📚 AQA Year 12 Music: Quick Reference to Key Formulae and Theorems | Year 12 AQA 音乐：公式定理速查手册
This quick reference guide consolidates the essential music theory formulas and theorems that every Year 12 AQA A-level Music student must master. From scale construction to harmonic progressions, these patterns underpin compositional analysis and performance understanding. Use this handbook as a rapid revision tool to reinforce your grasp on the building blocks of Western tonal music.
本速查手册汇总了每位 Year 12 AQA A-level 音乐学生必须掌握的核心乐理公式和定理。从音阶构建到和声进行，这些模式是作品分析和表演理解的基础。请将本手册作为快速复习工具，巩固您对西方调性音乐构成要素的掌握。
1. Major Scale Formula | 大调音阶公式
The diatonic major scale is built from an unchanging sequence of tones (T) and semitones (S). The pattern can be remembered by the mnemonic 'Two tones, semitone, three tones, semitone'. It is the foundation of Western harmony and melody.
自然大调音阶由一个固定的全音(T)和半音(S)序列构建。该模式可记为“两个全音，半音，三个全音，半音”。它是西方和声与旋律的基石。
T T S T T T S
Applying this pattern to any starting note produces a major scale. For example, C major: C (T) D (T) E (S) F (T) G (T) A (T) B (S) C. The semitones naturally occur between E-F and B-C. To build a G major scale, we start on G and follow the same sequence, which yields G, A, B, C, D, E, F♯, G – the F must be raised to F♯ to maintain the T-T-S pattern between E and the leading note.
将此模式应用于任何一个起始音，即可产生大调音阶。例如，C大调：C (T) D (T) E (S) F (T) G (T) A (T) B (S) C。半音自然出现在E-F和B-C之间。要构建G大调，从G开始遵循相同序列，得到 G, A, B, C, D, E, F♯, G – F必须升高为F♯，以在E和导音之间保持全-全-半的模式。
2. Minor Scale Types and Formulas | 小调音阶类型与公式
The minor mode has three commonly used variants, each with a distinct pattern of tones and semitones. The natural minor (Aeolian) descends directly from the major scale but starts on the sixth degree. Its formula is: T S T T S T T.
小调有三种常用变体，每种都有独特的全音和半音模式。自然小调（爱奥里亚）直接源自大调音阶，但从第六级音开始。其公式为：T S T T S T T。
Using A natural minor as an example: A (T) B (S) C (T) D (T) E (S) F (T) G (T) A. The harmonic minor raises the seventh degree to create a leading tone, producing a characteristic augmented second (T+S, three semitones) between the sixth and seventh. Its pattern: T S T T S T+S S.
以A自然小调为例：A (T) B (S) C (T) D (T) E (S) F (T) G (T) A。和声小调将第七级升高以创建导音，从而在六级和七级之间产生一个特征性的增二度（T+S，三个半音）。其模式：T S T T S T+S S。
The melodic minor adapts for smoother voice leading: ascending, it raises both the sixth and seventh degrees (T S T T T T S), resembling a major scale with a flattened third; descending, it reverts to the natural minor form (T T S T T S T).
旋律小调为更平滑的声部进行而调整：上行时，升高六级和七级（T S T T T T S），类似于降低了三级的大调音阶；下行时，恢复为自然小调形式（T T S T T S T）。
3. Key Signatures – Circle of Fifths | 调号——五度圈
Key signatures are derived from the circle of fifths. Sharps are added in the order: F♯ C♯ G♯ D♯ A♯ E♯ B♯, remembered as 'Father Charles Goes Down And Ends Battle'. For flats, the order reverses: B♭ E♭ A♭ D♭ G♭ C♭ F♭, or 'Battle Ends And Down Goes Charles Father'.
调号源自五度圈。升号按顺序添加：F♯ C♯ G♯ D♯ A♯ E♯ B♯，可记为"Father Charles Goes Down And Ends Battle"。降号顺序相反：B♭ E♭ A♭ D♭ G♭ C♭ F♭，即"Battle Ends And Down Goes Charles Father"。
Each major key has a relative minor a minor third below (e.g., C major – A minor). The following table shows key signatures up to four sharps and flats, common in Year 12 studies.
每个大调都有一个关系小调，位于下方小三度（例如，C大调 – A小调）。下表展示了Year 12学习中常见的多达四个升号和降号的调号。
| Major Key / 大调 | Number of Sharps/Flats / 升降号数量 | Relative Minor / 关系小调 |
|---|---|---|
| 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 |
| E Major | 4♯ (F♯ C♯ G♯ D♯) | C♯ minor |
| F Major | 1♭ (B♭) | D minor |
| B♭ Major | 2♭ (B♭ E♭) | G minor |
| E♭ Major | 3♭ (B♭ E♭ A♭) | C minor |
| A♭ Major | 4♭ (B♭ E♭ A♭ D♭) | F minor |
4. Interval Quick Reference | 音程速查表
An interval is the distance in pitch between two notes, measured in semitones. The following table links the number of semitones to the full interval name, using C as the lower reference. Recognize these patterns quickly for score analysis and ear training.
音程是两音之间的音高距离，以半音度量。下表将半音数与完整的音程名称联系起来，以C为低音参考。在乐谱分析和听觉训练中应快速识别这些模式。
| Semitones / 半音数 | Interval Name / 音程名称 | Example from C / C上例子 |
|---|---|---|
| 0 | Perfect unison (P1) | C-C |
| 1 | Minor 2nd (m2) | C-D♭ |
| 2 | Major 2nd (M2) | C-D |
| 3 | Minor 3rd (m3) | C-E♭ |
| 4 | Major 3rd (M3) | C-E |
| 5 | Perfect 4th (P4) | C-F |
| 6 | Augmented 4th / Diminished 5th (A4/d5) | C-F♯ |
| 7 | Perfect 5th (P5) | C-G |
| 8 | Minor 6th (m6) | C-A♭ |
| 9 | Major 6th (M6) | C-A |
| 10 | Minor 7th (m7) | C-B♭ |
| 11 | Major 7th (M7) | C-B |
| 12 | Perfect Octave (P8) | C-C' |
5. Triad Chord Construction | 三和弦构建公式
en third to fifth. This can be summarised by the pattern of thirds (M = major 3rd, 4 semitones; m = minor 3rd, 3 semitones).
四种三和弦的性质都是通过在根音上叠加两个三度（大三度或小三度）构建的。公式由半音间距定义：根音到三音，再三音到五音。可以用三度模式总结（M=大三度，4个半音；m=小三度，3个半音）。
- Major triad (M + m): root + 4 semitones + 3 semitones. Example: C-E-G.
- Minor triad (m + M): root + 3 semitones + 4 semitones. Example: D-F-A.
- Diminished triad (m + m): root + 3 semitones + 3 semitones. Example: B-D-F.
- Augmented triad (M + M): root + 4 semitones + 4 semitones. Example: C-E-G♯.
- 大三和弦（大+小）：根音 + 4 半音 + 3 半音。例如：C-E-G。
- 小三和弦（小+大）：根音 + 3 半音 + 4 半音。例如：D-F-A。
- 减三和弦（小+小）：根音 + 3 半音 + 3 半音。例如：B-D-F。
- 增三和弦（大+大）：根音 + 4 半音 + 4 半音。例如：C-E-G♯。
6. Chord Inversions and Figured Bass | 和弦转位与数字低音
Inversions change the bass note while retaining the same chord membership. For triads, we have root position (5 3), first inversion (6 3 or simply 6), and second inversion (6 4). The figures represent intervals above the bass note.
转位改变了低音，但保留相同的和弦音。对于三和弦，我们有根音位置（5 3）、第一转位（6 3 或简写6）和第二转位（6 4）。这些数字表示低音上方音程。
For seventh chords (essential in AQA harmony), the figures are: root position (7 5 3), first inversion (6 5 3, often abbreviated 6 5), second inversion (6 4 3, often 4 3), and third inversion (6 4 2, often 4 2 or simply 2). A dominant seventh in root position, e.g., G-B-D-F, is figured 7.
对于七和弦（AQA和声中必不可少），数字低音为：根音位置（7 5 3）、第一转位（6 5 3，常缩写为6 5）、第二转位（6 4 3，常写为4 3）和第三转位（6 4 2，常写为4 2或简写2）。属七和弦根音位置，例如G-B-D-F，标记为7。
7. Cadence Patterns | 终止式模式
Cadences are chord progressions that signal the end of a phrase. They follow strict formulaic progressions that AQA expects you to recognise by ear and in notation. The four standard cadences are:
终止式是标志乐句结束的和弦进行。它们遵循严格的公式化进行，AQA要求您在听觉和记谱中识别。四种标准终止式为：
- Perfect (Authentic) V-I: Creates a strong sense of finality. The leading note rises to the tonic. In minor, V includes the raised leading note.
- Imperfect (Half) I-V, ii-V, IV-V: Ends on V, leaving the phrase sounding unfinished.
- Plagal IV-I: The 'Amen' cadence, moving from the subdominant to tonic.
- Interrupted (Deceptive) V-vi: V resolves to the submediant instead of the tonic, creating surprise.
- 完全终止 V-I：营造强烈的终止感。导音上行至主音。在小调中，V包含升高的导音。
- 半终止 I-V, ii-V, IV-V：结束于V，使乐句听起来未完成。
- 变格终止 IV-I：“阿门”终止，从下属和弦进行到主和弦。
- 伪终止 V-vi：V进行到下中和弦而非主和弦，制造惊奇感。
8. Common Chord Progressions | 常见和弦进行
Harmonic formulae drive the structure of Western functional harmony. Recognising these patterns accelerates analysis and informs your own composition work.
和声公式驱动着西方功能和声的结构。识别这些模式可以加快分析速度，并为您的创作提供信息。
- I-IV-V-I: The fundamental building block. In C major: C – F – G – C.
- I-vi-IV-V (the '50s progression): C – Am – F – G. Also known as the doo-wop progression.
- ii-V-I: Common in jazz and Classical cadences. Dm – G – C.
- Circle progression: Roots move down by a perfect fifth (or up a fourth): I – IV – vii° – iii – vi – ii – V – I. This underpins many Baroque sequences.
- IV-iv-I
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