📚 Year 9 AQA Music: Formula & Theorem Quick Reference Handbook | Year 9 AQA 音乐：公式定理速查手册
Music may seem like a world of creativity and emotion, but underpinning every melody, chord and rhythm are clear, repeatable formulas. In Year 9 AQA Music, understanding these musical ‘formulas’ – from building scales and intervals to constructing cadences – is the quickest route to confident listening, composing and performing. This handbook collects the essential formulas and theorems you will meet, presented as clear rules you can apply instantly.
音乐看起来像是充满创造力和情感的世界，但每一段旋律、每一个和弦和每一种节奏背后，都有清晰、可重复的公式。在 Year 9 AQA 音乐课程中，理解这些音乐“公式”——从构建音阶、音程到构造终止式——是通向自信听力、作曲和表演的最快捷径。这本手册收集了你将会遇到的核心公式与定理，以清晰的规则呈现，让你能立刻运用。
1. Note Values and Beat Formulas | 音符时值与节拍公式
In simple time, the beat relationship between notes follows a strict doubling or halving pattern. A semibreve (whole note) lasts for 4 beats. A minim (half note) is half of that: 2 beats. A crotchet (quarter note) represents 1 beat. Dividing further, a quaver (eighth note) equals ½ beat, and a semiquaver (sixteenth note) is ¼ beat. The formula to remember is: each note value is half the duration of the next larger note.
在单拍子中，音符之间的时值关系遵循严格的一倍或一半的规律。全音符持续4拍。二分音符是它的一半：2拍。四分音符代表1拍。继续划分，八分音符等于 ½ 拍，十六分音符为 ¼ 拍。要记住的公式是：每个音符的时值是它上面一个更大音符时值的一半。
| English Name | 中文名称 | Beats (4/4) |
|---|---|---|
| Semibreve | 全音符 | 4 |
| Minim | 二分音符 | 2 |
| Crotchet | 四分音符 | 1 |
| Quaver | 八分音符 | ½ |
| Semiquaver | 十六分音符 | ¼ |
When a dot is added, the note gains half of its original value. For example, a dotted minim = 2 + 1 = 3 beats; a dotted crotchet = 1 + ½ = 1½ beats. This is the dotted note formula: Dotted value = original value + (original value × ½).
当附点被加上时，音符增加它原有时值的一半。例如，附点二分音符 = 2 + 1 = 3拍；附点四分音符 = 1 + ½ = 1½ 拍。这就是附点音符公式：附点时值 = 原时值 + (原时值 × ½)。
2. Time Signature Formulas | 拍号公式
A time signature is expressed as a fraction-like symbol. The top number indicates how many beats are in each bar; the bottom number tells you what type of note counts as one beat. The formula ‘Top shows beats, bottom shows count’ helps you decode any time signature instantly. For example, 4/4 means 4 crotchet beats per bar; 3/4 means 3 crotchet beats; 2/2 means 2 minim beats; 6/8 means 6 quaver beats, usually grouped in two dotted-crotchet pulses.
拍号像分数一样呈现。上面的数字表示每小节有多少拍；下面的数字告诉你以哪种音符为一拍。公式“上数拍子，下数单位”能让你立刻读懂任何拍号。例如，4/4 表示每小节4个四分音符的拍子；3/4 表示3个四分音符拍；2/2 表示2个二分音符拍；6/8 表示6个八分音符拍，通常组合成两个附点四分音符的脉动。
In Year 9 you will mainly use simple time (each beat divides into 2 equal parts) and compound time (each beat divides into 3). Check the bottom number: 4 = crotchet beat, 8 = quaver beat. A quick test: if the top number is a multiple of 3 and greater than 3 (like 6,9,12), it is often compound time.
在 Year 9 你主要用到单拍子（每拍分成2等份）和复拍子（每拍分成3等份）。看下面的数字：4 = 四分音符为一拍，8 = 八分音符为一拍。快速检验：如果上方数字是3的倍数且大于3（如6、9、12），通常是复拍子。
3. Major Scale Formula | 大调音阶公式
Every major scale follows the same sequence of tones (T) and semitones (S). Starting from any note, apply the formula: T T S T T T S. For instance, C major: C -D (T), D-E (T), E-F (S), F-G (T), G-A (T), A-B (T), B-C (S). No sharps or flats are needed; the formula builds the scale naturally.
每一个大调音阶都遵循相同的全音（T）与半音（S）序列。从任意音开始，套用公式：全 全 半 全 全 全 半。例如 C 大调：C-D（全音），D-E（全音），E-F（半音），F-G（全音），G-A（全音），A-B（全音），B-C（半音）。不需要任何升降号，公式自然构建出音阶。
When you start on G, the formula forces an F♯ to maintain the T T S T T T S pattern: G-A (T), A-B (T), B-C (S), C-D (T), D-E (T), E-F♯ (T), F♯-G (S). This is why key signatures exist – they are a direct result of the scale formula.
当你从 G 开始时，公式要求使用 F♯ 才能保持 全全半全全全半 的模式：G-A（全），A-B（全），B-C（半），C-D（全），D-E（全），E-F♯（全），F♯-G（半）。这就是调号存在的原因——它们是音阶公式的直接产物。
4. Minor Scale Formulas | 小调音阶公式
The natural minor scale uses the formula T S T T S T T. A minor (the relative minor of C major) demonstrates this: A-B (T), B-C (S), C-D (T), D-E (T), E-F (S), F-G (T), G-A (T). Notice it uses the same notes as C major but starts on A, producing a different interval pattern.
自然小调音阶使用公式 全 半 全 全 半 全 全。A 小调（C大调的关系小调）演示了这点：A-B（全），B-C（半），C-D（全），D-E（全），E-F（半），F-G（全），G-A（全）。注意它使用与 C 大调相同的音符，但从 A 开始，产生了不同的音程模式。
The harmonic minor raises the 7th degree by a semitone, creating an exotic semitone step between the 6th and 7th. Formula: T S T T S T+½ S (where T+½ is an augmented second, three semitones). In A harmonic minor: G becomes G♯, so F-G♯ spans three semitones, and G♯-A is a semitone.
和声小调将第七级音升高半音，在第六级和第七级之间制造了一个异域风情的半音阶。公式：全 半 全 全 半 增二度 半（增二度为三个半音）。在 A 和声小调中：G 变为 G♯，因此 F-G♯ 跨三个半音，G♯-A 为半音。
The melodic minor (ascending) raises both the 6th and 7th degrees to smooth the melody: T S T T T T S. Descending, it often reverts to natural minor. A melodic minor ascending: A-B (T), B-C (S), C-D (T), D-E (T), E-F♯ (T), F♯-G♯ (T), G♯-A (S).
旋律小调（上行）将第六级和第七级都升高，以平滑旋律：全 半 全 全 全 全 半。下行时常还原为自然小调。A 旋律小调上行：A-B（全），B-C（半），C-D（全），D-E（全），E-F♯（全），F♯-G♯（全），G♯-A（半）。
5. Key Signature Identification Formula | 调号判别公式
For major keys with sharps: take the last sharp in the key signature and go up a semitone. That note names the major key. For example, if the last sharp is D♯, the key is E major. For major keys with flats: the second-to-last flat in the key signature names the key (except F major, which has one flat, B♭). So a key signature with B♭, E♭, A♭ – the second-to-last is E♭, giving E♭ major.
对于带升号的大调：取调号中最后一个升号，再往上走一个半音，那个音名就是大调。例如，最后一个升号是 D♯，调就是 E 大调。对于带降号的大调：看倒数第二个降号，它就是你大调的名称（除了 F 大调，它只有一个降号 B♭）。所以调号有 B♭、E♭、A♭——倒数第二个是 E♭，即 E♭ 大调。
To find the relative minor: go down three semitones from the major tonic. Thus, E major’s relative minor is C♯ minor; E♭ major’s relative minor is C minor. You can also count the sixth degree of the major scale, which always gives the relative minor.
寻找关系小调：从大调主音向下数三个半音。因此，E 大调的关系小调是 C♯ 小调；E♭ 大调的关系小调是 C 小调。你也可以数大调音阶的第六级音，它永远是关系小调的主音。
6. Interval Formulas | 音程公式
An interval is the distance between two notes, described by a number (2nd, 3rd, 4th, etc.) and a quality (perfect, major, minor, augmented, diminished). The number is simply the count of letter names, inclusive: C to E spans C-D-E, three letters, so it’s a 3rd. Then apply the semitone count formula. A major 3rd = 4 semitones; a minor 3rd = 3 semitones; a perfect 5th = 7 semitones; a perfect 4th = 5 semitones. Use the major scale of the lower note as your reference: if the upper note belongs to that major scale, the 2nd, 3rd, 6th and 7th are major, and the 4th, 5th and octave are perfect. Any narrowing by a semitone makes it minor or diminished; widening makes it augmented.
音程是两个音之间的距离，由一个数字（二度、三度、四度等）和性质（纯、大、小、增、减）来描述。数字只是所包含字母名的计数：C 到 E 经过 C-D-E，三个字母，所以是三度。然后套用半音数公式。大三度 = 4个半音；小三度 = 3个半音；纯五度 = 7个半音；纯四度 = 5个半音。以下方音的大调音阶为参照：如果上方音属于那个大调音阶，那么二度、三度、六度和七度就是大音程，四度、五度和八度是纯音程。每缩小一个半音，就变成小或减音程；每扩大一个半音，就变成增音程。
| Interval | Semitones | Example |
|---|---|---|
| Minor 2nd | 1 | E-F |
| Major 2nd | 2 | C-D |
| Minor 3rd | 3 | A-C |
| Major 3rd | 4 | C-E |
| Perfect 4th | 5 | C-F |
| Perfect 5th | 7 | C-G |
| Octave | 12 | C-C |
A quick theorem: if you invert an interval, the qualities swap (major becomes minor, perfect stays perfect) and the numbers add up to 9. So an inverted major 3rd is a minor 6th.
速记定理：如果你转位一个音程，性质会互换（大变小，小变大，纯保持不变），数字相加等于9。所以大三度转位后是小六度。
7. Triad Chord Building Formulas | 三和弦构建公式
A triad is a three-note chord built by stacking intervals. The two most common formulas are: Major triad = root + major 3rd (4 semitones) + perfect 5th (7 semitones from root). Minor triad = root + minor 3rd (3 semitones) + perfect 5th (7 semitones from root). You can also think ‘play a note, skip one, skip one’ within the scale, but using semitone counting gives the exact formula in any situation.
三和弦是由叠加音程构成的三音和弦。两种最常见的公式是：大三和弦 = 根音 + 大三度（4个半音） + 纯五度（距根音7个半音）。小三和弦 = 根音 + 小三度（3个半音） + 纯五度（距根音7个半音）。你当然可以在音阶内“弹一个音，跳过一个，再跳过一个”来思考，但使用半音计数可以在任何情况下给出精确公式。
Diminished triad formula: root + minor 3rd + diminished 5th (6 semitones from root). Augmented triad formula: root + major 3rd + augmented 5th (8 semitones from root). In Year 9, focus on the major and minor shapes in all inversions.
减三和弦公式：根音 + 小三度 + 减五度（距根音6个半音）。增三和弦公式：根音 + 大三度 + 增五度（距根音8个半音）。Year 9 阶段主要集中掌握大、小三和弦及其所有转位。
To describe a chord’s inversion: root position – root in the bass; first inversion – 3rd in the bass; second inversion – 5th in the bass. The intervals above the bass change, but the chord retains its identity.
描述和弦转位的公式：原位——根音在低音；第一转位——三音在低音；第二转位——五音在低音。低音上方的音程会变化，但和弦身份不变。
8. Chord Progression and Cadence Formulas | 和弦进行与终止式公式
Cadences are musical punctuation points, each with a formula. A perfect cadence (V-I) moves from dominant to tonic: it sounds final and complete. A plagal cadence (IV-I) is the ‘Amen’ cadence. An imperfect cadence ends on V (e.g., I-V, II-V, IV-V), leaving the music incomplete. An interrupted cadence goes V-VI, creating a surprise. These are defined by the chords, not the melody, and are fundamental to composition and listening.
终止式是音乐的标点，每个都有自己的公式。正格终止（V-I）从属和弦进行到主和弦：听起来结束且完整。变格终止（IV-I）是“阿门”终止。不完全终止以 V 结束（如 I-V、II-V、IV-V），让音乐不完整。阻碍终止进行到 V-VI，制造意外感。它们由和弦定义，而非旋律，是作曲与听力的基础。
In a major key, the primary triads I, IV and V are all major; in a natural minor key, i and iv are minor, but V is often major (using the harmonic minor raised 7th) to create a stronger cadence. The formula for a strong perfect cadence in a minor key is therefore V-i, not v-i.
在大调中，主、下属、属三和弦都是大和弦；在自然小调中，i 和 iv 是小和弦，但 V 常为大和弦（使用和声小调升七级）以制造更强的终止。因此小调中强大的正格终止公式是 V-i，而非 v-i。
9. Transposition and Clef Formulas | 移调与谱号公式
Transposition moves a melody up or down by a consistent interval. The formula: keep the same interval relationship. If you transpose a C major melody up a major 2nd into D major, every note is raised by a tone (2 semitones) and the key signature changes accordingly. A quick theorem: moving from one key to another uses the interval between their tonics as the transposition interval.
移调是按相同音程将旋律向上或向下移动。公式：保持相同的音程关系。如果你将一段 C 大调旋律向上移大二度到 D 大调，每个音都升高一个全音（2个半音），并且调号相应改变。速记定理：从一个调转换到另一个调，使用它们主音之间的音程作为移调音程。
Clefs define pitch ranges on the staff. The treble clef (G clef) curls around the second line, marking it as G above middle C. The bass clef (F clef) starts on the fourth line, marking it as F below middle C. Many Year 9 pieces use the grand staff. The formula for reading bass clef: the lines from bottom to top are G-B-D-F-A (Good Boys Do Fine Always); spaces are A-C-E-G (All Cows Eat Grass).
谱号定义了五线谱上的音高范围。高音谱号（G 谱号）环绕第二线，将其标记为中央 C 上方的 G。低音谱号（F 谱号）始于第四线，将其标记为中央 C 下方的 F。许多 Year 9 乐曲使用大谱表。低音谱号读谱公式：线从下往上为 G-B-D-F-A (Good Boys Do Fine Always)；间为 A-C-E-G (All Cows Eat Grass)。
10. Tempo, Dynamics and Articulation Quick-Reference | 速度、力度与奏法速查
These terms are not mathematical formulas, but they function as performance theorems. Tempo marks give precise speeds: Largo (very slow, broadly), Adagio (slow), Andante (walking pace), Moderato (moderate), Allegro (fast, lively), Presto (very fast). Dynamics range from pianissimo (pp, very soft) to fortissimo (ff, very loud), with crescendo (cresc., gradually louder) and diminuendo (dim., gradually softer). Articulation marks such as legato (smooth, indicated by a slur), staccato (short, detached, shown by a dot above/below the note) and accent (marked >, strong attack) work like a performance formula to shape character.
这些术语不是数学公式，但起着演奏定理的作用。速度标记给出精确速度：Largo（非常慢，宽广的）、Adagio（慢）、Andante（步行速度）、Moderato（中速）、Allegro（快，活泼的）、Presto（非常快）。力度范围从 pianissimo（pp，极弱）到 fortissimo（ff，极强），并配有 crescendo（cresc.，渐强）和 diminuendo（dim.，渐弱）。奏法标记如 legato（连奏，用连线表示）、staccato（断奏，短促分离，由音符上方/下方的圆点表示）和 accent（重音，标记 >，强烈击发）如同演奏公式，塑造音乐性格。
A useful theorem: a slur over two notes of the same pitch is a tie, combining their durations; a slur over different pitches indicates legato playing. Always check the context to apply the correct formula.
一个有用的定理：在同音高的两个音符上的连线是连音线，将它们的时值合并；不同音高上的连线则指示连奏。永远要检查上下文以应用正确的公式。
11. Rhythmic Device Formulas | 节奏手法公式
Syncopation is a deliberate disruption of the regular metric accent; its formula places emphasis on a weak beat or between beats. For example, accenting the ‘and’ of 2 in 4/4 time creates syncopation. Dotted rhythms and ties are common tools to achieve this. Another formula: hemiola shifts the feel from three groups of two beats to two groups of three beats (or vice versa), giving a brief cross-rhythm effect, often found in Baroque music.
切分音是对正规节拍重拍的有意破坏；它的公式将重音放在弱拍或拍子之间。例如，在 4/4 拍中强调第二拍的“and”就制造了切分。附点节奏和连音线是实现切分的常用工具。另一个公式：赫米奥拉将律动感由三组两拍转为两组三拍（或反之），产生短暂的交叉节奏效果，常见于巴洛克音乐。
Ostinato is a persistently repeated musical phrase or rhythm. A rhythmic ostinato is a repeated rhythm pattern; a melodic ostinato repeats a pitch/rhythm combination. The formula: choose a short, distinctive idea and anchor it unchanged throughout a section.
固定音型是持续重复的音乐短句或节奏。节奏固定音型是重复的节奏模式；旋律固定音型重复音高与节奏的结合。公式：选一个短小、有特色的点子，在整个段落中不变地反复。
12. Texture and Structure Recognition | 织体与结构辨认公式
Texture can be analysed with simple formulas: monophonic = a single melodic line alone. Homophonic = melody with chordal accompaniment (most common in Year 9 songs). Polyphonic = two or more independent melodies interweaving. A quick theorem: if you hear one clear melody and block chords underneath, it is homophony; if you can hum two distinct tunes at once, it is polyphony.
织体可以用简单公式分析：单声部 = 一条单独的旋律线条。主调织体 = 旋律加上和弦伴奏（Year 9 歌曲中最为常见）。复调织体 = 两条或更多独立旋律交织。速记定理：如果你听到一条清晰的旋律，下方是块状和弦，这就是主调织体；如果你能同时哼唱两条不同的旋律，那就是复调织体。
Common musical structures also follow formulaic designs: Binary form (AB), Ternary form (ABA), Rondo form (ABACA), and Theme and Variations (A A’ A” …). The letters represent contrasting sections. Identifying these structures in listening is a key AQA skill.
常见的音乐结构也遵循公式化设计：二部曲式（AB）、三部曲式（ABA）、回旋曲式（ABACA）以及主题与变奏（A A’ A” …）。字母代表对比段落。在听力中辨认这些结构是 AQA 关键技能。
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