📚 Year 12 WJEC Music: Quick Reference Formulas & Theorems | Year 12 WJEC 音乐：公式定理速查手册
This article serves as a concise yet comprehensive reference for the essential theoretical building blocks of Western tonal music, directly aligned with the Year 12 WJEC Music specification. Think of it as your go-to ‘formula sheet’ – a collection of patterns, interval structures, and harmonic rules that underpin analysis, composition, and aural skills. All concepts are presented with clear, systematic definitions that can be applied immediately to your set works and creative tasks.
本文是为 Year 12 WJEC 音乐课程量身定制的核心乐理速查手册。你可以把它看作一份“公式表”，涵盖了音阶、音程、和弦、终止式等西方调性音乐的基本构成规则，直接服务于分析、作曲与听力训练。每个概念均以系统化定义呈现，便于快速查阅并运用在你的指定作品研习和创作实践中。
1. Major Scale Formula | 大调音阶公式
A major scale follows a fixed pattern of whole tones (W) and semitones (H): W – W – H – W – W – W – H. Starting from any tonic note, applying this sequence guarantees the correct major scale. For example, C major: C – D (W), D – E (W), E – F (H), F – G (W), G – A (W), A – B (W), B – C (H). The key signature reflects the required sharps or flats to preserve this interval pattern.
大调音阶遵循固定的全音（W）与半音（H）排列模式：全 – 全 – 半 – 全 – 全 – 全 – 半。无论从哪个主音出发，套用这一序列就能得到正确的大调音阶。例如 C 大调：C – D（全），D – E（全），E – F（半），F – G（全），G – A（全），A – B（全），B – C（半）。调号正是为了维持这个音程模式而添加必要的升号或降号。
2. Natural Minor Scale Formula | 自然小调音阶公式
The natural minor scale pattern is W – H – W – W – H – W – W. It can also be derived from the major scale by lowering the 3rd, 6th, and 7th degrees by a semitone. A minor (natural): A – B (W), B – C (H), C – D (W), D – E (W), E – F (H), F – G (W), G – A (W). This scale shares the same key signature as its relative major, which is a minor third above the tonic.
自然小调的模式为全 – 半 – 全 – 全 – 半 – 全 – 全。也可以从大调音阶推导，将第 III、VI、VII 级降低半音。a 自然小调：A – B（全），B – C（半），C – D（全），D – E（全），E – F（半），F – G（全），G – A（全）。自然小调与其关系大调共享同一调号，关系大调的主音位于小调主音上方小三度。
3. Harmonic and Melodic Minor Scales | 和声与旋律小调音阶
The harmonic minor scale raises the 7th degree of the natural minor by a semitone, creating an augmented second between the 6th and 7th degrees. Pattern: W – H – W – W – H – (W+H) – H (where W+H is an augmented second, three semitones). In A harmonic minor: A – B – C – D – E – F – G♯ – A. The melodic minor scale in its ascending form raises both the 6th and 7th degrees: W – H – W – W – W – W – H; descending, it reverts to natural minor. This dual-form is crucial for voice leading and melodic contour in tonal compositions.
和声小调将自然小调的第 VII 级升高半音，在 VI–VII 级之间产生增二度。模式：全 – 半 – 全 – 全 – 半 – (全+半) – 半（其中全+半为增二度，三个半音）。a 和声小调：A – B – C – D – E – F – G♯ – A。旋律小调上行时将第 VI、VII 级同时升高半音：全 – 半 – 全 – 全 – 全 – 全 – 半；下行时恢复为自然小调。这种双形态对声部进行和旋律轮廓非常重要。
4. Intervals: Quality and Semitone Count | 音程：性质与半音数
Intervals are measured by two parameters: the number of scale steps (2nd, 3rd, 4th, etc.) and the quality (perfect, major, minor, augmented, diminished). The semitone count defines the quality precisely. Below is a quick reference for common intervals within an octave, expressed in semitones.
音程由两个参数定义：级数（二度、三度、四度等）和性质（纯、大、小、增、减）。半音数精确决定性质。下表列出了八度内常见音程的半音数速查。
| Interval Name | Semitones | Example (from C) |
|---|---|---|
| Minor 2nd | 1 | C – D♭ |
| Major 2nd | 2 | C – D |
| Minor 3rd | 3 | C – E♭ |
| Major 3rd | 4 | C – E |
| Perfect 4th | 5 | C – F |
| Augmented 4th / Diminished 5th | 6 | C – F♯ |
| Perfect 5th | 7 | C – G |
| Minor 6th | 8 | C – A♭ |
| Major 6th | 9 | C – A |
| Minor 7th | 10 | C – B♭ |
| Major 7th | 11 | C – B |
| Perfect Octave | 12 | C – C |
Always count the letter names first to determine the interval number, then check the semitones to verify the quality. Compound intervals (larger than an octave) follow the same logic, with the number being 7 plus the simple interval number (e.g. a major 9th is an octave plus a major 2nd).
计算音程时先数音名字母确定度数，再用半音数核对性质。复音程（超过八度）遵循相同逻辑，度数为 7 加单音程度数（例如大九度 = 八度 + 大二度）。
5. Triad Construction | 三和弦的构成
A triad is a three-note chord built in stacked thirds. There are four qualities, defined by the intervals above the root: major triad = major 3rd + perfect 5th (e.g., C – E – G); minor triad = minor 3rd + perfect 5th (e.g., D – F – A); diminished triad = minor 3rd + diminished 5th (e.g., B – D – F); augmented triad = major 3rd + augmented 5th (e.g., C – E – G♯). In root position, the semitone pattern from the root to the fifth tells you everything you need.
三和弦是由三度叠置构成的三个音。按根音上方的音程关系分为四种性质：大三和弦 = 大三度 + 纯五度（如 C – E – G）；小三和弦 = 小三度 + 纯五度（如 D – F – A）；减三和弦 = 小三度 + 减五度（如 B – D – F）；增三和弦 = 大三度 + 增五度（如 C – E – G♯）。在根音位置，根音到五音的音程结构直接决定了和弦性质。
6. Seventh Chords | 七和弦
Adding a third above the fifth of a triad creates a seventh chord. The five common types are memorised by the quality of triad plus the quality of the 7th: major seventh (major triad + major 7th, e.g. C – E – G – B); dominant seventh (major triad + minor 7th, e.g. G – B – D – F); minor seventh (minor triad + minor 7th, e.g. D – F – A – C); half-diminished seventh (diminished triad + minor 7th, e.g. B – D – F – A); diminished seventh (diminished triad + diminished 7th, e.g. B – D – F – A♭). The semitone structure of each is unique and recognisable.
在三和弦的五音上方再叠加一个三度即构成七和弦。五种常见七和弦由三和弦性质加七音性质记忆：大七和弦（大三和弦 + 大七度，如 C – E – G – B）；属七和弦（大三和弦 + 小七度，如 G – B – D – F）；小七和弦（小三和弦 + 小七度，如 D – F – A – C）；半减七和弦（减三和弦 + 小七度，如 B – D – F – A）；减七和弦（减三和弦 + 减七度，如 B – D – F – A♭）。每种七和弦的半音结构都是独特且易于辨认的。
7. Chord Inversions | 和弦转位
When the lowest note is not the root, the chord is inverted. First inversion has the 3rd in the bass (figured bass: 6, or 6/3); second inversion has the 5th in the bass (6/4); for seventh chords, third inversion has the 7th in the bass (4/2). In Roman numeral analysis, inversion is shown by a small letter (e.g., I⁶ for tonic first inversion in C major: E – G – C) or figured bass symbols. The interval content above the bass note changes, affecting stability and voice-leading.
当最低音不是根音时，和弦即为转位。第一转位以三音为低音（数字低音标记 6 或 6/3）；第二转位以五音为低音（6/4）；七和弦还有第三转位，以七音为低音（4/2）。罗马数字分析中，转位用小写字母或数字低音表示（如 C 大调主和弦第一转位 I⁶：E – G – C）。低音上方的音程结构改变，影响稳定性和声部进行倾向。
8. Roman Numeral Analysis and Diatonic Chords | 罗马数字分析与自然音和弦
In any major key, the chords built on each scale degree follow a fixed quality pattern: I (major), ii (minor), iii (minor), IV (major), V (major), vi (minor), vii° (diminished). For a harmonic minor key, the raised leading tone alters the dominant and leading-tone chords: i (minor), ii° (dim), III⁺ (augmented, or III from natural minor), iv (minor), V (major), VI (major), vii° (dim). This formula is the core toolkit for functional harmony and cadential analysis in all WJEC set works.
在大调中，每个音级上建立的和弦性质固定：I（大），ii（小），iii（小），IV（大），V（大），vi（小），vii°（减）。和声小调中，由于升高的导音，属功能组和弦改变：i（小），ii°（减），III⁺（增，或用自然小调 III 级），iv（小），V（大），VI（大），vii°（减）。这套模式是功能和声与终止式分析的基础工具，适用于 WJEC 所有指定作品。
9. Cadences | 终止式
Cadences are the punctuation of tonal music. There are four main types, each with a distinct chord progression formula: perfect cadence V – I (or V⁷ – I), the strongest close; imperfect cadence (any chord to V), ending on the dominant; plagal cadence IV – I, the ‘Amen’ cadence; and interrupted/deceptive cadence V – vi (or V – VI in minor), which evades the tonic. Memorising the two-chord formulas and their bass movements is essential for score analysis.
终止式是调性音乐的标点符号。主要有四种类型，各有固定的双和弦进行公式：正格终止 V – I（或 V⁷ – I），最为完满；半终止（任何和弦到 V），停在属和弦；变格终止 IV – I，“阿们终止”；阻碍终止 V – vi（或小调 V – VI），回避主和弦。熟记这些二和弦公式及其低音进行是乐谱分析的关键。
10. Circle of Fifths and Key Signatures | 五度圈与调号
The circle of 5ths arranges keys by ascending perfect 5ths (clockwise) or ascending perfect 4ths (counter-clockwise). Each step clockwise adds one sharp (key signature order: F♯, C♯, G♯, D♯, A♯, E♯, B♯); each step counter-clockwise adds one flat (B♭, E♭, A♭, D♭, G♭, C♭, F♭). Relative minors share the same key signature. For example, G major (1 sharp) has relative E minor; F major (1 flat) has relative D minor. This cycle forms the backbone of common-practice modulation schemes.
五度圈按上行纯五度（顺时针）或上行纯四度（逆时针）排列所有调。顺时针每进一步增加一个升号（调号顺序：F♯, C♯, G♯, D♯, A♯, E♯, B♯）；逆时针增加一个降号（B♭, E♭, A♭, D♭, G♭, C♭, F♭）。关系小调共享同一调号。例如 G 大调（1 升）的关系小调是 e 小调；F 大调（1 降）的关系小调是 d 小调。这一循环是共性实践时期转调体系的基础。
11. Modes of the Major Scale | 大调调式
Each degree of the major scale can act as a tonic to create a mode. The seven modern diatonic modes are: Ionian (same as major, pattern W–W–H–W–W–W–H); Dorian (W–H–W–W–W–H–W); Phrygian (H–W–W–W–H–W–W); Lydian (W–W–W–H–W–W–H); Mixolydian (W–W–H–W–W–H–W); Aeolian (natural minor, W–H–W–W–H–W–W); Locrian (H–W–W–H–W–W–W). The characteristic note(s) that distinguish a mode from the parallel major or minor are key to modal analysis and composition.
以大调音阶的每一级作为主音即可形成调式。七种现代自然音调式为：伊奥尼亚（同大调，全全半全全全半）；多利亚（全半全全全半全）；弗里几亚（半全全全半全全）；利底亚（全全全半全全半）；混合利底亚（全全半全全半全）；爱奥利亚（自然小调，全半全全半全全）；洛克里亚（半全全半全全全）。区分调式与平行大小调的特征音是调式分析与创作的关键。
12. Modulation Techniques | 转调技巧
Modulation is the process of changing key within a piece. Common techniques include: pivot chord modulation (a chord diatonic in both old and new keys, analysed with a dual Roman numeral, e.g., C major: F chord is IV in C and VI in A minor); direct/phrase modulation (sudden shift without pivot); and sequential modulation (a pattern moved diatonically or chromatically). Closely related keys (neighbours on the circle of 5ths) are the most frequent destinations: the dominant, subdominant, and their relative minors. Identification of the pivot and confirmation of the new key via a cadence are essential for WJEC exam responses.
转调是在乐曲内部改变调性的过程。常用技巧包括：共同和弦转调（在旧调与新调中均为自然音和弦，用双重罗马数字分析，如 C 大调中 F 和弦是 C 的 IV 也是 a 小调的 VI）；直接转调（无共同和弦的突然转换）；模进转调（旋律模式作自然或半音移位）。近关系调（五度圈上相邻的调）是最常见的转调目标：属调、下属调及其关系小调。识别共同和弦以及通过终止式确认新调是 WJEC 考试答题的核心能力。
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