📚 Year 10 AQA Music: Key Formulae & Theorems Quick Reference | Year 10 AQA 音乐：公式定理速查手册
Music may feel like an art of intuition, but beneath the surface lies a web of consistent patterns, intervals, and structural rules that act like mathematical formulas. This quick reference handbook breaks down the essential ‘formulae’ and ‘theorems’ you need for Year 10 AQA GCSE Music — from note value equations to chord building and cadence sequences. Use it to memorise the building blocks that underpin listening, appraising, and composing with confidence.
音乐或许像一门凭直觉的艺术，但在其表层之下，存在着如同数学公式一般稳定的模式、音程和结构规则。这本速查手册分解了 Year 10 AQA GCSE 音乐所需要的关键“公式”与“定理”——从音值等式到和弦构建与终止式序列。用它来熟记那些支撑听力、评估和创作的基石，自信应对考试。
1. Note Value Equations | 音符时值公式
English: In simple time, note values follow a strict multiplicative relationship. A semibreve equals 2 minims, a minim equals 2 crotchets, a crotchet equals 2 quavers, a quaver equals 2 semiquavers. Therefore: 1 semibreve = 2 minims = 4 crotchets = 8 quavers = 16 semiquavers. The dot after a note adds half its original value: dotted minim = 3 crotchets, dotted crotchet = 3 quavers. In compound time (e.g., 6/8), the beat is a dotted crotchet, divided into 3 quavers.
中文：在单拍子中，音符时值遵循严格的倍数关系。全音符等于2个二分音符，二分音符等于2个四分音符，四分音符等于2个八分音符，八分音符等于2个十六分音符。因此：1个全音符 = 2个二分音符 = 4个四分音符 = 8个八分音符 = 16个十六分音符。附点加在音符后增加原时值的一半：附点二分音符 = 3个四分音符，附点四分音符 = 3个八分音符。在复拍子（如6/8拍）中，拍子是附点四分音符，细分为3个八分音符。
2. Ties, Triplets, and Irregular Groupings Formula | 连线、三连音与不规则分组公式
English: A tie merges two notes of the same pitch into a single sustained sound; its total duration equals the sum of both tied note values. Triplets squeeze three notes into the time normally given to two: a triplet of quavers in simple time lasts as long as one beat (2 normal quavers). The formula: Triplet note value × 3 = 2 × normal note value. Other tuplets follow the same ratio principle, such as quintuplets: 5 in the time of 4.
中文：连线将两个相同音高的音符合并为一个持续的音；其总时值等于两个被连音符的时值之和。三连音将三个音符塞入原本给两个音符的时间中：在单拍子里，一组八分音符的三连音时长等于一拍（2个普通八分音符）。公式：三连音单个音符时值 × 3 = 2 × 普通音符时值。其他多连音遵循同样的比率原理，例如五连音：5个音符的时间代替四个。
3. Interval Calculation: The Semitone Formula | 音程计算：半音公式
English: Intervals are measured by the number of letter names (2nd, 3rd, 4th, etc.) and the exact number of semitones. The quality (major, minor, perfect, augmented, diminished) depends on these semitone counts. Key reference: a perfect unison = 0 semitones; minor 2nd = 1 semitone; major 2nd = 2; minor 3rd = 3; major 3rd = 4; perfect 4th = 5; augmented 4th / diminished 5th = 6; perfect 5th = 7; minor 6th = 8; major 6th = 9; minor 7th = 10; major 7th = 11; perfect octave = 12. From the tonic, each scale degree of a major scale gives a major or perfect interval; lowering a major interval by a semitone makes it minor; lowering a perfect interval makes it diminished.
中文：音程由字母名称数目（二度、三度、四度等）和确切的半音数量共同决定。性质（大、小、纯、增、减）取决于这些半音计数。关键参考：纯一度 = 0个半音；小二度 = 1；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。从主音出发，大调音阶的每个音级构成大音程或纯音程；将大音程降低半音变为小音程；将纯音程降低半音变为减音程。
4. Major Scale Construction Theorem | 大调音级构建定理
English: Every major scale follows the fixed pattern of tones (T) and semitones (S): T–T–S–T–T–T–S. Starting on any note, this pattern generates the correct sharps or flats for that key signature. Example: C major uses all white keys (no accidentals); G major (G, A, B, C, D, E, F♯) requires F♯ to satisfy the T between E and F♯ and S between F♯ and G. This pattern is the ‘formula’ behind all 12 major scales.
中文：所有大调音阶都遵循固定的全音（T）与半音（S）模式：T–T–S–T–T–T–S。从任意音符开始，此模式生成该调号正确的升号或降号。例如：C大调使用所有白键（无临时记号）；G大调（G, A, B, C, D, E, F♯）需要升F，以保证E到F♯的全音和F♯到G的半音。这一模式是全部12个大调背后的“公式”。
5. Minor Scale Variants: Three Theorems | 小调音阶变体：三条定理
English: Natural minor scale pattern: T–S–T–T–S–T–T. Harmonic minor raises the 7th degree by a semitone, creating an augmented 2nd between the 6th and 7th degrees (T–S–T–T–S–1½–S). Melodic minor ascending raises the 6th and 7th degrees (T–S–T–T–T–T–S), while descending reverts to the natural minor. These three forms are vital for recognising key and mood in listening questions.
中文：自然小调音阶模式：T–S–T–T–S–T–T。和声小调将第七级音升高半音，在第六级与第七级之间形成一个增二度（T–S–T–T–S–1½–S）。旋律小调上行升高第六级和第七级（T–S–T–T–T–T–S），下行则还原为自然小调。这三种形式对于在听力题目中识别调性与情绪至关重要。
6. Chord Building Formulas (Triads & 7ths) | 和弦构建公式（三和弦与七和弦）
English: Chords are built by stacking thirds. A major triad = root + 4 semitones (major 3rd) + 3 semitones (minor 3rd). A minor triad = root + 3 semitones + 4 semitones. A diminished triad = root + 3 + 3. An augmented triad = root + 4 + 4. For seventh chords: Dominant 7th = major triad + minor 7th above root (10 semitones from root); Major 7th = major triad + major 7th (11 semitones); Minor 7th = minor triad + minor 7th (10 semitones). Use these semitone stacks to identify or write chords quickly.
中文：和弦通过三度叠置构成。大三和弦 = 根音 + 4个半音（大三度）+ 3个半音（小三度）。小三和弦 = 根音 + 3 + 4。减三和弦 = 根音 + 3 + 3。增三和弦 = 根音 + 4 + 4。七和弦方面：属七和弦 = 大三和弦 + 根音上方小七度（距根音10个半音）；大七和弦 = 大三和弦 + 大七度（11个半音）；小七和弦 = 小三和弦 + 小七度（10个半音）。利用这些半音堆叠可快速识别或写出和弦。
7. Circle of Fifths & Key Signature Theorem | 五度圈与调号定理
English: Moving clockwise on the circle of fifths adds one sharp each step, while the key is a perfect fifth higher: C (0♯) → G (1♯) → D (2♯) → A (3♯) → E (4♯) → B (5♯) → F♯ (6♯). The new sharp is the leading note of the new key. Moving anticlockwise adds one flat: C → F (1♭) → B♭ (2♭) → E♭ (3♭) → A♭ (4♭) → D♭ (5♭) → G♭ (6♭). The relative minor is always a minor 3rd below its major tonic; e.g., A minor is relative to C major.
中文：沿五度圈顺时针每步增加一个升号，调性向上纯五度：C（0♯）→ G（1♯）→ D（2♯）→ A（3♯）→ E（4♯）→ B（5♯）→ F♯（6♯）。新增的升号总是新调的导音。逆时针每步增加一个降号：C → F（1♭）→ B♭（2♭）→ E♭（3♭）→ A♭（4♭）→ D♭（5♭）→ G♭（6♭）。关系小调总是在其大调主音下方小三度；例如，a小调是C大调的关系小调。
8. Cadence Sequence Formulas | 终止式序列公式
English: Cadences are the musical ‘punctuation’ at the end of a phrase. Perfect cadence: V → I (or V7 → I), sounds finished. Plagal cadence: IV → I (the ‘Amen’ cadence). Imperfect cadence: any chord followed by V, sounds unfinished. Interrupted cadence: V → vi (or V → VI in minor), a surprise move. Recognising these roman numeral pairs is essential for the AQA listening paper, especially in chord identification questions.
中文：终止式是乐句结尾的音乐“标点符号”。正格终止：V → I（或V7 → I），听感结束。变格终止：IV → I（“阿们”终止）。不完全终止：任意和弦接V，听感未结束。阻碍终止：V → vi（或小调中的V → VI），出人意料的进行。识别这些罗马数字对子是 AQA 听力考试的关键，尤其在和弦识别题目中。
9. Inversions & Figured Bass Algebra | 转位与数字低音公式
English: Triads can be in root position (5/3), first inversion (6/3 or simply 6), or second inversion (6/4). The figures represent intervals above the bass note. A C major triad in root position: bass C, intervals a 3rd (E) and 5th (G) above; in first inversion, bass E, intervals a 3rd (G) and 6th (C) — thus labelled 6. In second inversion, bass G, intervals a 4th (C) and 6th (E) — labelled 6/4. This numbering works for all chords and is a powerful shorthand for harmonic analysis.
中文：三和弦可以是原位（5/3）、第一转位（6/3或简写 6）、第二转位（6/4）。数字代表低音上方的音程距离。以C大三和弦为例：原位低音C，上方有三度音E和五度音G；第一转位低音E，上方有三度音G和六度音C——因此标记为6。第二转位低音G，上方有四度音C和六度音E——标记为6/4。这一编号体系适用于所有和弦，是和声分析的强大速记法。
10. Time Signature & Metric Accent Theorem | 拍号与节拍重音定理
English: Simple time has beats that divide into 2 (e.g., 2/4, 3/4, 4/4); top number shows beats per bar. Compound time has beats that divide into 3 (6/8, 9/8, 12/8); the beat is a dotted note. Formula to find the number of beats in compound time: top number ÷ 3. Thus 6/8 = 2 dotted crotchet beats per bar. Accent patterns follow the strong–weak rule: in 4/4, strong–weak–medium–weak; in 3/4, strong–weak–weak; in 6/8, strong–weak (with each beat split into 3 quavers). AQA questions often ask you to identify meter from accent patterns.
中文：单拍子的每拍二等分（如2/4、3/4、4/4）；上方数字表示每小节拍数。复拍子的每拍三等分（6/8、9/8、12/8）；拍子是附点音符。计算复拍子拍数的公式：上方数字 ÷ 3。因此6/8 = 每小节2个附点四分音符拍。重音模式遵循强弱规律：4/4拍中，强–弱–次强–弱；3/4拍，强–弱–弱；6/8拍，强–弱（每拍再细分为3个八分音符）。AQA 常要求从重音模式辨别拍号。
11. Dynamics & Expression – The Italian ‘Alphabet’ | 力度与表情术语速查
English: Dynamics and tempo markings are a vocabulary every AQA candidate must know. Gradual changes: crescendo (cresc.) = gradually louder, diminuendo (dim.) = gradually softer. Static dynamics: pp (pianissimo, very soft), p (piano, soft), mp (mezzo-piano, moderately soft), mf (mezzo-forte, moderately loud), f (forte, loud), ff (fortissimo, very loud). Articulation: staccato (short, detached), legato (smoothly), accent (> or sfz). These function as expressive ‘formulae’ that you must recognise both aurally and in notation.
中文：力度与速度标记是每个AQA考生必须掌握的词汇。渐变标记：crescendo (cresc.) = 渐强，diminuendo (dim.) = 渐弱。固定力度：pp（pianissimo，很弱），p（piano，弱），mp（mezzo-piano，中弱），mf（mezzo-forte，中强），f（forte，强），ff（fortissimo，很强）。运音法：staccato（断奏，短而分离），legato（连奏，平滑），重音（> 或 sfz）。这些相当于表情“公式”，你必须从听觉和记谱两方面都能识别。
12. Ornamentation & Shorthand Decoration Formulae | 装饰音与速记装饰公式
English: Common ornaments each have a performance formula. Trill (tr): rapid alternation between the written note and the note above, usually starting on the upper note in Baroque style. Mordent: upper mordent is a single rapid alternation (note–upper–note); lower mordent has a vertical line through it and goes note–lower–note. Turn: a four-note figure around the main note (upper–main–lower–main). Appoggiatura: a small note that takes half the value of the following note and leans expressively. Acciaccatura: a crushed, very short grace note played before the beat. These ornaments frequently appear in set works and dictation tasks.
中文：常见装饰音各有演奏“公式”。颤音（tr）：在本音与上方二度音之间快速交替，巴洛克风格常从上方音开始。波音：上波音是一次快速交替（本音–上方音–本音）；下波音中间有一条竖线，演奏为本音–下方音–本音。回音：围绕本音的四音组合（上方音–本音–下方音–本音）。倚音：一个较小的音符，占后面音符时值的一半，富有表情地倚靠。碎音：短促的、在拍子之前的极短装饰音。这些装饰音频繁出现在规定曲目和听写任务中。
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