📚 Year 9 Edexcel Music: Formula and Theorem Quick Reference Handbook | Year 9 Edexcel 音乐：公式定理速查手册
This handbook provides a concise summary of essential music theory ‘formulas’ and rules needed for the Year 9 Edexcel Music curriculum. Mastering these patterns will help you analyse, compose and perform with confidence. Use it as a quick revision tool to reinforce your understanding of scales, chords, cadences and more.
本手册为Year 9 Edexcel音乐课程浓缩整理了核心音乐理论“公式”与规则。掌握这些模式将帮助你在分析、作曲和演奏中信心倍增。把它当作快速复习工具，巩固你对音阶、和弦、终止式等知识的理解。
1. Major Scale Formula | 大调音阶公式
The formula for any major scale is a sequence of whole and half steps: W–W–H–W–W–W–H (where W = whole step / 2 semitones, H = half step / 1 semitone). For example, C major: C–D (W), D–E (W), E–F (H), F–G (W), G–A (W), A–B (W), B–C (H).
任何大调音阶的公式为全音与半音序列：全–全–半–全–全–全–半（W = 全音 / 2个半音，H = 半音 / 1个半音）。例如C大调：C–D（W），D–E（W），E–F（H），F–G（W），G–A（W），A–B（W），B–C（H）。
2. Minor Scale Formulas | 小调音阶公式
There are three common minor scale patterns. Natural minor: W–H–W–W–H–W–W. Harmonic minor: W–H–W–W–H–WH–H (the gap between the 6th and 7th degrees is an augmented 2nd of 3 semitones). Melodic minor ascending: W–H–W–W–W–W–H (raised 6th and 7th); descending usually reverts to the natural minor form.
常见的小调音阶有三种形式。自然小调：全–半–全–全–半–全–全。和声小调：全–半–全–全–半–增二度–半（第6级到第7级为增二度，3个半音）。旋律小调上行：全–半–全–全–全–全–半（升高第6、7级）；下行通常使用自然小调。
3. Key Signature Formulas | 调号速记公式
Order of sharps: F♯ C♯ G♯ D♯ A♯ E♯ B♯ (Father Charles Goes Down And Ends Battle). To find the major tonic from a sharp key signature, take the last sharp and go up a semitone. Order of flats: B♭ E♭ A♭ D♭ G♭ C♭ F♭ (Battle Ends And Down Goes Charles Father). For flat keys, the second-to-last flat is the tonic, except in F major (one flat).
升号顺序：F♯ C♯ G♯ D♯ A♯ E♯ B♯（可记为Father Charles Goes Down And Ends Battle）。从升号调号找大调主音：取最后一个升号并升高半音。降号顺序：B♭ E♭ A♭ D♭ G♭ C♭ F♭（Battle Ends And Down Goes Charles Father）。降号调中，倒数第二个降号即为主音（只有一个降号的F大调除外）。
4. Interval Calculation Formula | 音程计算公式
An interval is the distance between two notes, measured in semitones. Use the following semitone formula to identify intervals quickly:
音程是两个音符之间的距离，以半音为单位。使用以下半音公式可快速识别音程：
| Semitones (半音数) | Interval Name (音程名称) |
|---|---|
| 0 | Perfect unison / 纯一度 |
| 1 | Minor 2nd / 小二度 |
| 2 | Major 2nd / 大二度 |
| 3 | Minor 3rd / 小三度 |
| 4 | Major 3rd / 大三度 |
| 5 | Perfect 4th / 纯四度 |
| 6 | Augmented 4th / Diminished 5th (tritone 增四度/减五度) |
| 7 | Perfect 5th / 纯五度 |
| 8 | Minor 6th / 小六度 |
| 9 | Major 6th / 大六度 |
| 10 | Minor 7th / 小七度 |
| 11 | Major 7th / 大七度 |
| 12 | Perfect octave / 纯八度 |
To work out an interval, count the letter names for the interval number, then count semitones to determine its quality (major, minor, perfect, etc.).
计算音程时，先数字母名称得到音程度数，再数半音确定性质（大、小、纯等）。
5. Triad Construction Formulas | 三和弦构建公式
A triad is a three-note chord built from a root, a third and a fifth. The quality is determined by the semitone stack:
三和弦是由根音、三音和五音组成的三音和弦。其性质由半音叠置决定：
- Major triad (大三和弦): root + 4 semitones (major 3rd) + 3 semitones (minor 3rd). Example: C–E–G (C E G)
- Minor triad (小三和弦): root + 3 + 4. Example: C–E♭–G (C E♭ G)
- Diminished triad (减三和弦): root + 3 + 3. Example: C–E♭–G♭ (C E♭ G♭)
- Augmented triad (增三和弦): root + 4 + 4. Example: C–E–G♯ (C E G♯)
This formula works on any starting note: just add the required number of semitones for the middle and top notes.
此公式适用于任何起始音：只需为中间音和冠音增加相应数量的半音即可。
6. Seventh Chord Formulas | 七和弦公式
Seventh chords add a fourth note – the seventh – above the root. The most important one for Year 9 is the dominant 7th (V7), which appears in perfect cadences. Build it using: major triad + minor 7th = root + 4 + 3 + 3 semitones. Example: G7 = G–B–D–F (G B D F).
七和弦在根音上方增加了第四个音——七音。Year 9最重要的七和弦是属七和弦（V7），常用于完全终止。构建公式为：大三和弦 + 小七度 = 根音 + 4 + 3 + 3个半音。例如G7 = G–B–D–F。
Other seventh chords include: Major 7th (4 + 3 + 4), Minor 7th (3 + 4 + 3), Half-diminished 7th (3 + 3 + 4), and Diminished 7th (3 + 3 + 3). These will be fully explored in later years.
其他七和弦包括：大七和弦（4+3+4）、小七和弦（3+4+3）、半减七和弦（3+3+4）和减七和弦（3+3+3），这些将在后续年级深入学习。
7. Cadence Formulas | 终止式公式
Cadences are chord progressions that end a phrase. Memories them using these harmonic formulas:
终止式是结束乐句的和弦进行，请用以下和声公式记忆：
- Perfect cadence (完全终止): V – I (or V7 – I). Sounds finished and final.
- Plagal cadence (变格终止): IV – I. Often called the ‘Amen’ cadence.
- Imperfect cadence (不完全终止): any chord (often I, ii or IV) – V. Sounds unfinished, like a comma.
- Interrupted cadence (阻碍终止): V – vi. A deceptive resolution that surprises the listener.
Roman numerals are based on the scale degrees: I = tonic, II = supertonic, IV = subdominant, V = dominant, VI = submediant.
罗马数字基于音阶级数：I = 主音，II = 上主音，IV = 下属音，V = 属音，VI = 下中音。
8. Time Signature and Rhythm Formulas | 拍号与节奏公式
Time signatures tell you how many beats are in each bar and what note value gets one beat. Simple time: the beat naturally divides into 2 (e.g. 2/4, 3/4, 4/4). Compound time: the beat divides into 3 (e.g. 6/8, 9/8, 12/8). In 6/8, there are two dotted-crotchet beats per bar.
拍号告诉你每小节有多少拍，以及以什么音符为一拍。单拍子：每拍可自然地分为两份（如2/4、3/4、4/4）。复拍子：每拍可三份（如6/8、9/8、12/8）。在6/8中，每小节有两个附点四分音符的拍子。
Note-value formulas (
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