📚 AQA Year 13 Music: Quick Reference to Formulas and Theorems | AQA 13年级音乐：公式定理速查手册
In the study of AQA Year 13 Music, mastering the 'formulas' behind scales, chords, and harmonic progressions is essential for both analysis and composition. This handbook compiles the core intervallic, structural, and contrapuntal 'theorems' that govern Western tonal music, presented in a clear, formulaic style for quick revision. Whether you are decoding a Haydn string quartet or crafting a chorale in the style of Bach, these patterns will serve as your technical foundation.
在 AQA 13 年级音乐的学习中，掌握音阶、和弦与和声进行背后的“公式”，对分析与创作都至关重要。本手册以清晰的公式化方式，汇编了西方调性音乐中核心的音程、结构与对位“定理”，便于快速复习。无论你是在解读海顿的弦乐四重奏，还是在模仿巴赫的风格创作众赞歌，这些模式都将成为你的技术基石。
1. Major Scale Formula | 大调音阶公式
The major scale follows a fixed sequence of tones (T) and semitones (S): T T S T T T S. In terms of whole steps (W) and half steps (H), this becomes W W H W W W H. Starting on any tonic note, applying this formula generates the seven notes of the major scale, defining the key’s signature and the basis for diatonic harmony.
大调音阶遵循固定的全音（T）与半音（S）序列：T T S T T T S。用全步（W）和半步（H）表示则为 W W H W W W H。从任意主音开始，应用该公式即可产生大调音阶的七个音，从而确定调号，并成为自然音和声的基础。
- Example: C major – C (T) D (T) E (S) F (T) G (T) A (T) B (S) C
- 示例：C 大调 – C（全）D（全）E（半）F（全）G（全）A（全）B（半）C
Major scale formula: W W H W W W H
2. Minor Scale Formulas | 小调音阶公式
Minor scales come in three forms, each with its own interval pattern. The natural minor follows the sequence T S T T S T T (W H W W H W W). The harmonic minor raises the 7th degree by a semitone, producing an augmented 2nd between the 6th and 7th notes: T S T T S (T+S) S. The melodic minor, used in ascending passages, raises both the 6th and 7th degrees: T S T T T T S, while descending it reverts to natural minor.
小调音阶有三种形式，各有其音程模式。自然小调遵循 T S T T S T T（W H W W H W W）。和声小调将第 VII 级升高半音，使得第 VI 级与第 VII 级之间出现增二度：T S T T S (T+S) S。旋律小调在上行时同时升高第 VI 级与第 VII 级：T S T T T T S；下行时则还原为自然小调。
| Minor type | Interval pattern (ascending) | Example in A |
|---|---|---|
| Natural minor | T S T T S T T | A B C D E F G A |
| Harmonic minor | T S T T S 3S S | A B C D E F G♯ A |
| Melodic minor | T S T T T T S (up) natural minor (down) |
A B C D E F♯ G♯ A up |
3. Triad Construction | 三和弦构造
act interval sizes. Using semitone counting from the root: a major triad consists of root + 4 semitones (major 3rd) + 3 semitones (minor 3rd) = 7 semitones to the 5th. A minor triad is root + 3 semitones (minor 3rd) + 4 semitones (major 3rd) = 7 semitones to the 5th. A diminished triad stacks two minor 3rds (3+3), and an augmented triad stacks two major 3rds (4+4).
三和弦是由根音上方叠加两个三度构成的三音和弦。和弦的性质（大、小、减、增）由具体的音程大小决定。以根音为起点，用半音数计算：大三和弦 = 根音 + 4 个半音（大三度）+ 3 个半音（小三度），到五音共 7 个半音。小三和弦 = 根音 + 3 个半音（小三度）+ 4 个半音（大三度），到五音也是 7 个半音。减三和弦由两个小三度叠加（3+3），增三和弦由两个大三度叠加（4+4）。
Triad formulas (semitone count from root to 3rd and 5th):
Major: 4 + 3 | Minor: 3 + 4 | Diminished: 3 + 3 | Augmented: 4 + 4
4. Seventh Chord Formulas | 七和弦公式
Seventh chords extend triads by adding a 7th above the root. The combination of the underlying triad quality and the type of 7th creates five common species. Using intervals relative to the root:
七和弦是在三和弦基础上叠加根音上方的七度音而成。由下方三和弦的性质与七度的类型组合，形成五种常见七和弦。以下是相对于根音的音程公式：
| Chord type | Triad + 7th interval | Example: C root |
|---|---|---|
| Major 7th | Major triad + major 7th | C‑E‑G‑B |
| Dominant 7th | Major triad + minor 7th | C‑E‑G‑B♭ |
| Minor 7th | Minor triad + minor 7th | C‑E♭‑G‑B♭ |
| Half-diminished 7th | Diminished triad + minor 7th | C‑E♭‑G♭‑B♭ |
| Diminished 7th | Diminished triad + diminished 7th | C‑E♭‑G♭‑B♭♭ |
In figured bass shorthand, inversions are indicated by intervals above the lowest note: first inversion 6/5, second inversion 4/3, third inversion 4/2.
在数字低音的简记法中，转位由低音上方的音程表示：第一转位 6/5，第二转位 4/3，第三转位 4/2。
5. Chord Inversions and Figured Bass | 和弦转位与数字低音
Inversions reorder the notes of a chord so that a tone other than the root becomes the lowest sounding pitch. The figured bass system provides a concise code:
转位改变了和弦音的排列顺序，使非根音成为最低音。数字低音体系提供了一种简明的编码：
| Chord type | Root position | 1st inversion | 2nd inversion | 3rd inversion (7th chords only) |
|---|---|---|---|---|
| Triad | 5/3 (often omitted) | 6 or 6/3 | 6/4 | — |
| 7th chord | 7 | 6/5 | 4/3 | 4/2 or 2 |
In AQA analysis tasks, recognising these figures helps identify the harmonic function and voice-leading of a passage without needing to reconstruct each chord exhaustively.
在 AQA 的分析任务中，识别这些数字有助于判断段落的和声功能与声部进行，而无需逐一完整重建每个和弦。
6. Cadence Types | 终止式类型
Cadences are the punctuation marks of tonal music. Their formulas depend on the harmonic progression at the end of a phrase:
终止式是调性音乐的标点符号。它们的公式取决于乐句末尾的和声进行：
- Perfect cadence: V → I (both chords in root position, soprano on tonic in the final chord)
- 正格终止： V → I（两个和弦均为根音位置，最后和弦的高音为主音）
- Imperfect cadence: Any chord → V (often I → V, II → V, IV → V)
- 半终止： 任意和弦 → V（常见 I → V, II → V, IV → V）
- Plagal cadence: IV → I (the 'Amen' cadence)
- 变格终止： IV → I（“阿门”终止）
- Interrupted (deceptive) cadence: V → vi (in major) or V → VI (in minor)
- 阻碍终止： V → vi（大调）或 V → VI（小调）
In chorale-style writing, the perfect cadence is the strongest close; the imperfect cadence creates expectation; the plagal cadence offers a softer resolution; and the interrupted cadence postpones finality.
在众赞歌风格写作中，正格终止最具收束力；半终止制造期待；变格终止带来柔和的解决；阻碍终止则推迟终结感。
7. Harmonic Progression Rules | 和声进行规则
Functional harmony follows preferred root movement patterns that can be summarised as 'circle of 5ths' movement. The foundational theorem is that chords tend to move down by 5th (or up by 4th) in well-formed progressions. A typical classical progression maps as:
功能和声遵循偏好的根音进行模式，可概括为“五度圈”运动。基本定理是：在结构良好的进行中，和弦倾向于向下五度（或向上四度）运动。典型的古典进行模式如下：
I → IV → vii° → iii → vi → ii → V → I
This sequence can be shortened, looped, or adapted. Secondary dominants and applied chords temporarily tonicise a chord by inserting its own dominant, expanding the vocabulary while obeying the same fifth-related logic.
这一序列可以缩短、循环或调整。副属和弦与借用和弦通过插入某个和弦自身的属和弦来临时主音化，在遵守五度关系逻辑的同时扩展了和声语汇。
8. Counterpoint Principles | 对位原则
In species counterpoint and chorale writing, several 'theorems' govern the relationship between voices:
在分类对位与众赞歌写作中，若干“定理”制约着声部之间的关系：
- Contrary motion is preferred: Voices move in opposite directions wherever possible.
- 优先使用反向进行： 声部尽可能朝相反方向运动。
- Parallel perfect intervals are forbidden: Perfect 5ths and perfect 8ves (octaves) must not move in parallel, as they destroy voice independence.
- 禁止平行完全音程： 纯五度与纯八度不可平行进行，因其破坏声部独立性。
- Hidden (direct) perfect intervals require care: When a perfect 5th or 8ve is approached by similar motion, the top voice should move by step.
- 隐伏（同向）完全音程需谨慎处理： 当纯五度或纯八度以同向进行进入时，高音声部应级进。
- Leading note resolves up: The 7th degree of the scale (leading tone) rises to the tonic in most common-practice styles.
- 导音上行解决： 音阶第 VII 级（导音）在大部分通用实践风格中向上解决到主音。
- 7th of a chord resolves down by step: In a dominant 7th or any chordal 7th, the dissonant 7th falls stepwise.
- 和弦七音下行级进解决： 在属七和弦或任何包含七音的和弦中，不协和的七音级进下行。
These principles can be treated as strict rules in Bach-style exercises.
这些原则在巴赫风格练习中被视为严格规则。
9. Musical Form Patterns | 曲式结构模式
Musical forms often follow predictable 'formulas' of thematic repetition and contrast. Key AQA set works typically exhibit:
音乐曲式往往遵循可预见的主题重复与对比的“公式”。AQA 常考作品通常包含以下结构：
- Binary form (AB): Two distinct sections, each usually repeated. Section A modulates to a related key (e.g. dominant), section B returns to the tonic.
- 二段体（AB）： 两个不同的段落，各通常重复一次。A 段转至关系调（如属调），B 段返回主调。
- Ternary form (ABA): A contrasting middle section framed by a return of the opening material. Often the return is written out or indicated by a da capo.
- 三段体（ABA）： 由开头部材料再现来框定对比性的中间段。再现段常被完整写出或用 da capo 指示。
- Sonata form: Exposition (first subject – transition – opment (motivic fragmentation, key instability) → Recapitulation (both subjects in tonic).
- 奏鸣曲式： 呈示部（第一主题 – 连接部 – 第二主题在属调或关系大调）→ 展开部（动机分裂、调性不稳定）→ 再现部（两个主题均回到主调）。
- Rondo form (ABACA...): A recurring refrain (A) alternates with contrasting episodes. The formula emphasises the persistence of a central theme.
- 回旋曲式（ABACA…）： 反复出现的叠部（A）与对比性的插部交替。这一公式强调中心主题的持续。
Memorising these structural templates allows you to map any work quickly in the AQA listening exam.
记忆这些结构模板，能让你在 AQA 听力考试中快速勾勒出任何作品的结构图谱。
10. Ornamentation Patterns | 装饰音公式
Ornaments follow standardised 'formulas' that define their rhythmic interpretation. In Baroque and Classical styles, these are essential to stylistic accuracy:
装饰音遵循标准化的“公式”，规定了其节奏诠释方式。在巴洛克与古典风格中，这对风格准确性至关重要：
| Ornament | Execution formula | Notation |
|---|---|---|
| Trill (tr.) | Rapid alternation between written note and upper neighbour, starting on the upper note (in Baroque) or main note (later). Ends with a turn. | tr. above note |
| Turn (𝄐) | Upper note – main note – lower note – main note. Placed directly above a note, it starts on the upper neighbour. | 𝄐 symbol |
| Mordent (𝄞, upper) | Main note – upper note – main note, played rapidly. | 𝄞 over note |
| Appoggiatura | A dissonant note that leans on the main note, taking half its value (or more), then resolves stepwise. | Small note before main note (not crossed) |
| Acciaccatura | A 'crushed' note played very briefly before the main note, often diatonically below or above. | Small note with a slash through stem |
In analysis, recognising the formula behind an ornament clarifies its rhythmic placement and expressive effect.
在分析中，识别装饰音背后的公式，可理清其节奏位置与表情效果。
11. Circle of Fifths and Key Relationships | 五度圈与调性关系
The circle of fifths is itself a theorem: moving clockwise by perfect 5ths adds one sharp each step; moving anticlockwise adds one flat. The relative minor of any major key lies a minor 3rd below the tonic, sharing the same key signature. These relationships allow quick determination of closely related keys – those adjacent on the circle – which are the most common modulatory destinations.
五度圈本身就是一个定理：顺时针按纯五度移动，每步增加一个升号；逆时针移动则增加一个降号。任何大调的关系小调位于主音下方小三度，共用同一调号。这些关系让你能快速确定近关系调——即圈上相邻的调——它们是最常见的转调目标。
Major: C (0) → G (1♯) → D (2♯) → A (3♯) → E (4♯) → B (5♯) → F♯ (6♯) → C♯ (7♯)
Minor: A (0) → E (1♯) → B (2♯) → F♯ (3♯) → C♯ (4♯) → G♯ (5♯) → D♯ (6♯) → A♯ (7♯) ... and flats similarly.
12. Composition Device Formulas | 创作手法公式
Common musical devices can also be expressed as repeatable formulas:
常见的音乐手法也可用可重复的公式来表达：
- Sequence: A melodic/harmonic pattern repeated at a higher or lower pitch. Formula: unit x transposed to T+2, T+4, etc.
- 模进： 一个旋律/和声模式在更高或更低的音高上重复。公式：将单元移高/移低 T+2, T+4 等半音级。
- Pedal point: A sustained or repeated note (usually tonic or dominant) while harmonies change above. Formula: drone bass + chord progression.
- 持续音： 在上方和声变化时保持或重复一个音符（通常是主音或属音）。公式：低音持续音 + 和弦进行。
- Octave displacement: A melody leaps by an octave to extend range. Formula: note x → x ± 12 semitones.
- 八度位移： 旋律通过八度跳跃来扩展音域。公式：音符 x → x ± 12 个半音。
- Diminution/Augmentation: a theme are halved (diminution) or doubled (augmentation). Formula: note value × ½ or × 2.
- 减值/增值： 将主题的节奏时值缩短一半（减值）或延长一倍（增值）。公式：原时值 × ½ 或 × 2。
These formulas help you identify and describe development processes in set works and unseen extracts.
这些公式可帮助你识别并描述指定作品及陌生片段中的展开手法。
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