📚 IGCSE CIE Music: Formula & Theorem Quick Reference Handbook | IGCSE CIE 音乐：公式定理速查手册
This quick reference handbook compiles the essential formulas, patterns and rules of music theory relevant to the IGCSE CIE Music syllabus. Use it as a rapid revision tool for intervals, scales, chords, cadences, key signatures and more.
本速查手册汇编了 IGCSE CIE 音乐课程相关的音乐理论基本公式、模式和规则。适用于音程、音阶、和弦、终止式、调号等知识的快速复习。
1. Scale Formulas | 音阶模式公式
Major scale pattern: T‑T‑S‑T‑T‑T‑S (Tone, Tone, Semitone, Tone, Tone, Tone, Semitone). In half‑step terms: W‑W‑H‑W‑W‑W‑H (Whole, Whole, Half, Whole, Whole, Whole, Half).
大调音阶模式：全‑全‑半‑全‑全‑全‑半（全音‑全音‑半音‑全音‑全音‑全音‑半音）。
Natural minor scale pattern: T‑S‑T‑T‑S‑T‑T (W‑H‑W‑W‑H‑W‑W). Descending is the same as ascending.
自然小调音阶模式：全‑半‑全‑全‑半‑全‑全。上行与下行相同。
Harmonic minor scale pattern: T‑S‑T‑T‑S‑T+S‑S (raises the 7th degree by a semitone, creating an augmented 2nd interval between the 6th and 7th degrees).
和声小调音阶模式：全‑半‑全‑全‑半‑增二度‑半（升高七级音，六级与七级之间形成增二度）。
Melodic minor scale (ascending): T‑S‑T‑T‑T‑T‑S (raises both 6th and 7th degrees). Descending reverts to natural minor.
旋律小调音阶（上行）：全‑半‑全‑全‑全‑全‑半（升高六级和七级音）。下行恢复为自然小调。
2. Interval Recognition Formulas | 音程识别公式
Every interval can be measured by the number of semitones between two notes. Use this table for quick identification.
每个音程都可用两个音之间的半音数量来衡量。可用下表快速识别。
| Semitones | English Interval | 中文音程 |
|---|---|---|
| 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（三全音） |
| 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 invert an interval, subtract the number of semitones from 12, and the quality flips: major becomes minor, perfect remains perfect, augmented becomes diminished.
音程转位时，用 12 减去半音数，性质互换：大变小，小变大，纯仍是纯，增变减。
3. Triad Chord Construction Formulas | 三和弦构成公式
A triad is built by stacking two thirds on the root. The semitone pattern between root–third and third–fifth defines the quality.
三和弦由根音上叠加两个三度构成。根音到三音、三音到五音之间的半音模式决定和弦性质。
es (major 3rd) + 3 semitones (minor 3rd). Total root to fifth = 7 semitones (perfect 5th).
大三和弦：根音 + 4 个半音（大三度）+ 3 个半音（小三度）。根音到五音共 7 个半音（纯五度）。
oot + 3 semitones (minor 3rd) + 4 semitones (major 3rd). Root to fifth also = 7 semitones.
小三和弦：根音 + 3 个半音（小三度）+ 4 个半音（大三度）。根音到五音也是 7 个半音。
Diminished triad: root + 3 + 3 semitones. Root to fifth = 6 semitones (diminished 5th).
减三和弦：根音 + 3 + 3 个半音。根音到五音是 6 个半音（减五度）。
Augmented triad: root + 4 + 4 semitones. Root to fifth = 8 semitones (augmented 5th).
增三和弦：根音 + 4 + 4 个半音。根音到五音是 8 个半音（增五度）。
4. Seventh Chord Formulas | 七和弦公式
Seventh chords add a third above the fifth. The four‑note stacking determines the type.
七和弦在五音上方再叠加一个三度。四音堆叠的模式决定其类别。
or triad + major 3rd (root + 4 + 3 + 4 semitones). Root to 7th = 11 semitones (major 7th).
大七和弦：大三和弦 + 大三度（根音 + 4 + 3 + 4 个半音）。根音到七音 11 个半音（大七度）。
t 7th: major triad + minor 3rd (root + 4 + 3 + 3). Root to 7th = 10 semitones (minor 7th).
属七和弦：大三和弦 + 小三度（根音 + 4 + 3 + 3）。根音到七音 10 个半音（小七度）。
r 7th: minor triad + minor 3rd (root + 3 + 4 + 3). Root to 7th = 10 semitones (minor 7th).
小七和弦：小三和弦 + 小三度（根音 + 3 + 4 + 3）。根音到七音 10 个半音（小七度）。
Half‑diminished 7th (min7♭5): diminished triad + major 3rd (root + 3 + 3 + 4). Root to 7th = 10 semitones.
半减七和弦（小七减五）：减三和弦 + 大三度（根音 + 3 + 3 + 4）。根音到七音 10 个半音。
minished triad + minor 3rd (root + 3 + 3 + 3). Root to 7th = 9 semitones (diminished 7th).
减七和弦：减三和弦 + 小三度（根音 + 3 + 3 + 3）。根音到七音 9 个半音（减七度）。
5. Cadence Formulas | 终止式公式
Cadences are chord progressions that conclude a phrase. They follow standard Roman‑numeral formulas in a given key.
终止式是结束乐句的和弦进行，在某一调性中遵循固定的罗马数字公式。
Perfect cadence (authentic): V → I (or V7 → I). Sound: strong and conclusive.
完全终止（正格终止）：V → I（或 V7 → I）。听感：坚实、结束感强。
Plagal cadence: IV → I. Often called the "Amen" cadence.
变格终止：IV → I。常称为“阿门终止”。
perfect cadence (half): any chord → V (commonly I → V, II → V, IV → V). Sounds unfinished.
不完全终止（半终止）：任何和弦到 V（常见 I → V、II → V、IV → V）。听感未结束。
Interrupted cadence (deceptive): V → vi (or V → IV, V → VI in major; occasionally V → ♭VI). Surprises the listener.
阻碍终止（诈伪终止）：V → vi（或在大调中 V → IV、V → VI；偶尔 V → ♭VI）。带来意外感。
In minor keys, always use the harmonic minor scale to determine chord qualities (e.g. V is major, VII is diminished).
在小调中，必须使用和声小调来确定和弦性质（例如 V 为大三和弦，VII 为减三和弦）。
6. Chord Inversions & Figured Bass | 和弦转位与数字低音
When a note other than the root is the lowest, the chord is inverted. Figured bass shorthand tells you the intervals above the bass.
当最低音不是根音时，和弦即处于转位状态。数字低音简写标示了低音上方的音程。
Root position triads: no figures or simply written as I, ii, etc. The bass is the root.
三和弦原位：无数字或直接写 I、ii 等。低音即根音。
First inversion triads: 3rd in the bass. Figure: I⁶ (the 6 means a 6th above the bass). Built as root + 3rd in bass, with intervals of a 6th and 3rd.
三和弦第一转位：三音在低音。数字标记：I⁶（表示低音上方有六度音）。低音上方音程为六度和三度。
Second inversion triads: 5th in the bass. Figure: I⁶₄ (a 6th and a 4th above the bass).
三和弦第二转位：五音在低音。数字标记：I⁶₄（低音上方有四度和六度）。
Seventh chord inversions: 1st inversion – V⁶₅ (bass is the 3rd of the chord); 2nd inversion – V⁴₃ (bass is the 5th); 3rd inversion – V⁴₂ or V² (bass is the 7th).
七和弦转位：第一转位 – V⁶₅（低音为七和弦的三音）；第二转位 – V⁴₃（低音为五音）；第三转位 – V⁴₂ 或 V²（低音为七音）。
7. Key Signatures & Circle of Fifths | 调号与五度循环圈
Key signatures follow a strict order of sharps and flats. Sharps: F♯ C♯ G♯ D♯ A♯ E♯ B♯. Flats: B♭ E♭ A♭ D♭ G♭ C♭ F♭.
调号中的升降号有固定顺序。升号顺序：F♯ C♯ G♯ D♯ A♯ E♯ B♯。降号顺序：B♭ E♭ A♭ D♭ G♭ C♭ F♭。
The circle of fifths shows major keys and their relative minors. Each clockwise step adds one sharp (or removes one flat). Each anticlockwise step adds one flat (or removes one sharp). Relative minor is a minor 3rd below the major tonic.
五度循环圈展示了大调及其关系小调。顺时针每步增加一个升号（或去掉一个降号）；逆时针每步增加一个降号（或去掉一个升号）。关系小调的主音在大调主音下方小三度。
| Sharps/Flats | Major Key | Relative Minor |
|---|---|---|
| 0 | C major | A minor |
| 1♯ | G major | E minor |
| 2♯ | D major | B minor |
| 3♯ | A major | F♯ minor |
| 4♯ | E major | C♯ minor |
| 5♯ | B major | G♯ minor |
| 6♯ | F♯ major | D♯ minor |
| 7♯ | C♯ major | 广告 / Sponsored 英文原版 The Cambridge Companion to the Beatles 剑桥披头士乐队研究指南 剑桥音… 音乐 备考教辅 · 正版现货 · 与本文同科同级别 查看详情 / View on Taobao
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