📚 A-Level Cambridge Music: Formula & Theorem Quick Reference Manual | A-Level 剑桥音乐：公式定理速查手册
This quick reference manual compiles essential musical formulas, rules, and theoretical “theorems” for the A-Level Cambridge Music syllabus. It is designed to help you rapidly recall interval structures, scale constructions, chord recipes, cadential patterns, voice leading rules, figured bass shortcuts, rhythmic divisions, ornament realisations, formal terminology, melodic decorations, and transposition methods – all in a clear bilingual format for effective exam revision.
本速查手册汇集了 A-Level 剑桥音乐课程中必备的音乐公式、规则与理论“定理”。旨在帮助你快速回顾音程构成、音阶构建、和弦配方、终止模式、声部进行法则、数字低音简写、节奏划分、装饰音演绎、曲式术语、旋律装饰音以及移调方法——全部以清晰的双语形式呈现，助力高效备考。
1. Intervals: Semitone Recipes | 音程：半音公式
Every interval can be defined by its number of semitones. The table below shows the core intervals within an octave, using the short-cut: perfect and major intervals are the starting points; minor intervals reduce a major by one semitone; diminished reduces a perfect or minor by one semitone; augmented increases a perfect or major by one semitone.
每个音程都可以用其半音数来定义。下表列出了八度以内的基本音程，记忆诀窍为：纯音程和大音程是出发点；小音程由大音程减少一个半音得到；减音程由纯或小音程再减半音；增音程由纯或大音程增加半音得到。
| Interval / 音程 | Semitones / 半音数 |
|---|---|
| Perfect unison / 纯一度 | 0 |
| Minor 2nd / 小二度 | 1 |
| Major 2nd / 大二度 | 2 |
| Minor 3rd / 小三度 | 3 |
| Major 3rd / 大三度 | 4 |
| Perfect 4th / 纯四度 | 5 |
| Augmented 4th / Diminished 5th (Tritone) / 增四度/减五度 (三全音) | 6 |
| Perfect 5th / 纯五度 | 7 |
| Minor 6th / 小六度 | 8 |
| Major 6th / 大六度 | 9 |
| Minor 7th / 小七度 | 10 |
| Major 7th / 大七度 | 11 |
| Perfect octave / 纯八度 | 12 |
When the interval quality changes: Augmented = major/perfect + 1 semitone; Diminished = minor/perfect − 1 semitone. Compound intervals add 7 to the simple interval number and 12 semitones.
当音程性质改变时：增＝大/纯 + 1个半音；减＝小/纯 − 1个半音。复音程只需将单音程数加7、半音数加12即可。
2. Scales: Construction Rules | 音阶：构成规则
The major scale follows the pattern of whole and half steps: Tone – Tone – Semitone – Tone – Tone – Tone – Semitone (TTSTTTS). The natural minor scale is T – S – T – T – S – T – T. For harmonic minor, raise the 7th degree by a semitone; for melodic minor, raise the 6th and 7th ascending, revert to natural minor descending.
大调音阶遵循全音和半音的模式：全–全–半–全–全–全–半（TTSTTTS）。自然小调为全–半–全–全–半–全–全。和声小调升高第VII级半音；旋律小调上行升高第VI、VII级，下行还原为自然小调。
| Scale Type / 音阶类型 | Formula (in semitones from tonic) / 公式 (从主音起半音数) |
|---|---|
| Major / 大调 | 0, 2, 4, 5, 7, 9, 11, 12 |
| Natural Minor / 自然小调 | 0, 2, 3, 5, 7, 8, 10, 12 |
| Harmonic Minor / 和声小调 | 0, 2, 3, 5, 7, 8, 11, 12 |
| Melodic Minor (ascending) / 旋律小调(上行) | 0, 2, 3, 5, 7, 9, 11, 12 |
| Chromatic / 半音阶 | All 12 semitones: 0,1,2,3,…,12 |
| Whole-tone / 全音阶 | 0, 2, 4, 6, 8, 10, 12 |
Key signatures follow the circle of fifths. For sharps: Father Charles Goes Down And Ends Battle (F♯, C♯, G♯, D♯, A♯, E♯, B♯). The major key is a semitone above the last sharp. For flats: Battle Ends And Down Goes Charles Father (B♭, E♭, A♭, D♭, G♭, C♭, F♭); the major key is the second-to-last flat. Minor keys share the same key signature (relative minor: 3 semitones below major).
调号遵循五度循环。升号顺序：F♯, C♯, G♯, D♯, A♯, E♯, B♯。大调主音为最后一个升号上方半音。降号顺序：B♭, E♭, A♭, D♭, G♭, C♭, F♭；大调主音为倒数第二个降号。关系小调使用相同调号，主音在大调主音下方小三度(3个半音)。
3. Chords: Triad and Seventh Chord Recipes | 和弦：三和弦与七和弦配方
Triads are stacks of two thirds. Their quality is determined by the sequence of major thirds (4 semitones) and minor thirds (3 semitones). The outer perfect 5th is 7 semitones; an augmented 5th is 8 semitones; a diminished 5th is 6 semitones.
三和弦由两个三度音程叠置而成。其性质由大三度(4半音)和小三度(3半音)的排列决定。外框纯五度为7半音；增五度为8半音；减五度为6半音。
| Chord / 和弦 | Stack (bottom to top) / 叠置 (由下至上) | Symbol example / 标记示例 |
|---|---|---|
| Major / 大三和弦 | Major 3rd + minor 3rd (4 + 3 semitones) | C, Cmaj |
| Minor / 小三和弦 | Minor 3rd + major 3rd (3 + 4 semitones) | Cm, c min |
| Diminished / 减三和弦 | Minor 3rd + minor 3rd (3 + 3 semitones) | C°, c dim |
| Augmented / 增三和弦 | Major 3rd + major 3rd (4 + 4 semitones) | C+, c aug |
Seventh chords add a third above the triad. Common formulas: Dominant 7th = major triad + minor 7th (4+3+3 semitones). Major 7th = major triad + major 7th (4+3+4). Minor 7th = minor triad + minor 7th (3+4+3). Half-diminished 7th = diminished triad + major 7th (3+3+4). Diminished 7th = diminished triad + diminished 7th (3+3+3).
七和弦在三和弦上方再加一个三度。常见构成：属七和弦=大三和弦+小七度(4+3+3半音)；大七和弦=大三和弦+大七度(4+3+4)；小七和弦=小三和弦+小七度(3+4+3)；半减七和弦=减三和弦+大七度(3+3+4)；减七和弦=减三和弦+减七度(3+3+3)。
4. Cadences: Harmonic Formulas | 终止式：和声公式
Cadences are the punctuation of music. The four principal cadential formulas in common-practice harmony are defined by the final two chords. They are always understood in terms of scale degrees (roman numerals) rather than specific pitch names.
终止式是音乐的“标点符号”。在共性实践和声中，四种基本终止公式由最后两个和弦定义，始终用音级（罗马数字）来表示。
| Cadence / 终止式 | Chord progression / 和弦进行 | Effect / 效果 |
|---|---|---|
| Perfect / 正格终止 | V – I (or V⁷ – I) | Strong, conclusive / 强烈、完结 |
| Plagal / 变格终止 | IV – I | Amen, softer close / “阿门”、柔和收束 |
| Imperfect / 不完全终止 | I – V, ii – V, IV – V, etc. | Temporary pause, asks for continuation / 短暂停顿、期待继续 |
| Interrupted / Deceptive / 阻碍终止 | V – vi (sometimes V – IV⁶) | Surprise, avoids expected tonic / 意外、避开预期主和弦 |
In analysis, always check for the leading note rising to the tonic in the V–I progression, and for the bass movement (stepwise in plagal, leap of a 4th/5th in perfect). The dominant seventh chord V⁷ strengthens the perfect cadence.
分析时，始终留意V–I进行中导音上行至主音，以及低音进行（变格终止为级进，正格终止为四/五度跳进）。属七和弦V⁷会加强正格终止的效果。
5. Harmonic Progressions: Common Patterns | 和声进行：常见模式
Many classical and popular pieces are built from a handful of functional progressions. The most fundamental is the circle-of-fifths sequence: iii – vi – ii – V – I. Other standard formulas include the “50s progression” and the “Pachelbel progression”.
许多古典与流行作品由少数几个功能性进行构建。最基础的是五度循环模进：iii – vi – ii – V – I。其他标准模式包括“50年代进行”和“帕赫贝尔进行”。
| Pattern / 模式 | Roman numerals (Major key) / 罗马数字 (大调) | Typical function / 常见功能 |
|---|---|---|
| Authentic / 正格进行 | I – IV – V – I | Complete statement / 完整陈述 |
| Pachelbel / 帕赫贝尔 | I – V – vi – iii – IV – I – IV – V | Gentle, stepwise bass / 温和低音级进 |
| 50s progression / 50年代进行 | I – vi – IV – V | Doo-wop, pop ballad / 嘟•喔普、流行情歌 |
| Jazz ii-V-I / 爵士 ii-V-I | ii⁷ – V⁷ – I△⁷ | Essential turnaround / 关键回转 |
| Descending tetrachord / 下行四音列 | I – V⁶ – vi – V or I – V⁶ – IV – V | Lament bass / 悲歌低音 |
When harmonising a melody, favour root movement by step (especially ii–V) or by fifths/fourths. Avoid weak progressions like V–IV unless part of a sequence.
为旋律配和声时，优先选择根音二度（尤其是ii–V）或四五度进行。除非作为模进的一环，避免V–IV这类削弱功能性的进行。
6. Voice Leading Rules | 声部进行规则
Smooth voice leading is the art of connecting chords with minimal movement. The ‘theorems’ of strict counterpoint and four-part harmony include prohibitions and preferred motions.
平稳的声部进行是以最小移动连接和弦的艺术。严格的对应法与四部和声中的“定理”包含禁止项与优先运动。
- Parallel 5ths and octaves: prohibited. Avoid two voices moving in perfect 5ths or octaves in similar motion. / 平行五八度：禁止。两声部同向运动形成纯五度或纯八度必须避免。
- Contrary and oblique motion preferred. When the bass leaps, upper voices often move by step in opposite direction. / 优先反向和斜向运动。当低音跳进时，上方声部常反向级进。
- Leading note resolution: The 7th degree (leading note) in major/minor keys resolves up by step to the tonic, especially when in an outer voice. / Published by TutorHao | A-Level 音乐 Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导