📚 Year 12 Edexcel Music: Formula & Theorem Quick Reference Handbook | Year 12 Edexcel 音乐：公式定理速查手册
Mastering music theory requires a firm grasp of its underlying 'formulas'—the rules for intervals, chord construction, cadences, and harmonic progressions. This quick reference handbook compiles the essential theorems and formulas you need for the Year 12 Edexcel Music course, enabling efficient revision and score analysis.
掌握音乐理论需要透彻理解其底层“公式”——音程构成、和弦构建、终止式以及和声进行的各项规则。本速查手册汇编了 Year 12 Edexcel 音乐课程必备的核心理论与公式，帮助你高效复习、精准分析乐谱。
1. Intervals & Semitone Formulas | 音程与半音公式
An interval is the distance between two pitches, measured in semitones. The quality (perfect, major, minor, augmented, diminished) and the number (2nd, 3rd, etc.) define each interval precisely. For instance, a perfect fifth spans 7 semitones, while a major third spans 4 semitones.
音程是两个音高之间的距离，以半音为单位，由音程的性质（纯、大、小、增、减）和度数（二度、三度等）共同定义。例如，纯五度包含7个半音，大三度包含4个半音。
| Interval Name | Semitones | 中文名称 |
|---|---|---|
| Perfect Unison | 0 | 纯一度 |
| Minor 2nd | 1 | 小二度 |
| Major 2nd | 2 | 大二度 |
| Minor 3rd | 3 | 小三度 |
| Major 3rd | 4 | 大三度 |
| Perfect 4th | 5 | 纯四度 |
| Augmented 4th/Diminished 5th | 6 | 增四度/减五度 |
| Perfect 5th | 7 | 纯五度 |
| Minor 6th | 8 | 小六度 |
| Major 6th | 9 | 大六度 |
| Minor 7th | 10 | 小七度 |
| Major 7th | 11 | 大七度 |
| Perfect Octave | 12 | 纯八度 |
When inverting intervals, the sum of the interval numbers always equals 9 (a 3rd inverts to a 6th, a 4th to a 5th). Perfect intervals remain perfect, major becomes minor, augmented becomes diminished, and vice versa.
转位音程时，原音程度数与转位音程度数之和恒为9（三度转位为六度，四度转位为五度）。纯音程转位后仍为纯，大音程转位为小，增音程转位为减，反之亦然。
2. Scales & Key Signatures | 音阶与调号
The major scale follows a fixed pattern of tones (T) and semitones (S): T, T, S, T, T, T, S. Minor scales come in three forms: natural, harmonic (raised 7th), and melodic (raised 6th and 7th ascending, natural descending).
大调音阶遵循固定的全音与半音模式：全、全、半、全、全、全、半。小调音阶有三种形式：自然小调、和声小调（升高第7级）和旋律小调（上行升高第6、7级，下行还原为自然）。
| Key Signature | Major Key | Relative Minor | 中文调名 |
|---|---|---|---|
| 0 sharps/flats | C major | A minor | C大调 / a小调 |
| 1 sharp | G major | E minor | G大调 / e小调 |
| 2 sharps | D major | B minor | D大调 / b小调 |
| 3 sharps | A major | F# minor | A大调 / 升f小调 |
| 4 sharps | E major | C# minor | E大调 / 升c小调 |
| 5 sharps | B major | G# minor | B大调 / 升g小调 |
| 1 flat | F major | D minor | F大调 / d小调 |
| 2 flats | B♭ major | G minor | 降B大调 / g小调 |
| 3 flats | E♭ major | C minor | 降E大调 / c小调 |
| 4 flats | A♭ major | F minor | 降A大调 / f小调 |
The circle of fifths arranges keys by ascending perfect fifth for sharps (G-D-A-E-B) and descending perfect fifth for flats (F-B♭-E♭-A♭). Relative minors share the same key signature and are found a minor third below the major tonic.
五度圈以纯五度上行排列升号调（G-D-A-E-B），纯五度下行排列降号调（F-降B-降E-降A）。关系小调共享相同调号，其主音在大调主音下方小三度。
3. Triads & Chord Formulas | 三和弦公式
A triad is a three-note chord built by stacking thirds above a root. The formula for a major triad is root + 4 semitones (major 3rd) + 3 semitones (minor 3rd). A minor triad flips the thirds: root + 3 semitones + 4 semitones.
三和弦是由根音上方三度叠置构成的三个音。大三和弦的公式为根音+4个半音（大三度）+3个半音（小三度）。小三和弦则为根音+3个半音+4个半音。
| Triad Type | Semitone Stack | Roman Numeral | 中文 |
|---|---|---|---|
| Major | 4 + 3 | I, IV, V (uppercase) | 大三和弦 |
| Minor | 3 + 4 | ii, iii, vi (lowercase) | 小三和弦 |
| Diminished | 3 + 3 | vii° | 减三和弦 |
| Augmented | 4 + 4 | III⁺ (rare in major) | 增三和弦 |
In Roman numeral analysis, uppercase numerals (I, IV, V) denote major triads, lowercase (ii, iii, vi) denote minor, and the diminished triad is marked with a small degree sign (vii°). An augmented triad uses a superscript plus (III⁺).
在和声标记中，大写罗马数字（I, IV, V）表示大三和弦，小写（ii, iii, vi）表示小三和弦，减三和弦在数字后加小度数号（vii°），增三和弦加上标加号（III⁺）。
4. Chord Inversions & Figured Bass | 和弦转位与数字低音
An inversion is determined by which chord member is in the bass. Root position places the root at the bottom; first inversion has the 3rd as the lowest note; second inversion uses the 5th. Figured bass provides a shorthand: root position (⁵⁄₃, often omitted), first inversion (⁶⁄₃, abbreviated to ⁶), second inversion (⁶⁄₄).
转位由最低音决定。原位和弦以根音为低音，第一转位以三音为低音，第二转位以五音为低音。数字低音符号为：原位 ⁵⁄₃（常省略），第一转位 ⁶⁄₃（简写为 ⁶），第二转位 ⁶⁄₄。
| C major Triad | Bass Note | Figured Bass | 中文 |
|---|---|---|---|
| Root (C–E–G) | C | (⁵⁄₃) | 原位 |
| 1st inversion (E–G–C) | E | ⁶ | 第一转位 |
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