📚 AS CCEA Music: Quick-Reference Formula & Theorem Handbook | AS CCEA 音乐：公式定理速查手册
Music theory at AS level is not merely about performance or historical context—it relies on a web of precise formulas, rules, and structural principles that underpin composition and analysis. This quick-reference handbook collects the essential 'formulas' and 'theorems' you need to master for the CCEA AS Music examination, from scale construction and chord building to cadences and form.
AS 阶段的音乐理论不仅关乎表演或历史背景——它依赖于一套精确的公式、规则和结构原则，支撑着作曲与分析。这本速查手册汇集了你为 CCEA AS 音乐考试必须掌握的核心“公式”与“定理”，涵盖音阶构建、和弦构成直至终止式与曲式。
1. Scale Formulas | 音阶公式
Major Scale: The ascending pattern in semitones is 2-2-1-2-2-2-1, or whole–whole–half–whole–whole–whole–half (W-W-H-W-W-W-H).
大调音阶：上行半音模式为 2-2-1-2-2-2-1，即全-全-半-全-全-全-半（W-W-H-W-W-W-H）。
Natural Minor Scale: The semitone pattern (derived from the Aeolian mode) is 2-1-2-2-1-2-2 (W-H-W-W-H-W-W).
自然小调音阶：半音模式（源自爱奥利亚调式）为 2-1-2-2-1-2-2（W-H-W-W-H-W-W）。
Harmonic Minor Scale: The semitone pattern is 2-1-2-2-1-3-1. The characteristic augmented 2nd (3 semitones) appears between the 6th and 7th degrees.
和声小调音阶：半音模式为 2-1-2-2-1-3-1。特有的增二度（3 个半音）出现在第六与第七级之间。
Melodic Minor Scale (Ascending): 2-1-2-2-2-2-1. The descending form reverts to the natural minor pattern.
旋律小调音阶（上行）：2-1-2-2-2-2-1。下行时回归自然小调模式。
Pentatonic Scales: Major pentatonic uses degrees 1-2-3-5-6 of the major scale (semitone gap formula: 2-2-3-2-3). Minor pentatonic uses degrees 1-♭3-4-5-♭7 (3-2-2-3-2).
五声音阶：大调五声使用大调的第 1-2-3-5-6 级（半音间隔公式：2-2-3-2-3）。小调五声使用 1-♭3-4-5-♭7 级（3-2-2-3-2）。
Blues Scale: Adds a flattened 5th to the minor pentatonic, producing a 6-note scale: 1-♭3-4-♭5-5-♭7.
蓝调音阶：在小调五声音阶中加入降五级，形成六声音阶：1-♭3-4-♭5-5-♭7。
2. Interval Formulas | 音程公式
| Interval (English) | 音程 (中文) | Semitones | Example from C |
|---|---|---|---|
| Perfect Unison | 纯一度 | 0 | C - C |
| Minor 2nd | 小二度 | 1 | C - D♭ |
| Major 2nd | 大二度 | 2 | C - D |
| Minor 3rd | 小三度 | 3 | C - E♭ |
| Major 3rd | 大三度 | 4 | C - E |
| Perfect 4th | 纯四度 | 5 | C - F |
| Augmented 4th / Diminished 5th | 增四度 / 减五度 | 6 | C - F♯ / G♭ |
| Perfect 5th | 纯五度 | 7 | C - G |
| Minor 6th | 小六度 | 8 | C - A♭ |
| Major 6th | 大六度 | 9 | C - A |
| Minor 7th | 小七度 | 10 | C - B♭ |
| Major 7th | 大七度 | 11 | C - B |
| Perfect Octave | 纯八度 | 12 | C - C' |
Interval Inversion Rule: minor; perfect remains perfect; augmented becomes diminished. Sum of interval numbers = 9.
音程转位规则：大音程转位后变为小音程；纯音程保持为纯；增音程变为减音程。原位与转位音程的度数之和为 9。
3. Chord Construction Formulas | 和弦构成公式
| Chord Type | 和弦类型 | Semitone Stack (from root) | Example (root C) |
|---|---|---|---|
| Major Triad | 大三和弦 | R + 4 + 3 | C-E-G |
| Minor Triad | 小三和弦 | R + 3 + 4 | C-E♭-G |
| Augmented Triad | 增三和弦 | R + 4 + 4 | C-E-G♯ |
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