📚 Year 12 AQA Music: Formula & Theorem Quick Reference Handbook | 公式定理速查手册
This reference handbook distills the essential theoretical ‘formulas’ and theorems required for Year 12 AQA Music. From the circle of fifths to cadence formulas and chord construction rules, every concept is presented as a repeatable pattern—much like a mathematical formula. Use these models to analyse set works, complete harmony exercises, and sharpen your aural skills with precision and confidence.
本速查手册精炼了 Year 12 AQA 音乐课程必备的理论“公式”与定理。从五度圈到终止式公式，再到和弦构建规则，每个概念都呈现为可复用的模式——如同数学公式一般。运用这些模型分析规定作品、完成和声练习，并精准自信地提升听力技能。
1. Circle of Fifths Formula | 五度圈公式
The circle of fifths is a fundamental formula for understanding key relationships. Moving clockwise, each key is a perfect fifth higher and gains one additional sharp; moving anticlockwise, each key is a perfect fifth lower and gains one additional flat. The relative minor sits a minor third below each major key. This formula governs key signatures, modulations, and chord progressions throughout Western tonal music.
五度圈是理解调性关系的基本公式。顺时针移动，每个调升高纯五度并增加一个升号；逆时针移动，每个调降低纯五度并增加一个降号。关系小调位于每个大调下方小三度。此公式支配着西方调性音乐中的调号、转调与和弦进行。
| Major Key | Sharps/Flats | Relative Minor |
| C major | 0 | A minor |
| G major | 1♯ (F♯) | E minor |
| D major | 2♯ (F♯, C♯) | B minor |
| A major | 3♯ (F♯, C♯, G♯) | F♯ minor |
| F major | 1♭ (B♭) | D minor |
| B♭ major | 2♭ (B♭, E♭) | G minor |
2. Interval Calculation Rules | 音程计算规则
Intervals are measured by counting letter names (the number) and then determining quality through semitone count. The formula for a perfect interval is a unison, fourth, fifth, or octave that matches the semitone count of the major scale from the tonic to that degree. Major intervals arise from the second, third, sixth, and seventh degrees of a major scale. Augment a perfect or major interval by expanding it a semitone; diminish it by reducing a semitone. Inversion of intervals follows the rule: the number always adds to 9, and quality flips (major ↔ minor, perfect ↔ perfect, augmented ↔ diminished). For example, a major third inverts to a minor sixth.
音程的测量先数字母名称（度数），再通过半音数确定性质。纯音程的公式是：同度、四度、五度或八度，且其半音数与从主音到该音级的大调音阶相匹配。大音程源自大调音阶的二度、三度、六度与七度。将纯音程或大音程扩大半音变为增音程；缩小半音变为减音程。音程转位遵循规律：度数相加总为9，性质翻转（大↔小，纯↔纯，增↔减）。例如，大三度转位为小六度。
Inversion Formula: New Number = 9 − Original Number, Quality swaps as described above.
转位公式：新度数 = 9 − 原度数，性质如上互换。
3. Triad Construction Formulas | 三和弦构建公式
A triad is built by stacking two thirds on a root. The formula for a major triad states: root + major third (4 semitones) + perfect fifth (7 semitones from root). A minor triad uses root + minor third (3 semitones) + perfect fifth. A diminished triad has root + minor third + diminished fifth (6 semitones), and an augmented triad is root + major third + augmented fifth (8 semitones). These formulas apply to any root, generating the chord’s quality regardless of key signature.
三和弦由根音上叠加两个三度构成。大三和弦公式：根音 + 大三度（4个半音）+ 纯五度（距根音7个半音）。小三和弦使用根音 + 小三度（3个半音）+ 纯五度。减三和弦为根音 + 小三度 + 减五度（6个半音），增三和弦为根音 + 大三度 + 增五度（8个半音）。这些公式适用于任何根音，无需调号即可生成和弦性质。
| Triad Quality | Structure (semitones from root) | Example on C |
| Major | 0 – 4 – 7 | C – E – G |
| Minor | 0 – 3 – 7 | C – E♭ – G |
| Diminished | 0 – 3 – 6 | C – E♭ – G♭ |
| Augmented | 0 – 4 – 8 | C – E – G♯ |
4. Seventh Chord Construction | 七和弦构建
Seventh chords add a third above the fifth of a triad, producing a four-note stack. The dominant seventh formula is a major triad plus a minor seventh (10 semitones from root). A major seventh chord is a major triad plus a major seventh (11 semitones), while a minor seventh chord combines a minor triad with a minor seventh. The half-diminished seventh formula uses a diminished triad with a minor seventh, and the fully diminished seventh uses a diminished triad with a diminished seventh (9 semitones). Memorising the semitone patterns helps you spell these chords instantly in any inversion.
七和弦在三和弦的五音上方再加一个三度，构成四音叠置。属七和弦公式：大三和弦 + 小七度（距根音10个半音）。大七和弦为大三和弦 + 大七度（11个半音），小七和弦由小三和弦 + 小七度组合而成。半减七和弦公式为减三和弦 + 小七度，全减七和弦则使用减三和弦 + 减七度（9个半音）。熟记半音模式可帮助你在任意转位中立刻拼写这些和弦。
Dominant 7th on G: G – B – D – F (0 – 4 – 7 – 10)
G上的属七和弦：G – B – D – F (0 – 4 – 7 – 10)
5. Chord Inversion Figured Bass | 和弦转位与数字低音
Chords are classified by which note is in the bass. The root position formula places the root in the bass and uses no figured bass symbol (or 5/3 in full analysis). First inversion puts the third in the bass, indicated by a 6 (short for 6/3). Second inversion places the fifth in the bass, shown as 6/4. For seventh chords, root position is 7, first inversion is 6/5, second inversion is 4/3, and third inversion (seventh in bass) is 4/2 or simply 2. These formulas remain consistent across all chord qualities and are essential for part-writing and harmonic analysis.
和弦按低音音符分类。原位公式将根音置于低音，不使用数字低音符号（或完整标记为5/3）。第一转位以三音为低音，用6（6/3的缩写）表示。第二转位以五音为低音，标记为6/4。对于七和弦，原位为7，第一转位为6/5，第二转位为4/3，第三转位（七音为低音）为4/2或简写为2。这些公式适用于所有和弦性质，是声部写作与和声分析的基础。
- Triad: Root = 5/3, 1st inv = 6, 2nd inv = 6/4
- Seventh: Root = 7, 1st inv = 6/5, 2nd inv = 4/3, 3rd inv = 4/2
- 三和弦：原位 = 5/3，第一转位 = 6，第二转位 = 6/4
- 七和弦：原位 = 7，第一转位 = 6/5，第二转位 = 4/3，第三转位 = 4/2
6. Cadence Formulas | 终止式公式
Cadences are the punctuation marks of tonal music, each defined by a specific chord progression formula. A perfect cadence moves V – I (or V⁷ – I) with both chords in root position and the tonic in the soprano at the final chord, creating a full close. An imperfect cadence ends on V, preceded by any chord (commonly I, ii, or IV). The plagal cadence (IV – I) is the ‘Amen’ cadence. An interrupted cadence sets up V – vi, deflecting the expected tonic. Recognising these formulas in score analysis allows you to map phrase structure with certainty.
终止式是调性音乐的标点符号，每种都由特定的和弦进行公式定义。正格终止进行为 V – I（或 V⁷ – I），两和弦均用原位且最后和弦高音部为主音，形成完全收束。不完全终止结束在 V，前面可以是任何和弦（常用 I、ii 或 IV）。变格终止（IV – I）即“阿门”终止。阻碍终止设置为 V – vi，使预期的解决偏转。在乐谱分析中识别这些公式，能让你确定地勾勒乐句结构。
| Cadence | Formula | Typical Use |
| Perfect | V – I | End of phrase / section |
| Imperfect | ? – V | Mid-phrase pause |
| Plagal | IV – I | ‘Amen’, codas |
| Interrupted | V – vi | Deceptive close |
7. Common Chord Progression Formulas | 常见和弦进行公式
Tonal harmony relies on a set of standard progression patterns acting like syntax. The most fundamental is the tonic–predominant–dominant–tonic (T–PD–D–T) model: I – IV – V – I in major, or i – iv – V – i in minor. The descending circle-of-fifths progression (vi – ii – V – I or iii – vi – ii – V – I) appears in countless Baroque and Classical works. The Pachelbel canon formula (I – V – vi – iii – IV – I – IV – V) is a prototype for many pop and classical sequences. Recognising these skeletons accelerates harmonic analysis and stylistic composition tasks.
调性和声依赖一套标准进行模式，如同语法。最基本的是主–下属–属–主（T–PD–D–T）模型：大调 I – IV – V – I，小调 i – iv – V – i。下行五度圈进行（vi – ii – V – I 或 iii – vi – ii – V – I）出现在无数巴洛克与古典作品中。帕赫贝尔卡农公式（I – V – vi – iii – IV – I – IV – V）是许多流行与古典序列的原型。识别这些骨架可加速和声分析及风格化作曲任务。
- Perfect cadence approach: ii⁶ – V⁷ – I (predominant inversion smoothly leads to dominant)
- 常见的正格终止铺垫：ii⁶ – V⁷ – I (下属转位平滑导向属和弦)
8. Modulation Pivot Chord Formula | 转调枢轴和弦公式
Modulation in common-practice style often uses a pivot chord that functions diatonically in both the old key and the new key. The formula is: identify a chord shared by the two keys—usually the chord built on a degree that is diatonic to both. For modulating from C major to G major, the pivot might be the tonic of C (I in C = IV in G), the submediant (vi in C = ii in G), or the mediant (iii in C = vi in G). After the pivot, the harmony immediately introduces the new leading tone and dominant to secure the modulation. This pivot chord formula is a critical analytical tool for AQA set works and the composition brief.
共性实践时期的转调常使用一个在旧调与新调中均属于自然音体系的枢轴和弦。公式为：找出两个调共有的和弦——通常是建立在两个调共有的音级上的和弦。从C大调转到G大调，枢轴可能是C的主和弦（C的I = G的IV）、下中音和弦（C的vi = G的ii）或中音和弦（C的iii = G的vi）。在枢轴之后，和声立即引入新的导音与属和弦以稳固转调。这一枢轴和弦公式是分析AQA规定作品与创作任务的关键工具。
Pivot in C → G: Chord Dm (ii in C → v in G? Actually Dm is ii in C, but in G it would be v, not diatonic. Better pivot: Am (vi in C = ii in G) or Em (iii in C = vi in G) or C (I in C = IV in G).
C → G的枢轴：Am（C的vi = G的ii）或C（C的I = G的IV）等。
9. Harmonic Rhythm Rules | 和声节奏规则
Harmonic rhythm—the rate at which chords change—follows patterned formulas in different genres. In Classical-era minuets, the harmonic rhythm often accelerates toward cadences: one chord per bar in the opening, two per bar approaching the dominant, and chord changes on every beat at cadential points. In Baroque chorales, harmonic rhythm is frequently steady, changing chords on each crotchet beat or minim beat. A sudden slowing of harmonic rhythm (a pedal point, for example) signals structural emphasis or approaching closure. The formula ‘quicker harmonic rhythm = heightened tension, slower harmonic rhythm = stability’ underpins much expressive analysis.
和声节奏——和弦变换的速率——在不同体裁中遵循模式化公式。在古典时期小步舞曲中，和声节奏常在接近终止时加快：开头每小节一个和弦，接近属和弦时每小节两个和弦，在终止处每一拍都有和弦变换。在巴洛克众赞歌中，和声节奏通常稳定，每四分音符或二分音符变换和弦。和声节奏突然放缓（例如持续音）表示结构重点或接近收束。“较快和声节奏 = 紧张加剧，较慢和声节奏 = 稳定”这一公式支撑着许多表现力分析。
10. Melodic Writing Rules | 旋律写作规则
AQA melody completion tasks rely on a set of interlocking formulas. The melodic contour should balance stepwise motion (conjunct) with a few carefully placed leaps (disjunct), often no larger than a perfect fifth unless followed by stepwise recovery in the opposite direction. Rhythmic formulas demand a climax point—often the highest pitch aligned with a strong beat or agogic accent. Sequences (repetition of a melodic pattern at a different pitch) must follow a consistent intervallic pattern and usually appear in pairs or trios. Complement the given opening with a congruent answering phrase; if the opening ends on scale degree 2, the answer often closes on the tonic, following the ‘question and answer’ formula.
AQA旋律续写任务依赖一系列相互关联的公式。旋律轮廓应平衡级进（联合进行）与少量精心布置的跳进（分离进行），跳进通常不超过纯五度，除非之后以反向级进恢复。节奏公式要求一个高潮点——往往是最高音与强拍或延长音重音对齐。模进（旋律模式在不同音高上重复）必须遵循一致的音程序列，通常成对或三个一组出现。补充给定的开头，用协调的应答乐句；若开头结束于音阶第2级，应答常收束于主音，遵循“问与答”公式。
- Leap resolution formula: leap → step in opposite direction
- 跳进解决公式：跳进 → 反向级进
11. Texture and Sonority Equations | 织体与音色公式
Texture in the AQA specification can be modelled as equations combining functions. Monophony = a single unaccompanied melodic line. Homophony = melody + chordal accompaniment (homorhythmic when all voices move together, melody-dominated homophony when an upper melody is supported by lower chords). Polyphony = two or more independent melodic lines combined (contrapuntal). Heterophony = simultaneous variation of a single melody. Sonority equations describe instrumental combinations: string quartet = violin I + violin II + viola + cello; concerto grosso = concertino (solo group) + ripieno (orchestra); continuo = harpsichord/organ + cello/bassoon. Analysing these ‘equations’ clarifies structural intent in set works.
AQA规范中的织体可模型化为功能组合等式。单音织体 = 单一无伴奏旋律线。主调织体 = 旋律 + 和弦伴奏（当所有声部同步移动时为同节奏主调织体，当上方旋律由下方和弦支撑时为旋律主导的主调织体）。复调织体 = 两条或多条独立旋律线结合（对位）。支声复调 = 同一旋律的共时变奏。音色等式描述器乐组合：弦乐四重奏 = 小提琴I + 小提琴II + 中提琴 + 大提琴；大协奏曲 = 主奏组 + 合奏组（乐队）；通奏低音 = 羽管键琴/管风琴 + 大提琴/巴松管。分析这些“等式”可明晰规定作品中的结构意图。
12. Performance Directions and Abbreviations | 演奏指示与缩略词表
A working knowledge of Italian, French, and German musical terms functions as a decoding formula for expression marks. From tempo (Allegro = fast, Andante = at a walking pace, Lento = slow) to dynamics (crescendo = gradually louder, diminuendo = gradually softer, sforzando = forced/accented) and playing techniques (pizzicato = plucked, arco = with the bow, con sordino = with mute), these formulae unlock period performance practice. In the AQA exam, recognising terms in score excerpts ensures correct interpretation of character and style.
熟练掌握意大利语、法语和德语音乐术语，可作为表情记号的解码公式。从速度（Allegro = 快板，Andante = 行板，Lento = 慢板）到力度（crescendo = 渐强，diminuendo = 渐弱，sforzando = 突强/重音）以及演奏技巧（pizzicato = 拨弦，arco = 用弓，con sordino = 加弱音器），这些公式解开了时期演奏实践。在AQA考试中，识别乐谱片段中的术语可确保正确诠释特征与风格。
| Term | Meaning | Category |
| cantabile | in a singing style | Expression |
| rubato | flexible tempo | Tempo |
| staccato | short and detached | Articulation |
| tutti | all together | Orchestration |
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