📚 AS WJEC Music: Formula & Theorem Quick Reference Guide | AS WJEC 音乐：公式定理速查手册
Welcome to the AS WJEC Music Formula & Theorem Quick Reference Guide. This handbook distils the essential patterns, rules and theoretical frameworks you need to memorise for the examination. Whether you are analysing a set work, completing a harmony exercise, or preparing for the listening paper, these "formulae" – from interval size and chord construction to cadence types and scale recipes – offer a reliable shortcut. Use this bilingual guide to reinforce your understanding and speed up recall under timed conditions.
欢迎使用 AS WJEC 音乐公式定理速查手册。本手册浓缩了考试中必须记忆的核心模式、规则与理论框架。无论你是在分析规定作品、完成和声练习，还是备考听力试卷，这些“公式”——从音程距离与和弦构成到终止式类型和音阶配方——都能提供可靠的捷径。使用这份双语指南巩固理解，帮助你在计时条件下快速回忆。
1. Interval Formulae | 音程公式
An interval is the pitch distance between two notes, measured in semitones. Its quality (major, minor, perfect, augmented, diminished) depends on the number of semitones and the letter-name span. Memorise the following core intervals as you would number facts.
音程是两个音之间的音高距离，以半音为单位。其性质（大、小、纯、增、减）取决于半音数量及音名字母跨度。请像记忆数字事实一样掌握以下核心音程。
Perfect Unison: 0 semitones | 纯一度：0 半音
Minor 2nd: 1 semitone | 小二度：1 半音
Major 2nd: 2 semitones | 大二度：2 半音
Minor 3rd: 3 semitones | 小三度：3 半音
Major 3rd: 4 semitones | 大三度：4 半音
Perfect 4th: 5 semitones | 纯四度：5 半音
Augmented 4th / Diminished 5th (Tritone): 6 semitones | 增四度/减五度（三全音）：6 半音
Perfect 5th: 7 semitones | 纯五度：7 半音
Minor 6th: 8 semitones | 小六度：8 半音
Major 6th: 9 semitones | 大六度：9 半音
Minor 7th: 10 semitones | 小七度：10 半音
Major 7th: 11 semitones | 大七度：11 半音
Perfect Octave: 12 semitones | 纯八度：12 半音
Augmented intervals are one semitone larger than perfect or major; diminished intervals are one semitone smaller than perfect or minor. Always count letter names first, then adjust with accidentals.
增音程比纯或大音程大半音；减音程比纯或小音程小半音。务必先计算音名跨度，再通过变音记号调整。
2. Chord Construction | 和弦结构
Chords are built by stacking intervals above a root. The quality of the third and fifth determines the triad type. For WJEC, you must spell major, minor, augmented and diminished triads, as well as common seventh chords.
和弦由根音上方叠加音程构成。三音和五音的性质决定三和弦类型。WJEC 考试要求你拼写大、小、增、减三和弦以及常用七和弦。
| Triad Type | Semitone Formula | Example (C root) | 中文 |
|---|---|---|---|
| Major | 4 + 3 | C–E–G | 大三和弦 |
| Minor | 3 + 4 | C–E♭–G | 小三和弦 |
| Augmented | 4 + 4 | C–E–G♯ | 增三和弦 |
| Diminished | 3 + 3 | C–E♭–G♭ | 减三和弦 |
Seventh chords add a fourth note. The most tested are: dominant 7th (major triad + minor 7th), major 7th (major triad + major 7th), minor 7th (minor triad + minor 7th), half-diminished 7th (diminished triad + minor 7th) and diminished 7th (diminished triad + diminished 7th). In Roman numeral analysis, label them V⁷, I⁷, ii⁷, viiø⁷ and vii°⁷ respectively.
七和弦增加第四个音。最高频考点为：属七（大三和弦+小七度）、大七（大三和弦+大七度）、小七（小三和弦+小七度）、半减七（减三和弦+小七度）和减七（减三和弦+减七度）。在罗马数字分析中，分别标记为 V⁷、I⁷、ii⁷、viiø⁷ 和 vii°⁷。
3. Scale Formulae | 音阶公式
Scales are sequences of tones (T) and semitones (S). The pattern defines the mode. Major and minor scales are the foundation; other modes appear in set works and composition tasks.
音阶是全音（T）和半音（S）的序列。排列模式决定了调式。大小调音阶是基础；其他调式会出现在规定作品与作曲任务中。
Major scale: T–T–S–T–T–T–S (e.g., C–D–E–F–G–A–B–C).
大调音阶：全–全–半–全–全–全–半（如 C–D–E–F–G–A–B–C）。
Natural minor: T–S–T–T–S–T–T (e.g., A–B–C–D–E–F–G–A).
自然小调：全–半–全–全–半–全–全（如 A–B–C–D–E–F–G–A）。
Harmonic minor: raise the 7th degree (e.g., A–B–C–D–E–F–G♯–A), creating an augmented 2nd between 6th and 7th.
和声小调：升高第七级（如 A–B–C–D–E–F–G♯–A），六级与七级间形成增二度。
Melodic minor (ascending): raise 6th and 7th (A–B–C–D–E–F♯–G♯–A); descending reverts to natural minor. For compound melodies, both forms are used.
旋律小调（上行）：升高六、七级（A–B–C–D–E–F♯–G♯–A）；下行还原自然小调。在复合旋律中两种形式均使用。
| Mode | Formula | 中文调式 |
|---|---|---|
| Ionian (major) | T–T–S–T–T–T–S | 伊奥尼亚（大调） |
| Dorian | T–S–T–T–T–S–T | 多利亚 |
| Phrygian | S–T–T–T–S–T–T | 弗里吉亚 |
| Lydian | T–T–T–S–T–T–S | 利底亚 |
| Mixolydian | T–T–S–T–T–S–T | 混合利底亚 |
| Aeolian (natural minor) | T–S–T–T–S–T–T | 爱奥利亚（自然小调） |
| Locrian | S–T–T–S–T–T–T | 洛克里亚 |
4. Key Signatures & Circle of Fifths | 调号与五度圈
Key signatures indicate the sharps or flats that consistently appear. The circle of fifths arranges keys so that adjacent keys differ by one accidental. Sharp keys move up by perfect 5ths: G (1♯), D (2♯), A (3♯), E (4♯), B (5♯), F♯ (6♯), C♯ (7♯). Flat keys move down by perfect 5ths: F (1♭), B♭ (2♭), E♭ (3♭), A♭ (4♭), D♭ (5♭), G♭ (6♭), C♭ (7♭).
调号标示持续出现的升降号。五度圈将各调按相差一个变音记号的规律排列。升号调向上纯五度：G（1♯）、D（2♯）、A（3♯）、E（4♯）、B（5♯）、F♯（6♯）、C♯（7♯）。降号调向下纯五度：F（1♭）、B♭（2♭）、E♭（3♭）、A♭（4♭）、D♭（5♭）、G♭（6♭）、C♭（7♭）。
For quick identification: the last sharp is always the leading note (Ti) of the major key; the second-to-last flat is the tonic of a flat major key. Relative minor keys share the same key signature and lie a minor 3rd below the major tonic.
快速识别技巧：最后一个升号为该大调的导音 (Ti)；倒数第二个降号是降号大调的主音。关系小调与平行大调调号相同，位于大调主音下方小三度。
| 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 / e小调 |
| 2♯ | D major | B minor | D大调 / b小调 |
| 3♯ | A major | F♯ minor | A大调 / f♯小调 |
| 1♭ | F major | D minor | F大调 / d小调 |
| 2♭ | B♭ major | G minor | 降B大调 / g小调 |
5. Cadences | 终止式
Cadences are harmonic punctuation marks at phrase ends. You must aurally and visually identify perfect, plagal, imperfect and interrupted cadences, and explain their effect.
终止式是乐句末尾的和声标点。你必须能听辨和视别完全终止、变格终止、不完全终止和阻碍终止，并说明其效果。
Perfect cadence: V–I (or V⁷–I). Sounds final, conclusive. In minor keys, the leading note is raised (use harmonic minor).
完全终止：V–I（或 V⁷–I）。听感完满、收束。在小调中导音需升高（使用和声小调）。
Plagal cadence: IV–I. Often called the "Amen" cadence; softer and less decisive than perfect.
变格终止：IV–I。常称“阿们”终止；比完全终止柔和、果断性较弱。
Imperfect cadence: any chord moving to V (e.g., I–V, ii–V, IV–V). Sounds incomplete, creating expectation.
不完全终止：任何和弦进行到 V（如 I–V、ii–V、IV–V）。听感未完成，制造期待。
Interrupted cadence: V–vi (or V–VI in minor). Surprises the listener by avoiding the tonic, often used for expressive effect.
阻碍终止：V–vi（小调中 V–VI）。通过回避主音使听者意外，常为表情效果而用。
6. Rhythm & Time Signatures | 节奏与拍号
Metre is organised into regular groupings of beats. Time signatures indicate how many beats per bar and what note value represents the beat. Simple time has beats divisible by 2; compound time has beats divisible by 3 dotted note units.
节拍由规律的拍子组合构成。拍号表示每小节几拍、以及何种音符为一拍。单拍子的拍可二分；复拍子的拍以附点音符为单位可三分。
Common simple metres: 2/4 (duple), 3/4 (triple), 4/4 (quadruple). Compound metres: 6/8 (duple compound, two dotted-crotchet beats), 9/8 (triple compound), 12/8 (quadruple compound).
常见单拍子：2/4（二拍子）、3/4（三拍子）、4/4（四拍子）。复拍子：6/8（二拍子复合，两个附点四分音符拍）、9/8（三拍子复合）、12/8（四拍子复合）。
Rhythmic devices: dotted rhythms (long–short), syncopation (accents on weak beats or offbeats), hemiola (3:2 cross-rhythm, especially in triple metre), triplets (three notes in the time of two). Be able to notate rests correctly; whole-bar rests are used in any metre.
节奏手法：附点节奏（长短型）、切分音（重音落在弱拍或拍间）、赫米奥拉（三对二交错节奏，尤见于三拍子）、三连音（两拍时值内奏三个音）。能正确记写休止符；全小节休止适用于任何拍号。
7. Italian Terms & Signs | 音乐表情术语与记号
A large bank of Italian terms appears on the WJEC paper. They cover tempo, dynamics, articulation and expression. Learn them systematically.
WJEC 试卷涉及大量意大利术语，涵盖速度、力度、奏法和表情。需系统学习。
| Term | Meaning | 中文 |
|---|---|---|
| Allegro | Fast, lively | 快板 |
| Andante | At a walking pace | 行板 |
| Adagio | Slow, stately | 柔板 |
| p (piano) | Quiet | 弱 | Published by TutorHao | AS 音乐 Revision Series | aleveler.com
