IGCSE Edexcel Music: Formula & Theorem Quick Reference Guide | IGCSE Edexcel 音乐：公式定理速查手册

📚 IGCSE Edexcel Music: Formula & Theorem Quick Reference Guide | IGCSE Edexcel 音乐：公式定理速查手册

This quick reference guide collects all the essential ‘formulas’ and ‘theorems’—from scale patterns and chord construction to cadences and key signatures—that you need to memorise for the IGCSE Edexcel Music exam. Use it as your last‑minute revision companion or a daily drill sheet.

本速查手册汇集了 IGCSE Edexcel 音乐考试中必须牢记的所有核心“公式”与“定理”——涵盖音阶模式、和弦构成、终止式及调号等。可用作考前冲刺或日常练习的贴身助手。

1. Scale Formulas | 音阶公式

Major scale: T – T – S – T – T – T – S (T=tone, S=semitone)

大调音阶：全 – 全 – 半 – 全 – 全 – 全 – 半

Natural minor scale: T – S – T – T – S – T – T

自然小调音阶：全 – 半 – 全 – 全 – 半 – 全 – 全

Harmonic minor scale: T – S – T – T – S – T+S – S (augmented 2nd between 6th and 7th)

和声小调音阶：全 – 半 – 全 – 全 – 半 – 增二度 – 半（第6级与第7级之间为增二度）

Melodic minor scale (ascending): T – S – T – T – T – T – S (raised 6th & 7th)

旋律小调音阶（上行）：全 – 半 – 全 – 全 – 全 – 全 – 半（升高第6、7级）

Pentatonic scale (major): intervals 1–2–3–5–6 (omit 4th and 7th)

五声音阶（大调）：音级 1–2–3–5–6（省略第4、7级）

Blues scale: 1–♭3–4–♯4–5–♭7 (adds ♯4/♭5 to minor pentatonic)

蓝调音阶：1–♭3–4–♯4–5–♭7（在小调五声音阶基础上添加♯4/♭5）

Whole-tone scale: T – T – T – T – T – T (six notes, all tones)

全音音阶：全 – 全 – 全 – 全 – 全 – 全（六个音，全为全音）

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2. Interval Quick Reference | 音程速查

Each interval is defined by the number of semitones and its quality (perfect, major, minor, augmented, diminished).

每个音程由半音数及音质（纯、大、小、增、减）定义。

Interval (English)	中文	Semitones
Perfect unison	纯一度	0
Minor 2nd	小二度	1
Major 2nd	大二度	2
Minor 3rd	小三度	3
Major 3rd	大三度	4
Perfect 4th	纯四度	5
Augmented 4th / Diminished 5th (tritone)	增四度/减五度（三全音）	6
Perfect 5th	纯五度	7
Minor 6th	小六度	8
Major 6th	大六度	9
Minor 7th	小七度	10
Major 7th	大七度	11
Perfect octave	纯八度	12

Inversion formula: invert the interval: perfect remains perfect, major ↔ minor, augmented ↔ diminished, and the sum of semitones equals 12.

音程转位公式：转位后纯仍为纯，大⇌小，增⇌减，半音数之和为12。

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3. Triad Construction | 三和弦构造

Major triad: Root + major 3rd (4 semitones) + perfect 5th (7 semitones). Example: C–E–G.

大三和弦：根音 + 大三度（4个半音） + 纯五度（7个半音）。例：C–E–G。

Minor triad: Root + minor 3rd (3 semitones) + perfect 5th (7 semitones). Example: A–C–E.

小三和弦：根音 + 小三度（3个半音） + 纯五度（7个半音）。例：A–C–E。

Diminished triad: Root + minor 3rd + diminished 5th (6 semitones). Example: B–D–F.

减三和弦：根音 + 小三度 + 减五度（6个半音）。例：B–D–F。

Augmented triad: Root + major 3rd + augmented 5th (8 semitones). Example: C–E–G♯.

增三和弦：根音 + 大三度 + 增五度（8个半音）。例：C–E–G♯。

Triad = Root + 3rd + 5th

三和弦 = 根音 + 三音 + 五音

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4. Seventh Chord Construction | 七和弦构造

Major 7th: Major triad + major 7th (11 semitones above root). Formula: M3 + m3 + M3.

大七和弦：大三和弦 + 大七度（距根音11个半音）。公式：大三度 + 小三度 + 大三度。

Dominant 7th: Major triad + minor 7th (10 semitones). Formula: M3 + m3 + m3.

属七和弦：大三和弦 + 小七度（10个半音）。公式：大三度 + 小三度 + 小三度。

Minor 7th: Minor triad + minor 7th. Formula: m3 + M3 + m3.

小七和弦：小三和弦 + 小七度。公式：小三度 + 大三度 + 小三度。

Half-diminished 7th (m7♭5): Diminished triad + minor 7th. Formula: m3 + m3 + M3.

半减七和弦（小七减五）：减三和弦 + 小七度。公式：小三度 + 小三度 + 大三度。

Diminished 7th: Diminished triad + diminished 7th (9 semitones). Formula: m3 + m3 + m3.

减七和弦：减三和弦 + 减七度（9个半音）。公式：小三度 + 小三度 + 小三度。

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5. Chord Inversions | 和弦转位

Inversions change the bass note while retaining the same chord tones. The figured bass system labels inversions using intervals above the bass.

转位改变低音但保留和弦音不变。数字低音用低音上方的音程标记转位。

Chord type	和弦类型	Root position	First inversion	Second inversion	Third inversion (7th chords)
Triad	三和弦	5/3 (e.g. I)	6/3 (e.g. I⁶)	6/4 (e.g. I⁶⁴)	N/A
7th chord	七和弦	7 (e.g. V⁷)	6/5 (e.g. V⁶⁵)	4/3 (e.g. V⁴³)	4/2 (e.g. V⁴² or V²)

To identify an inversion, examine the interval between the lowest note and the root: root position has the root in the bass; 1st inversion has the 3rd; 2nd inversion has the 5th; 3rd inversion has the 7th (for seventh chords).

识别转位：看最低音与根音的关系——原位根音在低音；第一转位三音在低音；第二转位五音在低音；第三转位七音在低音（七和弦）。

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6. Key Signatures & Circle of Fifths | 调号与五度圈

The circle of fifths organises keys by ascending fifths (clockwise) adding sharps, and descending fifths (counter‑clockwise) adding flats.

五度圈通过上行五度（顺时针）增加升号，下行五度（逆时针）增加降号来组织调性。

Order of sharps: F♯ – C♯ – G♯ – D♯ – A♯ – E♯ – B♯ (Father Charles Goes Down And Ends Battle)

升号顺序：F♯ – C♯ – G♯ – D♯ – A♯ – E♯ – B♯（发哆嗦来拉米西）

Order of flats: B♭ – E♭ – A♭ – D♭ – G♭ – C♭ – F♭ (Battle Ends And Down Goes Charles’ Father)

降号顺序：B♭ – E♭ – A♭ – D♭ – G♭ – C♭ – F♭（西米拉来唆哆发）

To find the relative minor, go down a minor 3rd (3 semitones) from the major tonic. Example: C major → A minor.

找关系小调：从大调主音向下小三度（3个半音）。例：C大调→a小调。

Major key / 大调	Sharps/升号数	Minor key / 小调
C	0	A minor
G	1♯	E minor
D	2♯	B minor
A	3♯	F♯ minor
E	4♯	C♯ minor
B	5♯	G♯ minor
F♯	6♯	D♯ minor

Similarly for flats: F (1♭, D minor), B♭ (2♭, G minor), E♭ (3♭, C minor), A♭ (4♭, F minor), D♭ (5♭, B♭ minor), G♭ (6♭, E♭ minor).

降号调同理：F（1♭，d小调），B♭（2♭，g小调），E♭（3♭，c小调），A♭（4♭，f小调），D♭（5♭，b♭小调），G♭（6♭，e♭小调）。

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7. Rhythm Formulas & Time Signatures | 节奏公式与节拍

Time signature breakdown: top number = beats per bar; bottom number = note value that gets one beat (4 = crotchet, 8 = quaver, 2 = minim).

拍号解析：上方数字 = 每小节拍数；下方数字 = 以何种音符为一拍（4＝四分音符，8＝八分音符，2＝二分音符）。

Simple time: each beat divides into two equal parts (e.g., 2/4, 3/4, 4/4). Compound time: each beat divides into three equal parts (e.g., 6/8, 9/8, 12/8).

单拍子：每拍均分为两份（如2/4、3/4、4/4）。复拍子：每拍均分为三份（如6/8、9/8、12/8）。

Note‑value pyramid:

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

Dotted notes: a dot adds half the value of the original note. Dotted minim = 3 crotchets; dotted crotchet = 3 quavers.

附点音符：附点增加原音符时值的一半。附点二分音符 = 3个四分音符；附点四分音符 = 3个八分音符。

Triplet formula: three notes played in the time of two of the same kind. A triplet quaver group equals one crotchet beat.

三连音公式：三个音在原本两个相同音符的时值内演奏。一组八分三连音等于一个四分音符的拍值。

Syncopation: emphasising weak beats or off‑beats, often tied across the barline.

切分音：强调弱拍或弱

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