (cresc.) gradually louder, diminuendo (dim.) gradually softer.
力度符号：pp（很弱），p（弱），mp（中弱），mf（中强），f（强），ff（很强）。渐强（cresc.）逐渐变强，渐弱（dim.）逐渐变弱。
Articulation formulas: ), Tenuto (held full value), Accent (> emphatic attack), Marcato (^ marked, heavy accent).
发音法公式：断奏（短而分离），连奏（平滑连接），保持音（奏满时值），重音（> 强调音头），特重音（^ 加强的重音）。
10. World Music Pattern Recognition | 世界音乐模式识别公式
Gamelan pelog & slendro scales: Pélog has 7 uneven intervals; Sléndro is a 5-tone equidistant scale. Use metallophones and gongs; colotomic structure marks time cycles.
甘美兰佩罗格与斯连德罗音阶：佩罗格有7个不均等音程；斯连德罗为5音等距音阶。使用金属琴与锣；句段结构标记时间循环。
African polyrhythm theorem: Multiple contrasting rhythm patterns performed simultaneously, often in a cycle. Common cycle of 12 or 16 pulses. Cross-rhythm formula: e.g., 3 against 4.
非洲复节奏定理：多条对比节奏型同时演奏，通常以循环形式。常见12或16基础脉冲的循环。交叉节奏公式：如3对4。
Indian tala formula: : Rhythmic cycle with fixed number of beats, divided into vibhags (sections). Theka is the bol (syllable) pattern. Tintal = 16 beats (4+4+4+4).
印度塔拉公式：固定拍数的节奏循环，划分为若干段。Theka是bol（音节）模式。丁塔尔 = 16拍（4+4+4+4）。
11. Score Annotation & Figured Bass Formulas | 乐谱注释与数字低音公式
Figured bass shorthand: osition; 6/5 = first inversion 7th; 4/3 = second inversion 7th; 4/2 = third inversion 7th.
数字低音速记：5/3 = 原位三和弦（常省略）；6/3或仅6 = 第一转位；6/4 = 第二转位。7 = 原位属七和弦；6/5 = 第一转位七和弦；4/3 = 第二转位七和弦；4/2 = 第三转位七和弦。
Transposing instruments theorem: Clarinet in B♭: part written a major 2nd higher than sounding pitch. Horn in F: written a perfect 5th higher. Trumpet in B♭: written major 2nd higher. Subtract intervals to find sounding pitch.
移调乐器定理：降B调单簧管：记谱比实际音高大二度。F调圆号：记谱高纯五度。降B调小号：记谱高大二度。减去相应音程得到实际音高。
12. Essential Musical Terms Quick Reference | 必备音乐术语速查
Refer to the table below for quick retrieval of common Italian, German, and French terms that appear across set works and analysis.
以下表格用于快速查找在指定作品和分析中出现的常见意大利语、德语及法语术语。
| Term | Meaning | 术语 | 含义 |
|---|---|---|---|
| rubato | flexible tempo | 伸缩处理 | 弹性速度 |
| dolce | sweetly | 柔和地 | 甜美地 |
| maestoso | majestic | 庄严地 | 宏伟地 |
| sotto voce | in an undertone | 低声地 | 轻声细语 |
| con sordino | with mute | 加弱音器 | 用弱音器 |
| calando | getting softer and slower | 渐弱并渐慢 | 逐渐消失 |
| attacca | proceed without pause | 紧接着 | 不间断继续 |
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