GCSE Cambridge Music: Formula & Theorem Quick Reference Handbook | GCSE Cambridge 音乐：公式定理速查手册

📚 GCSE Cambridge Music: Formula & Theorem Quick Reference Handbook | GCSE Cambridge 音乐：公式定理速查手册

Welcome to your pocket-sized formula and theorem handbook for the Cambridge IGCSE Music syllabus. This guide condenses essential music theory rules – from interval arithmetic and scale patterns to chord spelling and cadence formulas – into clear, bilingual summaries. Each section presents a concept first in English, then followed immediately by its Chinese equivalent, ensuring you can revise effectively and build a solid foundation for both the listening and composing papers.

欢迎使用这本为剑桥 IGCSE 音乐大纲设计的公式与定理速查手册。手册将核心乐理规则——从音程算术、音阶模式到和弦拼写与终止式公式——浓缩成清晰的双语总结。每一小节先以英文呈现概念，紧接着给出对应的中文版本，帮助你高效复习，为听力与作曲考试打下坚实基础。

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1. Intervals: Semitone Count & Name | 音程：半音数与名称

An interval measures the pitch distance between two notes. The size in semitones determines its quality (perfect, major, minor, augmented, diminished). Use the table below to identify intervals quickly in both aural and score-based questions.

音程衡量两个音之间的音高距离。以半音数为单位的大小决定了音程的性质（纯、大、小、增、减）。使用下表可快速在听力与读谱题中识别音程。

Semitones	Interval Name (English) / 中文名称	Abbreviation
0	Perfect Unison / 纯一度	P1
1	Minor 2nd / 小二度	m2
2	Major 2nd / 大二度	M2
3	Minor 3rd / 小三度	m3
4	Major 3rd / 大三度	M3
5	Perfect 4th / 纯四度	P4
6	Augmented 4th / Diminished 5th / 增四度/减五度	A4/d5
7	Perfect 5th / 纯五度	P5
8	Minor 6th / 小六度	m6
9	Major 6th / 大六度	M6
10	Minor 7th / 小七度	m7
11	Major 7th / 大七度	M7
12	Perfect Octave / 纯八度	P8

iginal semitones. The quality pairings are: perfect ↔ perfect, major ↔ minor, augmented ↔ diminished.

记住：音程转位后，半音数 = 12 - 原半音数。性质配对规律为：纯 ↔ 纯，大 ↔ 小，增 ↔ 减。

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2. Scale Formulas | 音阶公式

Every scale is built from a fixed pattern of tones (T) and semitones (S). Memorising these formulas allows you to construct any major or minor scale without a key signature.

每种音阶都由固定的全音（T）与半音（S）模式构成。记住以下公式，即可在无调号的情况下构建任何大调或小调音阶。

Major Scale (Ionian): T – T – S – T – T – T – S

大调音阶（伊奥尼亚）：全 – 全 – 半 – 全 – 全 – 全 – 半

Natural Minor (Aeolian): T – S – T – T – S – T – T

自然小调（伊奥利亚）：全 – 半 – 全 – 全 – 半 – 全 – 全

Harmonic Minor: T – S – T – T – S – Augmented 2nd – S

和声小调：全 – 半 – 全 – 全 – 半 – 增二度 – 半

Melodic Minor (ascending): T – S – T – T – T – T – S
(descending = natural minor)

旋律小调（上行）：全 – 半 – 全 – 全 – 全 – 全 – 半
（下行同自然小调）

For the chromatic scale, simply fill every semitone step. The whole-tone scale uses only tones (T–T–T–T–T–T), while the pentatonic major omits the 4th and 7th degrees (use degrees 1,2,3,5,6).

半音阶填满每一个半音即可；全音音阶只使用全音（全–全–全–全–全–全）；大调五声音阶省略第四和第七级音（使用第1、2、3、5、6级）。

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

Key signatures are visual reminders of a scale's sharps or flats. Recognising them instantly is essential for score reading and dictation.

调号是音阶中升号或降号的视觉提示。快速识别调号对于读谱与听写至关重要。

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。

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。

Sharp keys: Tonic = last sharp + a semitone.

升号调：主音 = 最后一个升号升高半音。

Flat keys: Tonic = the penultimate flat (except F major = 1 flat).

降号调：主音 = 倒数第二个降号（F大调例外，只有一个降号）。

Use the circle of fifths to visualise the relationship among keys. Moving clockwise adds a sharp each time; moving anticlockwise adds a flat. The relative minor shares the same key signature and is found a minor third below the major tonic.

借助五度圈可直观各调关系。顺时针方向每次增加一个升号；逆时针方向每次增加一个降号。关系小调共享同一调号，位于大调主音下方小三度。

Major Key / 大调	Relative Minor / 关系小调	Sharps/Flats
C / C大调	A minor / a小调	0
G / G大调	E minor / e小调	1# (F#)
D / D大调	B minor / b小调	2# (F#, C#)
A / A大调	F# minor / 升f小调	3# (F#, C#, G#)
F / F大调	D minor / d小调	1b (Bb)
Bb / 降B大调	G minor / g小调	2b (Bb, Eb)
Eb / 降E大调	C minor / c小调	3b (Bb, Eb, Ab)

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4. Chords: Triads & Inversions | 和弦：三和弦与转位

A chord is a stack of intervals above a root. The four types of triads are built from combinations of major or minor thirds measured in semitones.

和弦是根音上方叠置的音程组成。三种弦（三和弦）的四类由大三度与小三度的半音组合决定。

Major triad: root + 4 semitones (M3) + 3 semitones (m3)

大三和弦：根音 + 4半音（大三度） + 3半音（小三度）

Minor triad: root + 3 semitones (m3) + 4 semitones (M3)

小三和弦：根音 + 3半音（小三度） + 4半音（大三度）

Augmented triad: root + 4 + 4 semitones

增三和弦：根音 + 4 + 4 半音

Diminished triad: root + 3 + 3 semitones

减三和弦：根音 + 3 + 3 半音

Inversions change the bass note while keeping the chord identity. Using Roman numerals in analysis, we add figures to indicate position: root position needs no figure; first inversion uses 6 (e.g. I⁶); second inversion uses 6/4 (I⁶₄). In popular chord symbols, inversions are shown using a slash: C/E means a C major chord with E in the bass.

转位在不改变和弦属性的同时变换低音。用罗马数字分析时，附加数字标记：原位不加数字；第一转位用⁶（如 I⁶）；第二转位用⁶₄（I⁶₄）。在流行和弦符号中，斜线表示转位：C/E 表示以 E 为低音的 C 大三和弦。

Dominant 7th chord formula: root + 4 + 3 + 3 semitones (major triad + minor 7th). Inversions follow similar figures: V⁷, V⁶₅, V⁴₃, V⁴₂ or V².

属七和弦公式：根音 + 4 + 3 + 3 半音（大三和弦 + 小七度）。转位标记类似：V⁷、V⁶₅、V⁴₃、V⁴₂ 或 V²。

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5. Cadences | 终止式

A cadence is a two-chord progression that ends a phrase. Identifying and labelling cadences is a core listening skill in the exam.

终止式是结束乐句的两个和弦进行。识别并标注终止式是考试的核心听力技能。

English / 中文	Chords / 和弦	Sound / 听感
Perfect / 正格终止	V – I	Finished, strong / 圆满、有力
Plagal / 变格终止	IV – I	Amen, church-like / 阿门、教会风格
Imperfect / 半终止	I/IV/ii – V	Pausing, unfinished / 暂停、未结束
Interrupted / 阻碍终止	V – vi (or VI)	Surprise, avoids expected I / 意外，避开预期主和弦

When tackling an exam question, listen for the final two chords of a phrase. A perfect cadence sounds resolute; an interrupted cadence sounds like a musical "twist". Minor keys may use V–I as a perfect cadence, often with a raised leading note.

做听力题时，注意乐句最后两个和弦。正格终止听感果断；阻碍终止听感如同音乐上的“转折”。小调中的正格终止常用 V–I，且常升高导音。

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6. Note Values, Rests & Dotted Rhythms | 音符、休止符与附点节奏

Understanding rhythmic notation is essential. The chart below shows the relative duration of notes and rests. A dot after a note adds half of its original value; a second dot adds half of the first dot's value.

理解节奏记谱至关重要。下表显示音符与休止符的相对时值。音符后的附点增加原时值的一半；双附点第二个附点增加第一个附点的一半。

Note / 音符	Rest / 休止符	Relative value / 相对时值	Dotted note value / 附点音符时值
Semibreve / 全音符	全休止符	4 beats	6 beats (4+2)
Minim / 二分音符	二分休止符	2 beats	3 beats (2+1)
Crotchet / 四分音符	四分休止符	1 beat	1½ beats (1+½)
Quaver / 八分音符	八分休止符	½ beat	¾ beat (½+¼)
Semiquaver / 十六分音符	十六分休止符	¼ beat	⅜ beat (¼+⅛)

Ties combine two notes of the same pitch, adding their values. Triplets divide a beat into three equal parts; write '3' above or below the notes.

延音线连接两个相同音高的音符，相加其时值。三连音将一拍均分为三份，在音符上方或下方标记“3”。

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7. Time Signatures & Metre | 拍号与节拍

The time signature tells you how many beats are in each bar (top number) and what note value gets one beat (bottom number). Metre groups strong and weak beats.

拍号告诉你每小节有几拍（上方数字）以及以何种音符为一拍（下方数字）。节拍

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