📚 Year 10 OCR Music: Formula & Theorem Quick Reference Handbook | Year 10 OCR 音乐：公式定理速查手册
Music, like mathematics, is built on precise patterns and logical structures. This quick reference handbook compiles the essential 'formulas' and 'theorems' you need for the Year 10 OCR Music course – from interval calculations and scale constructions to chord building and cadence patterns. Mastering these building blocks will sharpen your analysis, improve your composition, and boost your confidence in the listening exam.
音乐，就像数学一样，建立在精确的模式和逻辑结构之上。这本速查手册汇集了 Year 10 OCR 音乐课程所需的基本“公式”和“定理”——从音程计算和音阶构成，到和弦构建和终止式模式。掌握这些构建模块将提升你的分析能力、改善你的作曲，并在听力考试中增强你的信心。
1. The Interval Formula: Counting Semitones | 音程公式：计算半音
rmine its quality (major, minor, perfect, augmented, diminished) using the semitone count. For example, a major third = 4 semitones; a perfect fifth = 7 semitones; an octave = 12 semitones.
每个音程都由两个音之间的半音数量来定义。先数字母名称（例如 C 到 E 是三度），然后通过半音数确定其性质（大、小、纯、增、减）。例如，大三度 = 4 个半音；纯五度 = 7 个半音；八度 = 12 个半音。
The table below shows the standard interval formulas. Memorising these will help you identify intervals quickly in scores and audio excerpts.
下表展示了标准音程公式。熟记这些将帮助你在乐谱和音频片段中快速识别音程。
| 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♯ / G♭ |
| 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 |
| Octave | 12 | C – C (higher) |
Interval inversion theorem: the sum of an interval' 9); a fourth inverts to a fifth. Major becomes minor, augmented becomes diminished, and perfect stays perfect.
音程转位定理：音程的度数与它的转位度数之和恒等于 9。三度转位成六度（3+6=9）；四度转位成五度。大音程变成小音程，增音程变成减音程，纯音程保持纯。
2. Major Scale Formula | 大调音阶公式
A major scale follows a fixed pattern of tones (T) and semitones (S): T-T-S-T-T-T-S. In whole steps (W) and half steps (H), it is W-W-H-W-W-W-H. This formula works from any starting note. For example, C major: C (T) D (T) E (S) F (T) G (T) A (T) B (S) C.
大调音阶遵循固定的全音（T）和半音（S）模式：T-T-S-T-T-T-S。用全步（W）和半步（H）表示，即为 W-W-H-W-W-W-H。这个公式适用于任何一个起始音。例如，C 大调：C (T) D (T) E (S) F (T) G (T) A (T) B (S) C。
You can derive any major key signature by applying the formula without worrying about accidentals until the end. This 'theorem' guarantees the correct diatonic notes.
你可以通过应用该公式推导出任何大调的调号，而不必担心临时变音记号，直到最后。这个“定理”保证了正确的自然音阶音符。
The following table shows how a few major keys are built using the W-W-H-W-W-W-H formula:
下表展示了若干大调如何通过 W-W-H-W-W-W-H 公式构建：
| Starting Note | Application of W-W-H-W-W-W-H | Resulting Key Signature |
|---|---|---|
| G | G-A-B
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