📚 IGCSE AQA Music: Formula & Theorem Quick Reference Handbook | IGCSE AQA 音乐：公式定理速查手册
This is your at-a-glance reference for the essential ‘formulas’ and ‘theorems’ of music theory for the IGCSE AQA Music specification. Just as maths has its laws, music has its structural rules – from interval patterns to chord progressions and rhythmic ratios. Master these building blocks and you will not only ace the written paper but also deepen your practical musicianship. Keep this handbook close for quick, targeted revision.
这是您为IGCSE AQA音乐考试打造的必备“公式”与“定理”速查手册。正如数学有定律，音乐也有其结构性规则——从音程模式到和弦进行以及节奏比值。掌握这些基础构件，您不仅能轻松应对笔试，还能加深您的实践音乐素养。请将此手册随身携带，以便进行快速、有针对性的复习。
1. Pitch & Clef Notation | 音高与谱号记谱法
The treble clef locates the G above middle C on the second line. The bass clef locates the F below middle C on the fourth line. Middle C sits on one ledger line below the treble staff or one ledger line above the bass staff. Alto clef centres on middle C at the third line, while tenor clef places middle C on the fourth line (up an octave from bass clef thinking). Ledger lines extend the staff in both directions.
高音谱号将中央C上方的G定位在第二线。低音谱号将中央C下方的F定位在第四线。中央C位于高音谱表下加一线或低音谱表上加一线。中音谱号以第三线为中央C，次中音谱号则将中央C置于第四线（比低音谱号高一个八度）。加线双向扩展谱表。
Accidentals apply for the remainder of a bar unless cancelled. A natural sign (♮) cancels a previous sharp or flat. Key signatures define the default sharps or flats for the entire piece or section. A sharp raises a note by a semitone; a flat lowers it. A double sharp (×) raises by two semitones, a double flat (𝄫) lowers by two semitones.
临时记号在同一小节内持续有效，除非被取消。还原记号（♮）取消之前的升号或降号。调号定义了整首作品或片段默认的升降音。升号将音符升高一个半音，降号降低一个半音。重升号（×）升高两个半音，重降号（𝄫）降低两个半音。
2. Interval Formulas | 音程公式
An interval is the distance between two pitches. Count the letter names for the numerical size (2nd, 3rd, etc.), then determine quality: Perfect (P) for unison, 4th, 5th, octave; Major (M) / minor (m) for 2nd, 3rd, 6th, 7th. Augmented (A) = one semitone larger than perfect or major. Diminished (d) = one semitone smaller than perfect or minor.
音程是两个音高之间的距离。先按字母名数出度数（二度、三度等），再确定性质：同度、四度、五度、八度为纯音程（P）；二度、三度、六度、七度为大/小音程。增音程（A）= 比纯或大音程多半音；减音程（d）= 比纯或小音程少半音。
Semitone quick reference: Minor 2nd = 1 semitone (e.g. E–F). Major 2nd = 2 semitones (C–D). Minor 3rd = 3 semitones (A–C). Major 3rd = 4 semitones (C–E). Perfect 4th = 5 semitones (C–F). Augmented 4th / Diminished 5th (tritone) = 6 semitones (F–B). Perfect 5th = 7 semitones (C–G). Minor 6th = 8 semitones (E–C). Major 6th = 9 semitones (C–A). Minor 7th = 10 semitones (D–C). Major 7th = 11 semitones (C–B). Octave = 12 semitones.
半音速查：小二度 = 1个半音（如E–F）。大二度 = 2个半音（C–D）。小三度 = 3个半音（A–C）。大三度 = 4个半音（C–E）。纯四度 = 5个半音（C–F）。增四度/减五度（三全音）= 6个半音（F–B）。纯五度 = 7个半音（C–G）。小六度 = 8个半音（E–C）。大六度 = 9个半音（C–A）。小七度 = 10个半音（D–C）。大七度 = 11个半音（C–B）。纯八度 = 12个半音。
Compound intervals exceed an octave: Major 9th = octave + major 2nd, Perfect 11th = octave + perfect 4th, etc. Inversion rule: Perfect intervals remain perfect; major becomes minor; augmented becomes diminished; and the interval number sums to 9 (e.g. 3rd ↔ 6th).
复音程超过八度：大九度 = 八度 + 大二度，纯十一度 = 八度 + 纯四度等。转位规则：纯音程转位仍是纯音程；大音程变小音程；增音程变减音程；度数总和为9（如三度↔六度）。
3. Major Scale Formula | 大调音阶公式
All major scales follow the step pattern: Tone – Tone – Semitone – Tone – Tone – Tone – Semitone (T T S T T T S). Starting on any note, apply this sequence to generate the correct major scale. For example, C major: C D E F G A B C uses no accidentals because E–F and B–C are natural semitones.
所有大调音阶遵循音级模式：全音 – 全音 – 半音 – 全音 – 全音 – 全音 – 半音（T T S T T T S）。从任意音开始，套用此序列即可生成正确的大调音阶。例如，C大调：C D E F G A B C不使用任何临时记号，因为E–F与B–C天然为半音。
Scale degree names (technical function): 1st = Tonic, 2nd = Supertonic, 3rd = Mediant, 4th = Subdominant, 5th = Dominant, 6th = Submediant, 7th = Leading note (when a semitone below tonic), 8th = Tonic. In natural minor, the 7th degree a whole tone below tonic is called the Subtonic.
音阶级数名称（功能术语）：第Ⅰ级 = 主音，第Ⅱ级 = 上主音，第Ⅲ级 = 中音，第Ⅳ级 = 下属音，第Ⅴ级 = 属音，第Ⅵ级 = 下中音，第Ⅶ级 = 导音（低于主音半音时），第Ⅷ级 = 主音。在自然小调中，低于主音全音的第Ⅶ级称作下主音。
4. Minor Scale Formulas | 小调音阶公式
Natural minor: T S T T S T T. It shares the same key signature as its relative major. Harmonic minor: raises the 7th degree by a semitone, creating an augmented 2nd between 6th and 7th (T S T T S 3S S). Melodic minor ascending: raises both 6th and 7th degrees (T S T T T T S). Melodic minor descending: same as natural minor.
自然小调：T S T T S T T。它与关系大调共享同一调号。和声小调：升高第Ⅶ级半音，在Ⅵ到Ⅶ级间形成增二度（T S T T S 3S S）。旋律小调上行：同时升高第Ⅵ和第Ⅶ级（T S T T T T S）。旋律小调下行：与自然小调相同。
Relative major/minor pairs are a minor 3rd apart: e.g., C major ↔ A minor. Parallel major/minor share the same tonic but differ in key signature (e.g., C major vs. C minor). The harmonic minor scale’s raised 7th creates a leading note, giving a stronger dominant-tonic pull. The melodic minor smooths out the augmented 2nd leap for easier melodic writing.
关系大小调相距小三度：例如C大调 ↔ a小调。同主音大小调共享主音但调号不同（如C大调与c小调）。和声小调升Ⅶ级产生导音，增强了属-主的倾向性。旋律小调抹平了增二度跳进，使旋律写作更流畅。
5. Chord Construction | 和弦构成
Triad construction: Root + 3rd + 5th. Major triad = major 3rd + perfect 5th (e.g. C–E–G). Minor triad = minor 3rd + perfect 5th (C–E♭–G). Diminished triad = minor 3rd + diminished 5th (B–D–F). Augmented triad = major 3rd + augmented 5th (C–E–G♯).
三和弦构成：根音 + 三音 + 五音。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（B–D–F）。增三和弦 = 大三度 + 增五度（C–E–G♯）。
Seventh chords: Dominant 7th = major triad + minor 7th (e.g. G–B–D–F). Major 7th = major triad + major 7th (C–E–G–B). Minor 7th = minor triad + minor 7th (A–C–E–G). Half-diminished 7th = diminished triad + minor 7th (B–D–F–A). Diminished 7th = diminished triad + diminished 7th (B–D–F–A♭).
七和弦：属七和弦 = 大三和弦 + 小七度（如G–B–D–F）。大七和弦 = 大三和弦 + 大七度（C–E–G–B）。小七和弦 = 小三和弦 + 小七度（A–C–E–G）。半减七和弦 = 减三和弦 + 小七度（B–D–F–A）。减七和弦 = 减三和弦 + 减七度（B–D–F–A♭）。
Chord inversions: Root position = root in bass (figured bass: 5/3). 1st inversion = 3rd in bass (6/3, often abbreviated to 6). 2nd inversion = 5th in bass (6/4). 3rd inversion for seventh chords = 7th in bass (4/2). In Roman numeral analysis, use superscript lowercase: I, ii, iii, IV, V, vi, viio for major keys.
和弦转位：原位 = 低音为根音（数字低音：5/3）。第一转位 = 低音为三音（6/3，常简写为6）。第二转位 = 低音为五音（6/4）。七和弦第三转位 = 低音为七音（4/2）。罗马数字分析中，大调用上标大小写：I, ii, iii, IV, V, vi, viio。
6. Chord Progressions & Cadences | 和弦进行与终止式
Cadence formulas: Perfect (V–I) sounds complete, final. Imperfect (I–V, ii–V, IV–V) ends on V, sounds unfinished. Plagal (IV–I) is the ‘Amen’ cadence. Interrupted (V–vi) surprises by moving to the submediant. In AQA, expect to identify these aurally and by score analysis.
终止式公式：正格终止（V–I）听起来完整、结束感强。不完全终止（I–V, ii–V, IV–V）结束在V级，听感未完成。变格终止（IV–I）为“阿们”终止。阻碍终止（V–vi）意外地走向下中音和弦。AQA考试中需通过聆听和乐谱分析识别这些终止式。
Common diatonic chord functions: Tonic (I, vi) = stability. Subdominant (IV, ii) = moving away. Dominant (V, viio) = tension needing resolution. The circle of fifths progression: iii → vi → ii → V → I moves in descending perfect 5ths (or ascending 4ths).
常见自然音和弦功能：主功能（I, vi）= 稳定。下属功能（IV, ii）= 离开主。属功能（V, viio）= 紧张需解决。五度循环进行：iii → vi → ii → V → I 以纯五度下行（或纯四度上行）移动。
Harmonic rhythm refers to the rate of chord change. In chorale-style music, standard voice-leading includes: avoid parallel 5ths and octaves; double the root preferably; resolve leading note up to tonic; keep common tones smooth.
和声节奏指和弦变换的速率。在众赞歌风格音乐中，标准声部进行包括：避免平行五度与平行八度；优先重复根音；导音上行解决至主音；共同音保持平稳。
7. Rhythm & Time Signature ‘Equations’ | 节奏与拍号“等式”
Time signature: top number = beats per bar, bottom number = beat unit (4 = crotchet, 8 = quaver, 2 = minim). Simple time beats divide into two equal parts; compound time beats divide into three. Duple = 2 beats, Triple = 3, Quadruple = 4. Compound duple: 6/8 (2 dotted crotchet beats). Compound triple: 9/8.
拍号：上方数字 = 每小节拍数，下方数字 = 节拍单位（4 = 四分音符，8 = 八分音符，2 = 二分音符）。单拍子每拍分两份；复拍子每拍分三份。二拍子 = 2拍，三拍子 = 3拍，四拍子 = 4拍。复二拍：6/8（2个附点四分音符拍）。复三拍：9/8。
Note value ratios: Semibreve = 2 minims = 4 crotchets = 8 quavers = 16 semiquavers. Dotted note adds half its value: dotted minim = 3 crotchets. Double dotted adds three-quarters: double dotted crotchet = 1 + 1/2 + 1/4 = 1.75 crotchets. Ties add duration across a bar line.
音符时值比例：全音符 = 2分音符 = 4四分音符 = 8八分音符 = 16十六分音符。附点音符增加原有时值一半：附点二分音符 = 3拍。双附点增加四分之三：双附点四分音符 = 1 + 1/2 + 1/4 = 1.75拍。延音线跨越小节线累加时值。
Syncopation shifts accent to a weak beat or off-beat. Hemiola in triple meter: accenting two-beat groups within 3/4, creating a 3:2 feel. Swung rhythm (jazz quavers) approximates triplet crotchet + quaver. Tempo markings: BPM (beats per minute) gives precise speed.
切分音将重音转移至弱拍或弱位。三拍子中的希米奥拉（Hemiola）：在3/4拍中强调两个拍点组，产生3:2感。摇摆节奏（爵士八分音符）近似三连音中前长后短。速度标记：BPM（拍每分钟）给出精确速度。
8. Key Relationships & Modulation ‘Theorems’ | 调性关系与转调“定理”
Closely related keys: Those whose tonic triads are diatonic to the original key – the relative minor/major, the dominant and its relative minor, the subdominant and its relative minor. For C major: A minor, G major, E minor, F major, D minor. The key signature difference is at most one accidental.
近关系调：其主三和弦属于原调自然音的那些调——关系小/大调、属调及其关系小调、下属调及其关系小调。以C大调为例：a小调、G大调、e小调、F大调、d小调。调号差异至多一个升降号。
Modulation types: Direct/phrase modulation – abrupt change without pivot chord. Pivot chord modulation – a chord common to both keys acts as the hinge. Sequential modulation – repeating a passage at a new pitch level. In analysis, identify the new tonic and the pivot chord; look for accidentals introducing the new leading note.
转调类型：直接/乐句转调——无共同和弦的突然转换。中介和弦转调——一个两调共有的和弦充当铰链。模进转调——在新高度重复片段。分析时，找出新主音和中介和弦；注意引入新导音的临时记号。
9. Dynamics & Expressive Terminology | 力度与表情术语
Dynamic formulas range from very soft to very loud: pp (pianissimo, very soft), p (piano, soft), mp (mezzo-piano, moderately soft), mf (mezzo-forte, moderately loud), f (forte, loud), ff (fortissimo, very loud). Gradual change: crescendo (cresc., get louder), diminuendo (dim.) or decrescendo (get softer). Sforzando (sfz) means suddenly accented.
力度标号从很弱到很强：pp（极弱），p（弱），mp（中弱），mf（中强），f（强），ff（极强）。渐变：crescendo（渐强），diminuendo或decrescendo（渐弱）。Sforzando (sfz) 表示突强。
Tempo modifiers: accelerando (accel., gradually faster), rallentando (rall., gradually slower), ritardando (rit., held back), rubato (flexible tempo). Mood and style: cantabile (singing), dolce (sweet), agitato (agitated), maestoso (majestic), leggiero (lightly). All Italian terms are standard for IGCSE AQA.
速度修饰：accelerando（accel., 逐渐加快），rallentando（rall., 逐渐减慢），ritardando（rit., 渐慢），rubato（弹性速度）。情绪与风格：cantabile（如歌的），dolce（甜美的），agitato（激动的），maestoso（庄严的），leggiero（轻巧的）。所有意大利术语均为IGCSE AQA标准。
10. Musical Forms & Structure ‘Patterns’ | 曲式结构“模式”
Binary form (AB): Two sections, often each repeated. Section A modulates to a related key (usually dominant); Section B returns to the tonic. Ternary form (ABA): Statement, contrast, return – the return may be written out or indicated by ‘da capo’. Rondo form: recurring main theme (A) alternating with contrasting episodes (ABACADA).
二段体（AB）：两个部分，常各自反复。A段转入近关系调（通常是属调）；B段返回主调。三段体（ABA）：陈述、对比、回归——回归可写出或用“da capo”指示。回旋曲式：主部主题（A）反复出现，交替插入对比插部（ABACADA）。
Theme and variations: a theme is presented then altered in successive statements through changes in melody, rhythm, harmony, texture, or orchestration. Sonata form (often encountered in Classical period): Exposition (1st subject tonic, 2nd subject dominant/related key), Development (thematic fragments, key exploration), Recapitulation (both subjects in tonic), optional Coda.
主题与变奏：先呈示主题，随后通过旋律、节奏、和声、织体或配器的变化在后续陈述中改变。奏鸣曲式（常见于古典时期）：呈示部（第一主题主调，第二主题属调或关系调）、发展部（主题片段、调性探索）、再现部（两主题均归主调）、可选尾声。
Strophic form (AAA…): same music repeated for each verse. Through-composed: no significant repetition of whole sections, music follows the narrative. 12-bar blues: I I I I | IV IV I I | V IV I I (often with 7th chords, swing rhythm).
分节歌曲形式（AAA…）：每段词相同音乐重复。通谱体：无明显段落反复，音乐随叙述发展。12小节布鲁斯：I I I I | IV IV I I | V IV I I（常用七和弦、摇摆节奏）。
11. Texture Descriptors | 织体描述符
Monophonic: single melodic line with no accompaniment (e.g., unaccompanied chant). Homophonic: melody with chordal accompaniment; often melody-dominated homophony. Polyphonic / contrapuntal: two or more independent melodic lines woven together (e.g., canon, fugue). Heterophonic: simultaneous variation of the same melody by multiple performers.
单声织体：无伴奏的单一旋律线条（如无伴奏圣咏）。主调织体：带和弦伴奏的旋律；常见旋律主导的主调织体。复调织体/对位：两个及以上独立旋律线条交织（如卡农、赋格）。支声织体：多位演奏者同时对同一旋律作不同变奏。
Imitation: a melody is restated in another part, often overlapping. Canon: strict imitation throughout. Antiphonal: dialogue between groups of performers. Melody and accompaniment: clearly distinct melody supported by broken chords, alberti bass, block chords, etc. Octave doubling thickens the texture without adding new melodic material.
模仿：一个声部在另一声部重新陈述旋律，常交叠。卡农：严格的全程模仿。应答式：两组演奏者之间的对话。旋律与伴奏：清晰区分的旋律由分解和弦、阿尔贝蒂低音、块状和弦等支撑。八度重叠加厚织体但不增加新旋律素材。
12. Ornaments & Articulation | 装饰音与演奏法
Trill (tr): rapid alternation between written note and the note above. Turn (∞): note above, written note, note below, written note. Mordent (upper, 短波浪线): written note, note above, written note. Lower mordent (short wave with vertical line): written note, note below, written note. Appoggiatura: leaning note that takes half the value of the main note. Acciaccatura (crushed note): played very quickly before the main note, indicated by a small note with a stroke through the stem.
颤音（tr）：本音与上方音快速交替。回音（∞）：上方音、本音、下方音、本音。上波音（短波浪线）：本音、上方音、本音。下波音（带竖线短波浪线）：本音、下方音、本音。倚音：占主要音一半时值的长倚音。碎音（短倚音）：在主音前极快奏出，用带斜杠的小音符表示。
Articulation: Staccato (dot) – short, detached. Legato (slur) – smooth, connected. Tenuto (line) – held for full value, slight emphasis. Accent (> ) – strong attack. Marcato (^) – marked, heavier accent. Slur over two notes may indicate a sigh or legato touch; over many notes indicates phrasing.
演奏法：断奏（圆点）——短促、分离。连奏（连线）——圆滑、连贯。保持音（横线）——奏足时值，稍加强调。重音（>）——强力起音。特重音（^）——更明显的加重。两音连线可表示叹息或连奏效果；多音连线表示乐句。
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