📚 AQA GCSE Music: Quick Reference Handbook of Formulae and Theorems | AQA GCSE 音乐：公式定理速查手册
This quick-reference guide distils the essential theoretical 'formulae' and rules of music required for the AQA GCSE Music examination. From time values and key signatures to chord construction and cadence patterns, each section presents information in a clear, bilingual format designed for rapid revision and confident application in listening, composing and performing tasks.
这份速查手册提炼了 AQA GCSE 音乐考试必需的核心理论“公式”与规则。从时值和调号到和弦构建及终止式模式，每一节均以清晰的中英双语呈现，旨在帮助同学们快速复习，并在听力、作曲和演奏中自信地运用这些知识。
1. Note Values and Rest Equivalents | 音符时值与休止符当量
In simple duple, triple or quadruple time, the relationships between note values follow a strict binary division. A semibreve equals two minims, four crotchets, eight quavers, sixteen semiquavers or thirty-two demisemiquavers. Each rest mirrors its corresponding note value exactly.
在单拍子中，音符时值之间的关系遵循严格的二分法。一个全音符等于两个二分音符、四个四分音符、八个八分音符、十六个十六分音符或三十二个三十二分音符。每一种休止符的时值都与其对应的音符完全一致。
| English Name | 中文名称 | Symbol | Relative Value | Rest Symbol |
|---|---|---|---|---|
| Semibreve | 全音符 | 𝄝 | 4 beats (⁴/₄) | 𝄻 |
| Minim | 二分音符 | 𝄞 (open head) | 2 beats | 𝄼 |
| Crotchet | 四分音符 | ♩ | 1 beat | 𝄽 |
| Quaver | 八分音符 | ♪ | ½ beat | 𝄾 |
| Semiquaver | 十六分音符 | ♬ | ¼ beat | 𝄿 |
The dotted rhythm formula extends a note' a dotted crotchet = 1 + ½ = 1.5 beats, frequently paired with a quaver to complete a beat.
附点节奏公式将音符时值延长原有时值的一半：附点音符 = 原音符 + (原音符 × ½)。例如，附点四分音符 = 1 + ½ = 1.5 拍，通常与一个八分音符组合成一拍完满的节奏。
2. Time Signatures and Metre | 拍号与节拍
Simple time divides each beat into two equal parts; compound time divides each beat into three equal parts, usually in dotted-beat groupings.
拍号的上方数字表示每小节的拍数，下方数字表示以何种音符为一拍（4代表四分音符，8代表八分音符，2代表二分音符）。单拍子将每一拍平均分为两份；复拍子将每一拍平均分为三份，通常以附点音符为一拍。
| Time Signature | Type | Beats per Bar & Beat Division | 中文描述 |
|---|---|---|---|
| 2/4 | Simple Duple | 2 crotchet beats, each divided into 2 quavers | 二拍子，四分音符为一拍 |
| 3/4 | Simple Triple | 3 crotchet beats | 三拍子，华尔兹常见 |
| 4/4 (C) | Simple Quadruple | 4 crotchet beats, common time | 四拍子，通用拍号 |
| 6/8 | Compound Duple | 2 dotted-crotchet beats, each split into 3 quavers | 复二拍，每小节两个附点四分音符组 |
| 9/8 | Compound Triple | 3 dotted-crotchet beats | 复三拍 |
| 12/8 | Compound Quadruple | 4 dotted-crotchet beats | 复四拍，常用于布鲁斯 |
2 or 2+3). Asymmetric metres are vital in 20th-century and world music contexts studied at GCSE.
不规则拍号如 5/4 或 7/8 包含不均匀的拍组（如 5/4 = 3+2 或 2+3）。不对称节拍在 GCSE 大纲涉及的 20 世纪音乐和世界音乐中尤为重要。
3. Key Signatures and the Circle of Fifths | 调号与五度圈
A key signature is determined by the number of sharps or flats at the start of a stave. The order of sharps is F♯, C♯, G♯, D♯, A♯, E♯, B♯; the order of flats is B♭, E♭, A♭, D♭, G♭, C♭, F♭ (the reverse of the sharp order). The Circle of Fifths shows the relationship: moving clockwise adds a sharp (or removes a flat), moving anti-clockwise adds a flat.
调号由谱表开始处的升号或降号数量决定。升号顺序为 F♯, C♯, G♯, D♯, A♯, E♯, B♯；降号顺序为 B♭, E♭, A♭, D♭, G♭, C♭, F♭（升号顺序的反向）。五度圈展示了关系：顺时针移动增加一个升号（或减少一个降号），逆时针移动增加一个降号。
Formula to identify a major key: For sharps, the major key is one semitone above the last sharp. For flats, the major key is the second-to-last flat (except F major, which has one flat). The relative minor is three semitones below its relative major.
识别大调调号的公式：对于升号调，主音在最后一个升号上方半音。对于降号调，主音是倒数第二个降号（F 大调只有一个降号，例外）。关系小调在其关系大调下方三个半音。
| Key Signature | Major Key | Relative Minor | 中文 |
|---|---|---|---|
| 0 ♯/♭ | C major | A minor | C 大调 / a 小调 |
| 1 ♯ | G major | E minor | G 大调 |
| 2 ♯ | D major | B minor | D 大调 |
| 1 ♭ | F major | D minor | F 大调 |
| 2 ♭ | B♭ major | G minor | 降 B 大调 |
4. Interval Calculation | 音程计算
An interval is the distance in pitch between two notes, counted in degrees of the scale (e.g. 2nd, 3rd) and qualified by quality: perfect (P), major (M), minor (m), augmented (A) or diminished (d). The following simple formulae help calculate intervals quickly:
音程是两个音之间的音高距离，以音级度数（如二度、三度）计算，并用性质限定：纯、大、小、增、减。以下简单公式可帮助快速计算音程。
- Perfect intervals are 1, 4, 5 and 8; if raised by a semitone they become augmented, if lowered they become diminished. 纯音程为 1、4、5、8 度；升高半音变增，降低半音变减。
- Major/minor intervals apply to 2, 3, 6 and 7. A major interval reduced by a semitone becomes minor; reduced further becomes diminished. A major interval expanded by a semitone becomes augmented. 大/小音程适用于 2、3、6、7 度。大音程降低半音变为小，再降变减；大音程升高半音变增。
- Tritone: Augmented 4th or diminished 5th, spanning exactly 6 semitones. 三全音：增四度或减五度，精确跨 6 个半音。
iminished 5th = 6, Perfect 5th = 7, Minor 6th = 8, Major 6th = 9, Minor 7th = 10, Major 7th = 11, Octave = 12.
半音计数是最快捷的方法：小二度 = 1 个半音，大二度 = 2，小三度 = 3，大三度 = 4，纯四度 = 5，增四度/减五度 = 6，纯五度 = 7，小六度 = 8，大六度 = 9，小七度 = 10，大七度 = 11，纯八度 = 12。
5. Scale Formulae: Major, Minor and Modes | 音阶公式：大调、小调与调式
A scale is built by a fixed pattern of tones (T) and semitones (S). The major scale uses the pattern T-T-S-T-T-T-S. Starting on any tonic, this formula yields the correct key signature.
音阶由固定全音 (T) 和半音 (S) 模式构成。大调音阶使用 T-T-S-T-T-T-S 模式。从任意主音出发，该公式可得出正确的调号。
- Natural minor: T-S-T-T-S-T-T, sharing the key signature of its relative major but starting on the 6th degree. 自然小调：T-S-T-T-S-T-T，与其关系大调共用相同调号，但始于第 6 级。
- Harmonic minor: natural minor with raised 7th degree (T-S-T-T-S-T+S-S). 和声小调：自然小调升高第 7 级 (T-S-T-T-S-增二度-S)，产生增二度音程。
- Melodic minor ascending: T-S-T-T-T-T-S (raised 6th & 7th); descending it reverts to natural minor. 旋律小调上行：T-S-T-T-T-T-S（升高 6、7 级）；下行还原为自然小调。
The modes required for AQA GCSE can be derived from the white-note scale but are better defined by their internal pattern starting from a given tonic:
AQA GCSE 需掌握的调式可从白键音阶推导，但最好通过给定主音的内部模式来定义：
| Mode | Pattern (T/S) | Character | 中文 |
|---|---|---|---|
| Dorian | T-S-T-T-T-S-T | Minor with raised 6th | 多利亚调式 |
| Phrygian | S-T-T-T-S-T-T | Minor with ♭2 | 弗里几亚调式 |
| Lydian | T-T-T-S-T-T-S | Major with raised 4th | 利底亚调式 |
| Mixolydian | T-T-S-T-T-S-T | Major with ♭7 | 混合利底亚调式 |
Other scales: Chromatic (all semitones), Whole-tone (all tones, 6 notes), Pentatonic (major: degrees 1 2 3 5 6; minor: 1 ♭3 4 5 ♭7).
其他音阶：半音阶（全为半音）、全音阶（全为全音，6 个音）、五声音阶（大调：1 2 3 5 6 级音；小调：1 ♭3 4 5 ♭7 级音）。
6. Chord Construction Rules | 和弦构建法则
Triads are built by stacking two thirds on a root. A major triad consists of a major 3rd plus a perfect 5th (e.g. C-E-G). A minor triad: minor 3rd + perfect 5th (C-E♭-G). Diminished triad: minor 3rd + diminished 5th (C-E♭-G♭). Augmented triad: major 3rd + augmented 5th (C-E-G♯).
三和弦由根音上方叠置两个三度构成。大三和弦：大三度 + 纯五度（如 C-E-G）。小三和弦：小三度 + 纯五度（C-E♭-G）。减三和弦：小三度 + 减五度（C-E♭-G♭）。增三和弦：大三度 + 增五度（C-E-G♯）。
Seventh chords are particularly useful in cadence and jazz. The formula: add a 7th interval above the root to the triad.
七和弦在终止式和爵士乐中尤为重要。公式：在三和弦基础上，叠加根音上方的七度音。
- Dominant 7th: major triad + minor 7th (e.g. G-B-D-F). 属七和弦：大三和弦 + 小七度。
- Major 7th: major triad + major 7th (C-E-G-B). 大七和弦：大三和弦 + 大七度。
- Minor 7th: minor triad + minor 7th (D-F-A-C). 小七和弦：小三和弦 + 小七度。
- Half-diminished: diminished triad + minor 7th. 半减七和弦：减三和弦 + 小七度。
Inversions are identified by the bass note: root position (root in bass), first inversion (3rd in bass, figured bass ⁶ or ⁶₃), second inversion (5th in bass, ⁶₄). Seventh chords add a third inversion (7th in bass, ⁴₂).
转位由低音确定：原位（根音在低音）、第一转位（三音在低音，数字低音记作 ⁶ 或 ⁶₃）、第二转位（五音在低音，⁶₄）。七和弦还有第三转位（七音在低音，⁴₂）。
7. Cadences and Chord Progressions | 终止式与和弦进行
A cadence is a two-chord formula that concludes a phrase. The four main cadences function like musical punctuation:
终止式是结束乐句的两个和弦公式，起音乐标点作用。四种主要终止式：
| Cadence | Chords | Effect | 中文 |
|---|---|---|---|
| Perfect (V-I) | Dominant to Tonic | Strong, final, period | 正格终止（完满/不完满） |
| Plagal (IV-I) | Subdominant to Tonic | 'Amen' ending | 变格终止 |
| Imperfect (I-V, II-V, IV-V) | Any chord to V | Unfinished, comma | 半终止 |
| Interrupted (V-VI) | Dominant to Submediant | Surprise, deflection | 阻碍终止 |
Common functional harmony formulae include the primary triads I, IV, V and their substitutions. The perfect cadence may be elevated by using a cadential ⁶₄ (I⁶₄–V–I). The progression ii–V–I is the essential jazz and Classical formula. In minor keys, V must be major (requires raised leading note).
常见功能和声公式包括主、下属、属三个正三和弦及其替代。完满终止可通过装饰性的终止式四六和弦 (I⁶₄–V–I) 提升。和弦进行 ii–V–I 是爵士乐和古典音乐的基础公式。小调中，V 级必须是大三和弦（需要升高导音）。
8. Dynamics and Tempo Markings | 力度与速度标记
Standard Italian terms and their abbreviations are formulaic indicators that AQA expects candidates to recognise and apply in analysis.
标准意大利术语及其缩写是公式化的指示符，AQA 要求考生在分析中识别并运用。
| Term | Meaning | 中文 |
|---|---|---|
| pp (pianissimo) | very soft | 很弱 |
| p (piano) | soft | 弱 |
| mp (mezzo-piano) | moderately soft | 中弱 |
| mf (mezzo-forte) | moderately loud | 中强 |
| f (forte) | loud | 强 |
| ff (fortissimo) | very loud | 很强 |
| cresc. (crescendo) | gradually louder | 渐强 |
| dim. (diminuendo) | gradually softer | 渐弱 |
| sfz (sforzando) | strong, sudden accent | 突强 |
o (fast, cheerful), Vivace (lively) and Presto (very fast) accompany metronome marks (e.g. ♩ = 120) that give an exact pulse formula.
速度标记如 Largo（慢而宽广）、Adagio（缓慢从容）、Andante（行板步伐）、Moderato（中速）、Allegro（快板欢快）、Vivace（活泼）、Presto（急板）等，常伴有节拍器速度标记（如 ♩ = 120），给出精确的脉冲公式。
9. Ornaments and Articulations | 装饰音与演奏法
Ornaments are formulaic melodic decorations notated by special symbols or small notes. AQA requires identification and an understanding of how they are performed.
装饰音是通过特殊符号或小音符标记的公式化旋律装饰。AQA 要求识别并理解其演奏方式。
- Trill (tr): rapid alternation between the written note and the note above. 颤音：在本音与上方音之间快速交替。
- Turn (𝄪): upper note, written note, lower note, written note. 回音：上方音-本音-下方音-本音。
- Mordent (upper: 𝆗, lower: 𝆘): single rapid alternation with the upper or lower auxiliary. 波音（上波音/下波音）：与本音上方或下方辅助音快速交替一次。
- Appoggiatura: a dissonant leaning note, taking half the value of the main note. 倚音：不协和倚靠音，占本音一半时值。
- Acciaccatura: a crushed note, played very quickly before the main note (shown with a slash). 碎音：带斜线的小音符，在本音前极速奏出。
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