📚 Year 7 CAIE Music: Quick Formula & Theorem Reference Guide | Year 7 CAIE 音乐：公式定理速查手册
Welcome to your handy reference guide for the key music theory ‘formulas’ and ‘theorems’ required in the Year 7 CAIE Music curriculum. Just as mathematicians need equations, musicians need rules for building scales, chords, rhythms, and understanding notation. This booklet distills those rules into clear, bite-sized statements for quick revision.
欢迎使用这本便捷的参考手册，涵盖了 Year 7 CAIE 音乐课程所需的关键乐理“公式”和“定理”。就像数学家需要方程式一样，音乐家也需要规则来构建音阶、和弦、节奏以及理解乐谱。这本小册子将这些规则提炼成清晰、精炼的表述，便于快速复习。
1. Note Values & Rests | 音符时值与休止符
Every sound in music has a precise length, written with different note shapes. Each note value has a matching silence – a rest. The relationships between them follow a strict ratio of 2:1 as you move from one level to the next.
音乐中的每一个音都有精确的时长，用不同的音符形状表示。每一种音符时值都有对应的休止符。音符之间的换算关系是严格的2:1递进。
Formula: 1 semibreve = 2 minims = 4 crotchets = 8 quavers = 16 semiquavers
公式：1个全音符 = 2个二分音符 = 4个四分音符 = 8个八分音符 = 16个十六分音符
| Name (English) | 中文名称 | Symbol | Rest Symbol | Beats in 4/4 |
|---|---|---|---|---|
| Semibreve | 全音符 | 𝄻 | 𝄼 | 4 |
| Minim | 二分音符 | 𝅗 | 𝄽 | 2 |
| Crotchet | 四分音符 | 𝅘 | 𝄾 | 1 |
| Quaver | 八分音符 | 𝅘𝅥 | 𝄿 | 1/2 |
| Semiquaver | 十六分音符 | 𝅘𝅥𝅮 | 𝅀 | 1/4 |
2. Time Signatures | 拍号
A time signature appears at the start of a piece, written as two numbers one above the other. The top number tells us how many beats fill each bar; the bottom number tells us which note value counts as one beat. The most common simple time signatures in Year 7 are 2/4, 3/4, and 4/4, where ‘4’ stands for a crotchet beat.
拍号出现在乐曲开头，由两个上下叠放的数字组成。上方数字表示每小节有几拍；下方数字表示以哪种音符为一拍。Year 7 最常见的单拍子有 2/4、3/4 和 4/4，其中的“4”代表以四分音符为一拍。
Theorem: In x/4 time, a crotchet = 1 beat; in x/8 time, a quaver = 1 beat.
定理：在 x/4 拍中，四分音符=1拍；在 x/8 拍中，八分音符=1拍。
| Time Signature | 拍号 | Beats per bar | Beat note |
|---|---|---|---|
| 2/4 | 四二拍 | 2 | Crotchet (四分音符) |
| 3/4 | 四三拍 | 3 | Crotchet |
| 4/4 | 四四拍 | 4 | Crotchet |
| 6/8 | 八六拍 | 6 (通常2个大拍) | Quaver (八分音符) |
3. The Major Scale Formula | 大调音阶公式
Every major scale is built from the same sequence of tones (whole steps) and semitones (half steps). Starting on any note, if you follow this pattern you will produce a major scale. The formula is often memorised as T-T-S-T-T-T-S (Tone, Tone, Semitone, Tone, Tone, Tone, Semitone).
所有大调音阶都遵循完全相同的全音和半音排列模式。从任意一个音开始，只要按照这个模式，就能得到一个大调音阶。记忆口诀：全全半全全全半。
Major Scale Formula: W – W – H – W – W – W – H (Whole, Whole, Half, Whole, Whole, Whole, Half)
大调音阶公式：全 – 全 – 半 – 全 – 全 – 全 – 半
Example: C major scale – C D E F G A B C. The semitones fall between E–F and B–C, just as the formula demands.
示例：C大调音阶 – C D E F G A B C。半音出现在E–F和B–C之间，完全符合公式要求。
4. The Natural Minor Scale Formula | 自然小调音阶公式
The natural minor scale uses a different pattern. Its unique sound comes from the third, sixth and seventh notes being a semitone lower than in the major scale. The formula is W–H–W–W–H–W–W.
自然小调音阶使用不同的排列模式。其独特的音响效果来自第三级、第六级和第七级音比大调低半音。公式为：全 – 半 – 全 – 全 – 半 – 全 – 全。
Natural Minor Formula: W – H – W – W – H – W – W
自然小调公式：全 – 半 – 全 – 全 – 半 – 全 – 全
Example: A natural minor scale – A B C D E F G A. The semitones fall between B–C and E–F.
示例：A 自然小调音阶 – A B C D E F G A。半音出现在 B–C 和 E–F 之间。
5. Circle of Fifths & Key Signatures | 五度圈与调号
Key signatures tell us which notes are consistently sharpened or flattened. Sharps and flats are added in a fixed order. A quick formula: the last sharp in a key signature is the leading note (7th degree) – go up one semitone to find the major key. For flat keys, the second-to-last flat names the major key.
调号告诉我们哪些音需要持续升高或降低。升号和降号的添加顺序是固定的。快速记忆法：调号中最后一个升号是导音（第7级），向上升半音即为主音；对于降号调，倒数第二个降号就是大调的主音。
| Key | 调 | Sharps / Flats | 升/降号 |
|---|---|---|---|
| C major | C大调 | No sharps/flats | 无 |
| G major | G大调 | F♯ | F♯ |
| D major | D大调 | F♯, C♯ | F♯, C♯ |
| F major | F大调 | B♭ | B♭ |
| B♭ major | 降B大调 | B♭, E♭ | B♭, E♭ |
Mnemonic for order of sharps: Father Charles Goes Down And Ends Battle (F♯ C♯ G♯ D♯ A♯ E♯ B♯). For flats: Battle Ends And Down Goes Charles’ Father (B♭ E♭ A♭ D♭ G♭ C♭ F♭).
升号顺序口诀：Father Charles Goes Down And Ends Battle（F♯ C♯ G♯ D♯ A♯ E♯ B♯）。降号顺序口诀：Battle Ends And Down Goes Charles’ Father（B♭ E♭ A♭ D♭ G♭ C♭ F♭）。
6. Intervals: Measuring Musical Distance | 音程：测量音与音的距离
An interval is the distance between two notes. The name has two parts: a number (2nd, 3rd, 4th, etc.) and a quality (major, minor, perfect). The number is simply the count of letter names from the bottom note to the top note, inclusive. The quality is found by counting semitones within the major scale of the bottom note.
音程是两个音之间的距离。音程名称由两部分组成：度数（二度、三度、四度等）和性质（大、小、纯）。度数只需数出两个音之间包含的音名数量；性质则依据较低音的大调音阶中的半音数判断。
| Interval | 音程 | Semitones | Example |
|---|---|---|---|
| Minor 2nd | 小二度 | 1 | E–F |
| Major 2nd | 大二度 | 2 | C–D |
| Minor 3rd | 小三度 | 3 | A–C |
| Major 3rd | 大三度 | 4 | C–E |
| Perfect 4th | 纯四度 | 5 | C–F |
| Perfect 5th | 纯五度 | 7 | C–G |
| Octave | 纯八度 | 12 | C–C’ |
7. Triad Construction | 三和弦构建
A triad is a three-note chord stacked in thirds. The two most common types are major and minor. The recipe for a major triad is: root + 4 semitones (major 3rd) + 3 semitones (minor 3rd). For a minor triad, swap the order: root + 3 semitones (minor 3rd) + 4 semitones (major 3rd).
三和弦是由三个按三度叠置的音组成的和弦。最常见的两种是大三和弦和小三和弦。大三和弦的配方：根音 + 4个半音（大三度）+ 3个半音（小三度）。小三和弦则调换顺序：根音 + 3个半音（小三度）+ 4个半音（大三度）。
Major triad = Root + 4s + 3s (s = semitones)
大三和弦 = 根音 + 4个半音 + 3个半音
Minor triad = Root + 3s + 4s
小三和弦 = 根音 + 3个半音 + 4个半音
Example: C major triad – C (root), E (C
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