📚 Year 10 WJEC Music: Formulas & Theorems Quick Reference Sheet | WJEC 十年级音乐：公式定理速查手册
This quick-reference guide collects the essential music theory rules, formulas, and ‘theorems’ needed for Year 10 WJEC Music. Use it to memorise rhythmic values, interval patterns, chord construction, and the logic behind key signatures and cadences. Each section pairs a concise English explanation with a Chinese translation so you can absorb the content in both languages.
本速查手册汇编了 WJEC 十年级音乐所需的核心理论规则、公式与“定理”。涵盖节奏时值、音程模式、和弦构建、调号逻辑和终止式规律等，每一条都配有中英双语解释，帮助你快速记忆与查漏补缺。
1. Time Signatures and Rhythm Formulas | 拍号与节奏公式
The time signature tells you how many beats are in each bar and what note value counts as one beat. In simple time, the beat is an undotted note; in compound time, the beat is a dotted note. The formula for recognising a compound time signature: the top number is a multiple of 3 (6, 9, 12), and the main beat divides into three.
拍号表明每小节的拍子数量和以哪种音符为一拍。单拍子的单位拍是非附点音符；复拍子的单位拍是附点音符。识别复拍子的公式：上方数字是 3 的倍数（6、9、12），单位拍可三等分。
- Simple duple: 2/4, 2/2 | 单二拍
- Simple triple: 3/4, 3/2 | 单三拍
- Simple quadruple: 4/4, 4/2 | 单四拍
- Compound duple: 6/8 (dotted crotchet beat) | 复二拍：6/8（附点四分音符为一拍）
- Compound triple: 9/8 | 复三拍：9/8
- Compound quadruple: 12/8 | 复四拍：12/8
The rhythmic value of a dotted note follows the formula: dotted note = original note value + half of that value. For example, a dotted minim equals a minim plus a crotchet (3 crotchet beats).
附点音符的时值公式：附点音符 = 原时值 + 该时值的一半。例如附点二分音符等于二分音符加四分音符（共三拍）。
ote value relationships: 1 semibreve = 2 minims = 4 crotchets = 8 quavers = 16 semiquavers
音符时值关系：1 全音符 = 2 二分音符 = 4 四分音符 = 8 八分音符 = 16 十六分音符
2. Notes and Rest Durations | 音符与休止符时值
Rests follow exactly the same duration formulas as notes. A semibreve rest hangs from the fourth line; a minim rest sits on the third line. The hierarchy of rests mirrors the note tree exactly.
休止符的时值与同名音符完全一致。全休止符挂在第四线下方，二分休止符坐在第三线上。休止符的层级关系与音符树严格对应。
When you add a dot to a rest, the same dotted rule applies: Dotted rest = rest + half its value. A double dotted note/rest adds half plus a quarter of the original value.
附点休止符同样遵循公式：附点休止符 = 原休止时值 + 其一半。复附点则再加原时值的四分之一。
In compound time, the ‘beat’ is usually a dotted note, so a bar in 6/8 has two dotted-crotchet beats, each divided into three quavers.
在复拍子中，“一拍”通常是附点音符，因此 6/8 拍的小节包含两个附点四分音符拍子，每拍再细分为三个八分音符。
3. Pitch and Clefs | 音高与谱号
Pitch is identified by letter name (A–G) plus accidentals. The treble clef (G clef) sets the second line as G above middle C; the bass clef (F clef) sets the fourth line as F below middle C. Middle C is placed on one ledger line between the two staves.
音高由字母名 A–G 加上变音记号标识。高音谱号（G 谱号）将第二线定为中央 C 上方的 G；低音谱号（F 谱号）将第四线定为中央 C 下方的 F。中央 C 位于两谱表之间的加线上。
| Clef | Note on line/space | 中文 |
|---|---|---|
| Treble | Lines: E G B D F (Every Good Boy Deserves Food) | 一线 E，二线 G，三线 B，四线 D，五线 F |
| Bass | Lines: G B D F A (Good Boys Do Fine Always) | 一线 G，二线 B，三线 D，四线 F，五线 A |
The formula for octave designation: from any C to the next C is an octave (8ve). The distance from C4 (middle C) to C5 is one octave higher.
八度公式：从一个 C 到相邻的 C 是一个八度。中央 C (C4) 到 C5 为高八度。
4. Interval Calculation | 音程计算
An interval is measured by its number (staff distance) and quality (major, minor, perfect, augmented, diminished). The number counts letter names: C to E is a 3rd. The quality is determined by the number of semitones.
音程由度数（五线谱距离）和性质（大、小、纯、增、减）决定。度数计算字母名数量：C 到 E 是三度。性质由所含半音数决定。
M2 = 2, m3 = 3, M3 = 4, P4 = 5, TT = 6, P5 = 7, m6 = 8, M6 = 9, m7 = 10, M7 = 11, P8 = 12
半音参考：小二度=1，大二度=2，小三度=3，大三度=4，纯四度=5，三全音=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
Interval inversion formula: 9 − the original number = inversion number, and the quality swaps: major ↔ minor, augmented ↔ diminished, perfect ↔ perfect.
音程转位公式：9 − 原度数 = 转位度数，性质互换：大↔小，增↔减，纯↔纯。例如大三度转位为小六度。
A perfect 4th inverted becomes a perfect 5th. A major 6th becomes a minor 3rd.
纯四度转位成纯五度，大六度转位成小三度。
5. Scale Construction | 音阶构建
Scales follow fixed formulas of tones (T) and semitones (S).
音阶遵循固定的全音（T）与半音（S）模式。
Major scale formula: T – T – S – T – T – T – S
大调音阶公式：全 – 全 – 半 – 全 – 全 – 全 – 半
Natural minor formula: T – S – T – T – S – T – T
自然小调公式：全 – 半 – 全 – 全 – 半 – 全 – 全
Harmonic minor raises the 7th degree: creates an augmented 2nd between 6th and 7th. Melodic minor ascending raises the 6th and 7th; descending is natural minor.
和声小调升高第 VII 级，产生 6-7 级之间的增二度。旋律小调上行升高 VI、VII 级，下行还原为自然小调。
The pentatonic major scale omits the 4th and 7th degrees; the blues scale adds a flattened 5th (♭5) to the minor pentatonic.
五声大调音阶省略 IV 和 VII 级；布鲁斯音阶在小调五声音阶中加入 ♭5 级（蓝色音）。
6. Key Signatures and the Circle of Fifths | 调号与五度圈
Key signatures place sharps or flats at the beginning of the staff. The order of sharps in a key signature is fixed: F♯ C♯ G♯ D♯ A♯ E♯ B♯. The order of flats: B♭ E♭ A♭ D♭ G♭ C♭ F♭.
调号在谱表开头标记升号或降号。升号调的顺序固定：F♯ C♯ G♯ D♯ A♯ E♯ B♯。降号调顺序：B♭ E♭ A♭ D♭ G♭ C♭ F♭。
Major key formula: for sharp keys, the tonic is a semitone above the last sharp. In A major (3 sharps: F♯ C♯ G♯), the last sharp is G♯, so the tonic is A.
大调调号定理：升号调的主音是最后一个升号上方小二度。如 A 大调（三个升号：F♯ C♯ G♯），最后升号为 G♯，上方小二度是 A。
For flat keys, the major tonic is the second-to-last flat. In E♭ major (3 flats: B♭ E♭ A♭), the second-to-last flat is E♭. For F major (1 flat) just memorise it.
降号调中，大调主音是倒数第二个降号。如 E♭ 大调（三个降号：B♭ E♭ A♭），倒数第二个降号是 E♭。F 大调只有一个降号需单独记忆。
The relative minor key shares the same key signature and is found a minor 3rd below the major tonic.
关系小调与主大调共用同一个调号，位于大调主音下方小三度。
7. Chord Construction Formulas | 和弦构造公式
Chords are built by stacking intervals measured in semitones above a root.
和弦通过按半音距离向上叠置音程来构建。
| Chord type | Semitone formula (intervals from root) | Example in C | 中文公式 |
|---|---|---|---|
| Major triad | 0 + 4 + 3 (R, M3, P5) | C E G | 大三和弦：根 + 4 半音 + 3 半音 |
| Minor triad | 0 + 3 + 4 (R, m3, P5) | C E♭ G | 小三和弦：根 + 3 + 4 |
| Diminished triad | 0 + 3 + 3 (R, m3, dim5) | C E♭ G♭ | 减三和弦：根 + 3 + 3 |
| Augmented triad | 0 + 4 + 4 (R, M3, aug5) | C E G♯ | 增三和弦：根 + 4 + 4 |
| Dominant 7th | 0 + 4 + 3 + 3 (M3, P5, m7) | C E G B♭ | 属七和弦：大三 + 小三 + 小三 |
| Major 7th | 0 + 4 + 3 + 4 (M3, P5, M7) | C E G B | 大七和弦：大三 + 小三 + 大三 |
| Minor 7th | 0 + 3 + 4 + 3 (m3, P5, m7) | C E♭ G B♭ | 小七和弦：小三 + 大三 + 小三 |
Build any chord by counting semitones from the root using these layer formulas. The 7th chord family always stacks one extra third on top of the triad.
运用上述叠加公式可构建任何和弦，只需从根音开始计算半音数。七和弦始终在三和弦上方再叠置一个三度。
8. Chord Inversions and Figured Bass | 和弦转位与数字低音
Triads have three positions. The formula for naming inversions uses figured bass symbols:
三和弦有三种位置。转位命名使用数字低音标记：
- Root position: 5/3 (often omitted) | 原位：5/3
- First inversion: 6 (third in bass) | 第一转位：6（三音在低音）
- Second inversion: 6/4 (fifth in bass) | 第二转位：6/4（五音在低音）
Seventh chords have four positions: root (7), first inversion 6/5, second inversion 4/3, third inversion 4/2 or 2.
七和弦有四种位置：原位记作 7，第一转位 6/5，第二转位 4/3，第三转位 4/2 或 2。
The interval content dictates the figures: a first-inversion triad contains a 3rd and a 6th above the bass, hence '6'.
数字由低音上方的音程决定：第一转位三和弦低音上方构成三度和六度，因此用数字“6”。
9. Cadences and Chord Progressions | 终止式与和弦进行
Cadences are the punctuation marks of music. The four main cadence formulas are defined by the chords at phrase endings:
终止式是音乐的标点。四种主要终止式由乐句末尾的和弦运动定义：
- Perfect cadence: V – I (sounds complete, like a full stop) | 正格终止：V – I（完满句号）
- Plagal cadence: IV – I ('Amen' cadence) | 变格终止：IV – I（阿门终止）
- Imperfect cadence: I – V, II – V, IV – V (ends on V, sounds unfinished) | 半终止：I–V / II–V / IV–V（停在 V，意犹未尽）
- Interrupted cadence: V – vi (surprise move) | 阻碍终止：V – vi（意外进行）
A chord progression formula using roman numerals often follows the pattern: I – IV – V – I or I – vi – IV – V. Common substitutions follow the circle of fifths root movement.
和弦进行的罗马数字公式常用 I–IV–V–I 或 I–vi–IV–V。常见的根音运动遵循五度圈规律。
In a major key, the triad quality on each scale degree follows a fixed theorem: I (Major), ii (minor), iii (minor), IV (Major), V (Major), vi (minor), vii° (diminished).
大调中，各音级上建立的三和弦性质固定：I 大三，ii 小三，iii 小三，IV 大三，V 大三，vi 小三，vii° 减三。
10. Musical Structure and Forms | 音乐结构
Musical forms are formulaic templates composers use. Binary form (AB) has two sections, each usually repeated. Ternary form (ABA) sees the first section return after a contrasting middle.
曲式是作曲家使用的模板公式。二部曲式 AB 包含两个通常各自反复的段落。三部曲式 ABA 在对比中段后再现首段。
Other common structures: Rondo (ABACA), Theme and Variations (A A' A'' ...), and Sonata form (Exposition, Development, Recapitulation).
其他常见结构：回旋曲
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