📚 IGCSE Cambridge Music: Formula & Key Facts Quick Reference | IGCSE剑桥音乐：公式定理速查手册
This rapid revision handbook collects the core musical 'formulas' and fixed patterns that Cambridge IGCSE Music candidates need for listening, composing and performing papers: note values, scale and chord construction, cadences, tempo and expression, instruments and form.
本速查手册汇集剑桥 IGCSE 音乐考生在听力、作曲和演奏试卷中需要的核心“公式”与固定模式：音符时值、音阶与和弦构建、终止式、速度与表情、乐器以及曲式。
1. Note Values and the Rhythm Tree | 音符时值与节奏树
The rhythm tree is a proportion system: each note value can be split into two smaller values in simple metre.
节奏树是一套比例系统：在单拍子中，每个音符时值都可以分成两个更小的时值。
1 semibreve = 2 minims = 4 crotchets = 8 quavers = 16 semiquavers
1 全音符 = 2 二分音符 = 4 四分音符 = 8 八分音符 = 16 十六分音符
A dot adds half of the original value, so a dotted crotchet equals one crotchet plus one quaver.
附点增加原时值的一半，因此附点四分音符等于一个四分音符加一个八分音符。
A tie joins two notes of the same pitch into one sustained sound; the second note is not re-articulated.
延音线将两个同音高的音符连成一个持续音；第二个音不再重新发音。
A triplet divides a note into three equal parts instead of two, shown by a small 3 above or below the note group.
三连音把一个音符均分为三等份而不是两等份，在音符群上方或下方标注小数字 3。
2. Time Signatures and Metre | 拍号与节拍
The top number of a time signature shows how many beats are in each bar; the bottom number shows the note value that carries one beat.
拍号上方的数字表示每小节有几拍；下方的数字表示以哪种音符为一拍。
4/4 = 4 crotchet beats per bar; 6/8 = 2 dotted crotchet beats per bar
4/4 = 每小节 4 个四分音符拍；6/8 = 每小节 2 个附点四分音符拍
Simple metre has beats that divide into 2, as in 2/4, 3/4 and 4/4.
单拍子的拍子以 2 为单位细分，如 2/4、3/4 和 4/4。
Compound metre has beats that divide into 3, as in 6/8, 9/8 and 12/8; each beat is a dotted note.
复拍子的拍子以 3 为单位细分，如 6/8、9/8 和 12/8；每一拍是一个附点音符。
3. Intervals: Counting and Quality | 音程：度数计算与性质
To find the interval number, count the letter names from the lower note to the upper note, including both notes.
计算音程度数时，从低音到高音数音名，并把两个音都算进去。
Quality is decided by semitone size or by comparing the upper note with the lower note's major scale.
音程性质由半音数量决定，或通过将高音与低音的大调音阶进行比较来判断。
| Semitones | Interval | 中文名称 |
|---|---|---|
| 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 | Tritone / Augmented 4th / Diminished 5th | 三全音 / 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 |
Perfect intervals (unison, 4th, 5th, octave) remain perfect in major and minor scales; major/minor intervals (2nd, 3rd, 6th, 7th) are major in the major scale and one semitone smaller in the minor scale.
纯音程（一度、四度、五度、八度）在大调和小调中保持纯；大小音程（二度、三度、六度、七度）在大调中是大音程，在小调中减小一个半音。
4. Scale Formulas: Major, Minor and Modes | 音阶构建公式：大小调与调式
Use T for tone and S for semitone. The major scale is the reference pattern for all key signatures.
用 T 表示全音，S 表示半音。大调音阶是所有调号的基础模式。
Major scale: T T S T T T S
大调音阶：全 全 半 全 全 全 半
Natural minor: T S T T S T T
自然小调：全 半 全 全 半 全 全
The harmonic minor raises the 7th degree, creating an augmented 2nd between the 6th and 7th degrees.
和声小调升高第 7 级，在第 6 级和第 7 级之间形成增二度。
Harmonic minor: T S T T S A2 S
