📚 A-Level WJEC Music: Quick Reference Guide to Formulas and Rules | A-Level WJEC 音乐：公式定理速查手册
This quick reference guide collects the essential musical formulas, rules, and theoretical principles required for the WJEC A-Level Music specification. From interval inversion to modulation shortcuts, each section presents key concepts in a concise, exam-friendly format. Use it to reinforce your appraising skills and support informed composition and performance decisions.
本速查手册汇集了 WJEC A-Level 音乐课程所需的核心音乐公式、规则与理论原则。从音程转位到转调捷径，每一节都以简明、适合考试复习的形式呈现关键概念。借助它强化你的听辨分析能力，同时为作曲与演奏决策提供理论支持。
1. Interval Inversion Formulas | 音程转位公式
To find the inversion of any interval, subtract the interval number from 9 and flip the quality: major becomes minor, minor becomes major, perfect stays perfect, augmented becomes diminished, and diminished becomes augmented.
要找出任何音程的转位，用 9 减去音程度数，并将性质反转：大音程变为小音程，小变大，纯音程保持纯，增音程变为减，减变为增。
For example: a Major 3rd (M3) inverts to a minor 6th (m6). A Perfect 4th (P4) inverts to a Perfect 5th (P5). An Augmented 4th (A4/dim5) inverts to a diminished 5th (d5/A4).
例如：大三度（M3）转位后为小六度（m6）；纯四度（P4）转位为纯五度（P5）；增四度（A4/减五度）转位为减五度（d5/增四度）。
The sum of the original interval number and its inversion always equals 9. Compound intervals (greater than an octave) should first be reduced to simple intervals before applying the formula.
原音程度数与转位音程度数之和恒为 9。复音程（大于八度）需先简化为单音程，再套用公式。
2. Chord Construction Formulas (Triads and Sevenths) | 三和弦与七和弦构建公式
A major triad consists of a root, a major third (4 semitones) and a perfect fifth (7 semitones). A minor triad: root, minor third (3 semitones), perfect fifth. A diminished triad: root, minor third, diminished fifth (6 semitones). An augmented triad: root, major third, augmented fifth (8 semitones).
大三和弦由根音、大三度（4 个半音）和纯五度（7 个半音）构成。小三和弦：根音、小三度（3 个半音）、纯五度。减三和弦：根音、小三度、减五度（6 个半音）。增三和弦：根音、大三度、增五度（8 个半音）。
For seventh chords, add the appropriate 7th above the root: Major 7th (11 semitones) for a major-major seventh; minor 7th (10 semitones) for a dominant seventh; minor 7th on a minor triad gives a minor seventh; diminished 7th (9 semitones) on a diminished triad yields a fully diminished seventh.
构建七和弦时，在根音上方加上相应的七度音：大大七和弦加大七度（11 个半音）；属七和弦加小七度（10 个半音）；小三和弦加小七度为小七和弦；减三和弦加减七度（9 个半音）为减减七和弦。
Dominant 7th = Root + 4 + 3 + 3 (semitones) → R, M3, P5, m7
属七和弦 = 根音 + 4 + 3 + 3（半音数）→ 根、大三度、纯五度、小七度
3. Key Signatures and the Circle of Fifths | 调号与五度循环圈
The order of sharps in key signatures is F♯ C♯ G♯ D♯ A♯ E♯ B♯. The order of flats is B♭ E♭ A♭ D♭ G♭ C♭ F♭. For major keys, the tonic is a semitone above the last sharp (e.g. F♯ major has six sharps: F♯ C♯ G♯ D♯ A♯ E♯ → tonic F♯). For flat keys, the tonic is the second-to-last flat (e.g. A♭ major: B♭ E♭ A♭ D♭ → tonic A♭).
调号中升号的顺序为 F♯ C♯ G♯ D♯ A♯ E♯ B♯。降号顺序为 B♭ E♭ A♭ D♭ G♭ C♭ F♭。找出大调主音：最后一个升号上方小二度即为主音（如 F♯ 大调有六个升号：F♯ C♯ G♯ D♯ A♯ E♯ → 主音 F♯）；降号调中，倒数第二个降号即为主音（如 A♭ 大调：B♭ E♭ A♭ D♭ → 主音 A♭）。
Relative minors share the same key signature; the tonic is a minor third below the major tonic (e.g. A minor is the relative of C major). Moving clockwise around the circle of fifths adds one sharp (or removes one flat); moving anticlockwise adds one flat (or removes one sharp).
关系小调共用同一调号，主音比大调主音低小三度（如 a 小调是 C 大调的关系调）。沿五度循环圈顺时针方向每步增加一个升号（或去掉一个降号），逆时针方向每步增加一个降号（或去掉一个升号）。
4. Scale Formulas (Major and Minor Modes) | 大调和小调音阶公式
The major scale follows the pattern of whole and half steps: W‑W‑H‑W‑W‑W‑H. In semitones: 2‑2‑1‑2‑2‑2‑1.
大调音阶遵循全音和半音的模式：全‑全‑半‑全‑全‑全‑半。用半音数表示：2‑2‑1‑2‑2‑2‑1。
Natural minor: W‑H‑W‑W‑H‑W‑W (2‑1‑2‑2‑1‑2‑2). Harmonic minor raises the 7th degree: W‑H‑W‑W‑H‑T‑ where T = augmented 2nd, 3 semitones). Melodic minor (ascending) raises the 6th and 7th: W‑H‑W‑W‑W‑W‑H; descending is the same as natural minor.
自然小调：全‑半‑全‑全‑半‑全‑全（2‑1‑2‑2‑1‑2‑2）。和声小调升高第 VII 级：全‑半‑全‑全‑半‑增二度‑半（增二度为 3 个半音）。旋律小调上行升高第 VI、第 VII 级：全‑半‑全‑全‑全‑全‑半；下行与自然小调相同。
The church modes can all be derived from the white-note scale: Dorian is 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 is natural minor; Ionian is major.
教会调式均源自白键音阶：多利亚调式为全‑半‑全‑全‑全‑半‑全；弗里几亚为半‑全‑全‑全‑半‑全‑全；利底亚为全‑全‑全‑半‑全‑全‑半；混合利底亚为全‑全‑半‑全‑全‑半‑全；爱奥尼亚即自然小调；伊奥尼亚即大调。
5. Cadence Identification Rules | 终止式识别规则
A perfect cadence (V–I or V–i) sounds final and conclusive. In a major key, both chords are major; in a minor key, V is always major (with raised leading note), I is minor. An imperfect cadence ends on V (I–V, ii–V, IV–V) and feels unfinished.
正格终止（V–I 或 V–i）听感完满、具有结束感。大调中两个和弦均为大三和弦；小调中 V 必须为大三和弦（升高导音），I 为小三和弦。半终止结束在 V 级（I–V、ii–V、IV–V），听感未完成。
A plagal cadence (IV–I) is the 'Amen' cadence; both chords are major in a major key, minor in a minor key. An interrupted cadence (V–vi in major, V–VI in minor) creates a surprise by avoiding the tonic.
变格终止（IV–I）即“阿门”终止；大调中两个和弦均为大三和弦，小调中均为小三和弦。阻碍终止（大调 V–vi，小调 V–VI）通过回避主和弦造成意外感。
Always check the bass line: perfect and plagal cadences move to the tonic in the bass; imperfect cadences end on the dominant bass; interrupted cadences end on the submediant bass.
务必检查低音线条：正格与变格终止的低音进行到主音；半终止的低音结束在属音；阻碍终止的低音结束在下中音。
6. Roman Numeral Analysis Convention | 罗马数字分析惯例
Use uppercase Roman numerals for major chords (I, IV, V) and lowercase for minor (ii, iii, vi). Diminished chords use lowercase with a circle: vii°. Augmented chords use uppercase with a plus: III⁺. In minor keys, the natural form of chords is assumed unless otherwise indicated; raised leading notes produce a major V or diminished vii°.
大写罗马数字表示大三和弦（I、IV、V），小写表示小三和弦（ii、iii、vi）。减三和弦用小写加圆圈：vii°；增三和弦用大写加加号：III⁺。在分析小调时，若无特别说明，默认采用自然小调的和弦结构；升高导音则产生大三和弦的 V 或减三和弦的 vii°。
Inversion is shown with figured bass numerals: root position has no added number; first inversion uses 6 (or 6/3); second inversion uses 6/4. Seventh chords add the relevant interval numbers: 7 (root), 6/5 (first), 4/3 (second), 4/2 (third).
转位用数字低音标记：原位不另加数字；第一转位用 6（或 6/3）；第二转位用 6/4。七和弦在数字上添加相应音程：原位 7；第一转位 6/5；第二转位 4/3；第三转位 4/2。
7. Voice Leading Dos and Don'ts | 声部进行准则
Move each voice by the smallest possible interval; retain common tones between chords where possible. Avoid parallel perfect fifths and octaves between any pair of voices. Avoid exposed (hidden) fifths and octaves when the soprano leaps and the bass moves in similar motion to a perfect interval.
每个声部应尽量作最小音程的移动；尽可能保留两和弦之间的共同音。任何两个声部之间禁止平行纯五度和平行八度。当女高音跳进且低音作同向进行到达纯音程时，应避免隐伏五度与隐伏八度。
The leading note (7th degree) must rise to the tonic when in an outer voice. Avoid augmented intervals melodically. In root-position chord progressions, avoid crossing voices and maintain a standard spacing (no more than an octave between tenor and alto, alto and soprano).
导音（第 VII 级）在外声部时必须上行解决到主音。旋律中避免增音程。在原位和弦进行中，避免声部交错，并保持声部之间的规范距离（男高音与女低音之间、女低音与女高音之间不超过八度）。
8. Figured Bass Quick Reference | 数字低音速查
| Figure | Meaning |
|---|---|
| 5/3 (or no figure) | Root-position triad |
| 6 (or 6/3) | First-inversion triad |
| 6/4 | Second-inversion triad |
| 7 | Root-position seventh chord |
| 6/5 | First-inversion seventh |
| 4/3 | Second-inversion seventh |
| 4/2 (or 2) | Third-inversion seventh |
Accidentals next to a figure apply to the interval above the bass note. A slash through a figure indicates that the note is raised (sharpened); a backward slash is sometimes used for a flat. A figure '5' with a slash means an augmented fifth.
数字旁边的临时记号指低音上方的该音程音需升降。数字上的一撇表示该音升高（升半音）；有时用反向撇号表示降半音。数字“5”加撇号表示增五度。
9. Harmonic Progression Shortcuts | 和声进行捷径
The most common root movements by falling fifth (or rising fourth) are the strongest progressions: I–IV–vii°–iii–vi–ii–V–I. The circle progression follows this sequence. Also effective are root movements by falling third (I–vi, IV–ii) and rising second (IV–V, V–vi).
最常见的根音进行是下行五度（或上行四度），此类进行和声动力最强：I–IV–vii°–iii–vi–ii–V–I。循环进行即按照此序列展开。此外，根音下行三度（I–vi、IV–ii）和上行二度（IV–V、V–vi）也非常有效。
Avoid root movements by falling second (except V–vi for interrupted cadences) unless prepared by a sequential pattern. The leading-tone triad (vii°) usually resolves to I; the dominant seventh (V⁷) resolves to I or vi. In minor, the subtonic harmony (♭VII) often moves to III or iv.
除非是模进式进行，一般应避免根音下行二度的进行（V–vi 的阻碍终止除外）。导三和弦（vii°）通常解决到 I；属七和弦（V⁷）解决到 I 或 vi。在小调中，下主音和弦（♭VII）常进行到 III 或 iv。
10. Non‑Chord Tone Formulas | 和弦外音公式
A passing tone (PT) is approached by step and left by step in the same direction, filling the gap between two chord tones usually a third apart. A neighbour tone (NT) moves by step away from a chord tone and returns to the same chord tone.
经过音（PT）以级进进入，以同方向级进离开，填补两个通常相距三度的和弦音之间的空隙。辅助音（NT）从和弦音出发级进，再级进返回同一和弦音。
An appoggiatura is approached by leap and resolved by step (usually downward). An escape tone (échappée) is approached by step and resolved by leap in the opposite direction. A suspension is prepared by a tied or repeated note, then resolved down by step; its three stages are preparation, suspension, resolution.
倚音以跳进进入，级进解决（通常下行）。规避音（échappée）以级进进入，反向跳进离开。延留音预先在同一声部中准备（同音连线或重复），然后下行级进解决；其三个阶段为：预备、延留、解决。
The formula for a suspension is labelled by the intervals above the bass: 4‑3 suspension, 7‑6, 9‑8, 2‑3 (bass suspension). A retardation is a suspension that resolves upward.
延留音按低音上方的音程标记：4‑3 延留、7‑6 延留、9‑8 延留、2‑3 延留（低音延留）。上行解决的延留音称为上行留音。
11. Modulation Cheat Sheet | 转调速查
at is diatonic to both the home key and the destination key. Common pivot chords: home key's ii = destination's vi; home key's IV = destination's I; home key's vi = destination's ii. In moving to the dominant, home key I = destination IV; ii = V; IV = ♭VII; vi = ii.
最快捷的共同和弦转调使用在原调与新调中均为自然音和弦的共同和弦。常见共同和弦：原调的 ii = 新调的 vi；原调的 IV = 新调的 I；原调的 vi = 新调的 ii。转到属调时，原调 I = 新调 IV；ii = V；IV = ♭VII；vi = ii。
Chromatic modulation often uses a dominant seventh or diminished seventh as a pivot enharmonically. The German augmented sixth chord (Gr⁺⁶) resolves to a dominant seventh chord, facilitating abrupt modulation.
半音转调常利用属七和弦或减七和弦作等音转调。德国增六和弦（Gr⁺⁶）可等音转换为属七和弦，从而实现突转。
A direct modulation (phrase modulation) occurs without a pivot, typically at a phrase boundary. Always confirm the new key with a perfect cadence.
直接转调（乐句转调）在无共同和弦的情况下直接进入新调，通常出现在乐句交界处。转调后务必用正格终止明确新调性。
12. Rhythm and Metre Formulas | 节奏与节拍公式
uadruple. Compound time: the beat divides into three equal parts; top number is typically 6, 9, or 12. To find the number of beats in compound metre, divide the top number by 3.
单拍子：每拍可分为两个等份。上方数字表示小节拍数：2 为二拍子，3 为三拍子，4 为四拍子。复拍子：每拍可分为三个等份，上方数字通常为 6、9 或 12。计算复拍子的拍数，将上方数字除以 3。
Regular metres: 2/4, 3/4, 4/4 (simple); 6/8, 9/8, 12/8 (compound). Asymmetrical metres: 5/8, 7/8, 11/8 etc., where beats are of unequal length (combinations of 2+3 or 3+2 etc.).
常见节拍：2/4、3/4、4/4（单拍子）；6/8、9/8、12/8（复拍子）。不对称节拍如 5/8、7/8、11/8 等，其拍点为不等长组合（如 2+3 或 3+2 等）。
Tempo markings are given in beats per minute (BPM). To calculate the duration of a bar, divide 60 by BPM and multiply by the number of beats in the bar. For compound time, it is often more practical to use dotted-crotchet BPM.
速度记号以每分钟拍数（BPM）表示。计算一小节的时长：将 60 除以 BPM，再乘以该小节的拍数。复拍子常用附点四分音符的 BPM 更为方便。
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