📚 IGCSE CCEA Music: Formulae & Theorems Quick Reference Handbook | IGCSE CCEA 音乐：公式定理速查手册
In CCEA IGCSE Music, marks are won by knowing the “formulae” behind notation, scales, intervals and harmony. This handbook condenses the essential rules into a quick reference for listening, composing and written papers.
在 CCEA IGCSE 音乐考试中，掌握记谱、音阶、音程与和声背后的“公式”是得分关键。本手册将核心规则浓缩成一份适用于听力、作曲与笔试试卷的速查资料。
1. Note Values and Rhythm Arithmetic | 音符时值与节奏算术
Every rhythm is a fraction of a whole note (semibreve). Learn the values so you can complete bars and calculate missing rests.
每个节奏都是全音符（semibreve）的分数。掌握时值有助于补全小节并计算缺失的休止符。
| Note | English name | Beats in 4/4 |
|---|---|---|
| 𝅝 | Semibreve | 4 |
| 𝅗𝅥 | Minim | 2 |
| 𝅘𝅥 | Crotchet | 1 |
| 𝅘𝅥𝅮 | Quaver | 1/2 |
| 𝅘𝅥𝅯 | Semiquaver | 1/4 |
A dot after any note adds half of that note’s value. For example, a dotted crotchet lasts 1 + 1/2 = 1.5 beats.
附点增加原音符时值的一半。例如，附点四分音符持续 1 + 1/2 = 1.5 拍。
Dotted note value = original note × 1.5
A triplet groups three notes into the time usually taken by two of the same note value.
三连音将三个相同音值的音符压缩到原本两个音符的时值内。
2. Simple and Compound Time | 单拍子与复拍子
Simple time beats divide into two equal parts; compound time beats divide into three.
单拍子的每一拍可分成两个均等部分；复拍子的每一拍可分成三个均等部分。
| Time signature | Type | Beats per bar |
|---|---|---|
| 2/4 | Simple duple | 2 crotchet beats |
| 3/4 | Simple triple | 3 crotchet beats |
| 4/4 | Simple quadruple | 4 crotchet beats |
| 6/8 | Compound duple | 2 dotted-crotchet beats |
| 9/8 | Compound triple | 3 dotted-crotchet beats |
| 12/8 | Compound quadruple | 4 dotted-crotchet beats |
In compound time, divide the top number by three to find the number of beats per bar; the beat unit is a dotted note.
在复拍子中，将上方数字除以 3 可得每小节拍数；拍单位是附点音符。
Compound beats per bar = top number ÷ 3
3. Major Scale Formula | 大调音阶公式
All major scales follow the same tone-semitone pattern: T T S T T T S.
所有大调音阶遵循相同的全音-半音模式：全 全 半 全 全 全 半。
T – T – S – T – T – T – S
Here, T means a tone (two semitones) and S means a semitone. C major uses C D E F G A B C with no sharps or flats.
其中 T 表示全音（两个半音），S 表示半音。C 大调使用 C D E F G A B C，没有升号或降号。
Use the same formula from any tonic to build the major scale, adding accidentals as needed.
从任意主音出发套用同一公式即可构建大调音阶，并按需加入临时记号。
4. Minor Scales: Natural, Harmonic, Melodic | 小调音阶：自然、和声、旋律
The three minor forms change only the 6th and 7th degrees from the natural minor base.
三种小调形式仅改变自然小调基础音阶中的第 6 级和第 7 级。
Natural minor: T – S – T – T – S – T – T
Harmonic minor: T – S – T – T – S – T+S – S
Melodic minor ascending: T – S – T – T – T – T – S
In the harmonic minor, the 7th degree is raised to create a leading note and an augmented second between degrees 6 and 7.
在和声小调中，第 7 级升高形成导音，并在第 6 级与第 7 级之间构成增二度。
The melodic minor ascends with raised 6th and 7th degrees, but descends using the natural minor pattern.
旋律小调上行时升高第 6 级与第 7 级，下行时则使用自然小调模式。
5. Key Signatures and Circle of Fifths | 调号与五度圈
Key signatures are written in a fixed order. Sharps appear F C G D A E B; flats appear B E A D G C F.
调号按固定顺序书写。升号顺序为 F C G D A E B；降号顺序为 B E A D G C F。
Sharps: F – C – G – D – A – E – B
Flats: B – E – A – D – G – C – F
To identify a major key from sharps, go one semitone above the last sharp. For flats, the second-to-last flat is the major key.
从升号识别大调：以最后一个升号上方半音为主音。从降号识别大调：倒数第二个降号即大调主音。
Every major key has a relative minor three semitones lower. For example, C major’s relative minor is A minor.
每个大调都有一个低于其主音三个半音的关系小调。例如，C 大调的关系小调是 A 小调。
Relative minor tonic = major tonic − 3 semitones
6. Intervals: Semitone Count and Quality | 音程：半音数与性质
Interval names combine a number (distance in letter names) and a quality (perfect, major, minor, augmented, diminished). Use semitone counts to check the quality.
音程名称由度数（字母音名距离）和性质（纯、大、小、增、减）组成。可用半音数核对性质。
| Semitones | Interval |
|---|---|
| 0 | Perfect unison |
| 1 | Minor 2nd |
| 2 | Major 2nd |
| 3 | Minor 3rd |
| 4 | Major 3rd |
| 5 | Perfect 4th |
| 6 | Tritone (A4/d5) |
| 7 | Perfect 5th |
| 8 | Minor 6th |
| 9 | Major 6th |
| 10 | Minor 7th |
| 11 | Major 7th |
| 12 | Perfect octave |
To invert an interval, subtract its number from 9. Major becomes minor, minor becomes major; perfect stays perfect; augmented becomes diminished.
音程转位时，用 9 减去原音程度数。大音程变小音程，小音程变大音程；纯音程仍为纯音程；增音程变减音程。
Interval inversion: new number = 9 − old number
7. Triad and Chord Formulae | 三和弦与和弦公式
A triad is built by stacking two thirds. The chord symbol tells you which third is major or minor.
三和弦由两个三度叠加而成。和弦标记说明其中哪一个是大小三度。
Major triad = root + major 3rd + perfect 5th (R + 4 + 3 semitones)
Minor triad = root + minor 3rd + perfect 5th (R + 3 + 4 semitones)
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