📚 A-Level AQA Music: Quick Reference Handbook of Formulas and Theorems | A-Level AQA 音乐：公式定理速查手册
This handbook compiles the essential musical "formulas" and theoretical principles required for AQA A-Level Music. Just as mathematics relies on equations, music theory depends on interval patterns, chord structures, cadential rules, and tuning ratios—all of which can be expressed as repeatable formulas. Use this quick-reference guide to reinforce your understanding and excel in analysis and composition tasks.
本手册汇集了AQA A-Level音乐所需的核心音乐“公式”与理论原理。正如数学依赖于方程式，音乐理论依赖于音程模式、和弦结构、终止规则和调律比率——所有这些都可以表达为可复用的公式。请利用本速查手册来巩固你的理解，并在分析与作曲作业中取得优异成绩。
1. Interval Construction Formulae | 音程构成公式
Every interval is defined by the number of semitones between two notes, combined with its quality (perfect, major, minor, augmented, diminished). Below are the core interval formulas.
每个音程由两个音之间的半音数量及其质量（纯、大、小、增、减）来定义。以下是核心音程公式。
| Interval / 音程 | Semitones | Formula Pattern |
|---|---|---|
| Perfect Unison / 纯一度 | 0 | Root only |
| Minor 2nd / 小二度 | 1 | Adjacent semitone |
| Major 2nd / 大二度 | 2 | Whole tone |
| Minor 3rd / 小三度 | 3 | 3 semitones |
| Major 3rd / 大三度 | 4 | 2 whole tones |
| Perfect 4th / 纯四度 | 5 | 5 semitones |
| Augmented 4th / Diminished 5th (Tritone) 增四度/减五度 | 6 | 3 whole tones |
| Perfect 5th / 纯五度 | 7 | 7 semitones |
| Minor 6th / 小六度 | 8 | 8 semitones |
| Major 6th / 大六度 | 9 | 9 semitones |
| Minor 7th / 小七度 | 10 | 10 semitones |
| Major 7th / 大七度 | 11 | 11 semitones |
| Perfect Octave / 纯八度 | 12 | 12 semitones |
When intervals invert, the number rule is: 9 minus the original interval number gives the inverted number (e.g., 3rd becomes 6th). The quality flips: major becomes minor, perfect remains perfect, augmented becomes diminished.
音程转位时，数字规则是：9减去原音程数得到转位音程数（例如三度变为六度）。性质反转：大变小，纯保持纯，增变减。
2. Scale Structures & Formulae | 音阶结构与公式
The major scale follows the tone-semitone pattern: Tone Tone Semitone Tone Tone Tone Semitone (T T S T T T S). In whole/half steps: W W H W W W H.
大调音阶遵循全音半音模式：全音 全音 半音 全音 全音 全音 半音（T T S T T T S）。用全半关系表示为 W W H W W W H。
Harmonic minor: Tone Semitone Tone Tone Semitone Augmented 2nd Semitone (T S T T S 3S S). Note the augmented 2nd between the 6th and 7th degrees, creating the characteristic sound.
和声小调：全音 半音 全音 全音 半音 增二度 半音（T S T T S A2 S）。注意第六级与第七级之间的增二度，营造出特征性音响。
Melodic minor ascending: Tone Semitone Tone Tone Tone Tone Semitone (T S T T T T S) – raises 6th and 7th. Descending: same as natural minor (T T S T T T S).
旋律小调上行：全音 半音 全音 全音 全音 全音 半音（T S T T T T S）——升高六级与七级。下行等同于自然小调（T T S T T T S）。
Church modes derived from the white-note series (use the same step pattern on different starting notes): Ionian (major), Dorian (minor raised 6th), Phrygian (minor lowered 2nd), Lydian (major raised 4th), Mixolydian (major lowered 7th), Aeolian (natural minor), Locrian (diminished).
中古调式源自白键音列（在不同起始音上使用相同的音阶排列）：伊奥尼亚（大调），多里亚（小调升六级），弗里几亚（小调降二级），利底亚（大调升四级），混合利底亚（大调降七级），爱奥利亚（自然小调），洛克里亚（减音阶）。
3. Chord Construction Formulae (Triads) | 三和弦构成公式
A triad is built by stacking two thirds above a root. The intervallic formula determines its quality:
三和弦由在根音上方叠加两个三度音构成。音程公式决定其性质：
Major triad: root + 4 semitones (major 3rd) + 3 semitones (minor 3rd)
大三和弦：根音 + 4个半音（大三度） + 3个半音（小三度）
Minor triad: root + 3 semitones (minor 3rd) + 4 semitones (major 3rd)
小三和弦：根音 + 3个半音（小三度） + 4个半音（大三度）
Diminished triad: root + 3 semitones + 3 semitones
减三和弦：根音 + 3个半音 + 3个半音
Augmented triad: root + 4 semitones + 4 semitones
增三和弦：根音 + 4个半音 + 4个半音
to spell any triad from a given root. For example, C major: C (0), E (4), G (3 more = 7).
利用这些公式，可以从任意根音构建三和弦。例如C大三和弦：C（0），E（+4），G（+3 = 7）。
4. Seventh Chord Formulae | 七和弦构成公式
Seventh chords add a fourth note a seventh above the root, producing richer tension. The most common seventh chord types and their construction:
七和弦在根音上方添加一个七度音，产生更丰富的紧张感。最常见的七和弦类型及其构建：
| Chord Type 和弦类型 | Triad Base 三和弦基础 | Added 7th 七音 | Semitone Stack 半音叠置 |
|---|---|---|---|
| Major 7th / 大七和弦 | Major | Major 7th (11 st) | 4 + 3 + 4 |
| Dominant 7th / 属七和弦 | Major | Minor 7th (10 st) | 4 + 3 + 3 |
| Minor 7th / 小七和弦 | Minor | Minor 7th (10 st) | 3 + 4 + 3 |
| Half-diminished 7th / 半减七和弦 | Diminished | Minor 7th (10 st) | 3 + 3 + 4 |
| Diminished 7th / 减七和弦 | Diminished | Diminished 7th (9 st) | 3 + 3 + 3 |
The diminished 7th chord is symmetrical: each interval between consecutive notes is
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