📚 IGCSE CAIE Music: Quick Reference Formula Handbook | IGCSE CAIE 音乐：公式定理速查手册
This article brings together the essential "formulas", patterns and rules you need for the CAIE IGCSE Music exam. Music is not mathematics, but it has its own internal logic - interval formulas, scale patterns, chord constructions, cadence formulas and structural templates that can be memorised and applied quickly under exam pressure. Use this handbook as a revision checklist: read a section, cover the page, and write the pattern out from memory.
本文汇总了 CAIE IGCSE 音乐考试中必需的核心“公式”、模式与规则。音乐不是数学，但它有自己的内在逻辑——音程公式、音阶模式、和弦构造、终止式公式与曲式模板，都可以被记忆，并在考试压力下快速调用。请把这份手册当作复习清单使用：读一节，遮住页面，然后凭记忆把模式默写出来。
1. Pitch and Intervals | 音高与音程
The semitone is the smallest interval in Western music. A tone is equal to two semitones.
半音是西方音乐中最小的音程。一个全音等于两个半音。
An interval is the distance in pitch between two notes. To name an interval you need two pieces of information: the number (2nd, 3rd, 5th, 7th, octave), found by counting the letter names inclusively, and the quality (major, minor, perfect, augmented, diminished), found from the exact number of semitones and the context of the key.
音程是两个音之间的音高距离。要为一个音程命名，你需要两项信息：一是度数（二度、三度、五度、七度、八度），由首尾音名字母含两端计数得出；二是性质（大、小、纯、增、减），由准确的半音数以及调性上下文决定。
| Interval | 音程 | Semitones | 半音数 | Example from C | 从 C 出发 |
| Perfect unison / 纯一度 | 0 | C → C |
| Minor 2nd / 小二度 | 1 | C → D♭ |
| Major 2nd / 大二度 | 2 | C → D |
| Minor 3rd / 小三度 | 3 | C → E♭ |
| Major 3rd / 大三度 | 4 | C → E |
| Perfect 4th / 纯四度 | 5 | C → F |
| Tritone (aug. 4th / dim. 5th) / 三全音 | 6 | C → F♯ / C → G♭ |
| Perfect 5th / 纯五度 | 7 | C → G |
| Minor 6th / 小六度 | 8 | C → A♭ |
| Major 6th / 大六度 | 9 | C → A |
| Minor 7th / 小七度 | 10 | C → B♭ |
| Major 7th / 大七度 | 11 | C → B |
| Perfect Octave / 纯八度 | 12 | C → C' |
nd augmented becomes diminished. For example, a major 3rd (4 semitones) inverts to a minor 6th (8 semitones), and 3 + 6 = 9.
转位公式：音程转位后，两个度数相加等于 9。大音程变 小音程，小音程变大音程，纯音程仍是纯音程，增音程变减音程。例如大三度（4 个半音）转位后是小六度（8 个半音），而 3 + 6 = 9。
or 2nd = 12 + 2 = 14 semitones. A minor 10th = octave + minor 3rd = 12 + 3 = 15 semitones.
复音程就是八度加上一个单音程。大九度 = 八度 + 大二度 = 12 + 2 = 14 个半音。小十度 = 八度 + 小三度 = 12 + 3 = 15 个半音。
2. Scale Formulas | 音阶公式
A major scale follows one fixed pattern of tones (T) and semitones (S). The two semitones always fall between degrees 3-4 and degrees 7-8.
大调音阶遵循一个固定的全音（T）与半音（S）模式。两个半音永远落在第 3-4 级与第 7-8 级之间。
Major: T T S T T T S (2 2 1 2 2 2 1 semitones)
自然小调：T S T T S T T (2 1 2 2 1 2 2 半音)
The natural minor scale uses a lowered 3rd, 6th and 7th compared with the major scale. The harmonic minor raises the 7th degree, creating an augmented 2nd (three semitones) between the 6th and 7th degrees - this is the sound examiners describe as "exotic" or "Eastern".
自然小调与同名大调相比，降低了第 3、6、7 级。和声小调升高第 7 级，从而在第 6 级与第 7 级之间形成增二度（三个半音）——这就是考官常形容为“异域”或“东方”色彩的音效。
Harmonic minor: T S T T S T+S S
The melodic minor raises both the 6th and 7th degrees when ascending, and reverts to the natural minor when descending. This avoids the awkward augmented 2nd in a melodic line.
旋律小调在上行时同时升高第 6 级与第 7 级，下行时则还原为自然小调。这样做是为了避免旋律线条中出现突兀的增二度。
Melodic minor up: T S T T T T S | down: T T S T T S T
Other scales you must recognise by ear and by sight:
以下其他音阶，你必须能凭听觉与谱面辨认：
- Chromatic | 半音阶: twelve consecutive semitones; conventionally written with sharps ascending and flats descending. / 连续十二个半音；习惯上上行用升号、下行用降号。
- Major pentatonic | 大调五声音阶: degrees 1 2 3 5 6 - no semitones, very common in folk and Chinese music. / 1 2 3 5 6 级——不含半音，在民歌与中国音乐中极常见。
- Minor pentatonic | 小调五声音阶: 1 ♭3 4 5 ♭7. / 1 ♭3 4 5 ♭7 级。
- Blues scale | 布鲁斯音阶: 1 ♭3 4 ♭5 5 ♭7, with the ♭5 as the "blue note". / 1 ♭3 4 ♭5 5 ♭7，其中 ♭5 是“布鲁斯音”。
- Whole-tone | 全音阶: all tones, no semitones - associated with Debussy and dreamlike textures. / 全部为全音，无半音——常与德彪西及梦幻般的织体相关。
3. Key Signatures and the Circle of Fifths | 调号与五度圈
Key signatures are written in a fixed order. Sharps always appear in the order F C G D A E B; flats always appear in the order B E A D G C F. The order never changes, whatever the key.
调号有固定的书写顺序。升号永远是 F C G D A E B 的顺序；降号永远是 B E A D G C F 的顺序。无论什么调，这个顺序都不会改变。
Two memory sentences: Father Charles Goes Down And Ends Battle (sharps) and Battle Ends And Down Goes Charles' Father (flats).
两句记忆口诀：Father Charles Goes Down And Ends Battle（升号）与 Battle Ends And Down Goes Charles' Father（降号）。
Two calculation shortcuts for finding the major key:
两个找出大调主音的计算捷径：
- For sharp keys: take the last sharp and go up one semitone. Last sharp = A♯, so the key is B major. / 升号调：取最后一个升号，向上一个半音。最后升号是 A♯，故为 B 大调。
- lat keys: take the second-to-last flat. Flats B E A D, second-to-last = A, so the key is A♭ major. Exception: one flat (B♭) is F major. / 降号调：取倒数第二个降号。降号为 B E A D，倒数第二个是 A，故为 A♭ 大调。例外：只有一个降号（B♭）时是 F 大调。
| Key signature | 调号 | Major | 大调 | Relative minor | 关系小调 |
| None | 无 | C major | A minor |
| 1♯ | G major | E minor |
| 2♯ | D major | B minor |
| 3♯ | A major | F♯ minor |
| 4♯ | E major | C♯ minor |
| 1♭ | F major | D minor |
| 2♭ | B♭ major | G minor |
| 3♭ | E♭ major | C minor |
| 4♭ | A♭ major | F minor |
The relative minor always sits a minor 3rd (3 semitones) below the major tonic, and shares the same key signature. The circle of fifths moving clockwise gives C G D A E B F
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