📚 IGCSE WJEC Music: Formula & Theorem Quick Reference Handbook | IGCSE WJEC 音乐：公式定理速查手册
In music, ‘formulas’ and ‘theorems’ take the form of scale patterns, chord-building rules, interval definitions, and rhythmic relationships. This quick reference handbook compiles the essential theoretical ‘formulas’ you need for the WJEC IGCSE Music syllabus, helping you to identify, construct, and analyse musical elements quickly and accurately.
在音乐中，“公式”和“定理”体现为音阶模式、和弦构建规则、音程定义和节奏关系。本速查手册汇编了 WJEC IGCSE 音乐课程所需的核心理论“公式”，帮助你快速准确地识别、构建和分析音乐元素。
1. Scale Formulas | 音阶公式
A major scale is built using the pattern of whole tones (T) and semitones (S): T – T – S – T – T – T – S. For example, in C major this gives the notes C, D, E, F, G, A, B, C.
大调音阶由全音（T）和半音（S）交替构成：T – T – S – T – T – T – S。例如 C 大调为 C、D、E、F、G、A、B、C。
The natural minor scale uses the pattern T – S – T – T – S – T – T. In A minor, this produces A, B, C, D, E, F, G, A.
自然小调采用模式 T – S – T – T – S – T – T。以 a 小调为例得到 A、B、C、D、E、F、G、A。
The harmonic minor scale raises the 7th degree by a semitone, creating an augmented 2nd interval between the 6th and 7th notes: T – S – T – T – S – 1½ – S in A minor: A, B, C, D, E, F, G♯, A.
和声小调将第 7 级升高半音，在第 6 与 7 音之间形成一个增二度：模式为 T – S – T – T – S – 1½ – S。a 和声小调：A、B、C、D、E、F、G♯、A。
The melodic minor scale ascends with a raised 6th and 7th (T – S – T – T – T – T – S) and descends as the natural minor. In A minor ascending: A, B, C, D, E, F♯, G♯, A; descending: A, G, F, E, D, C, B, A.
旋律小调上行时升高第 6 和第 7 级（T – S – T – T – T – T – S），下行时还原为自然小调。a 旋律小调上行：A、B、C、D、E、F♯、G♯、A；下行：A、G、F、E、D、C、B、A。
The major pentatonic scale removes the 4th and 7th degrees, using scale degrees 1, 2, 3, 5, 6. In C: C, D, E, G, A.
大调五声音阶去掉第 4 和第 7 级，使用音阶的第 1、2、3、5、6 级。C 大调五声音阶：C、D、E、G、A。
The blues scale adds a flattened 5th (blue note) to the minor pentatonic: 1, ♭3, 4, ♭5, 5, ♭7. In C: C, E♭, F, G♭, G, B♭.
布鲁斯音阶在小调五声音阶中加入降第 5 级（蓝音）：1, ♭3, 4, ♭5, 5, ♭7。C 布鲁斯音阶：C, E♭, F, G♭, G, B♭。
2. Chord Construction | 和弦构成
A major triad is built from a root, a major 3rd (4 semitones above the root) and a perfect 5th (7 semitones above the root). C major: C – E – G.
大三和弦由根音、大三度（距根音 4 个半音）和纯五度（距根音 7 个半音）构成。C 大三和弦：C – E – G。
A minor triad uses a root, a minor 3rd (3 semitones) and a perfect 5th (7 semitones). A minor: A – C – E.
小三和弦由根音、小三度（3 个半音）和纯五度（7 个半音）构成。a 小三和弦：A – C – E。
An augmented triad has a major 3rd (4 semitones) and an augmented 5th (8 semitones). C augmented: C – E – G♯.
增三和弦包含大三度（4 个半音）和增五度（8 个半音）。C 增三和弦：C – E – G♯。
A diminished triad stacks two minor 3rds (3 + 3 semitones). B diminished: B – D – F.
减三和弦堆叠两个小三度（3 + 3 个半音）。B 减三和弦：B – D – F。
A dominant 7th chord is a major triad plus a minor 7th (10 semitones from the root): C⁷ = C – E – G – B♭.
属七和弦是大三和弦叠加一个小七度（距根音 10 个半音）：C⁷ = C – E – G – B♭。
A major 7th chord adds a major 7th (11 semitones): Cmaj⁷ = C – E – G – B.
大七和弦加入大七度（11 个半音）：Cmaj⁷ = C – E – G – B。
A minor 7th chord combines a minor triad with a minor 7th: Am⁷ = A – C – E – G.
小七和弦是小三和弦加小七度：Am⁷ = A – C – E – G。
Chord inversions are named by the lowest note: root position (root in bass), 1st inversion (3rd in bass), 2nd inversion (5th in bass). For a 7th chord, 3rd inversion places the 7th in the bass.
和弦转位由最低音命名：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）。七和弦的第三转位将七音放在低音。
Major triad formula: Root + 4 semitones + 3 semitones
大三和弦公式：根音 + 4 个半音 + 3 个半音
3. Interval Identification | 音程识别
Interval quality and size are determined by the number of semitones between two notes. Here is a quick-reference table:
音程的性质与大小由两音之间的半音数决定。下面是速查表：
| Semitones / 半音数 | Interval Name / 音程名称 | Example from C / C 音上的例子 |
|---|---|---|
| 0 | Perfect Unison (P1) / 纯一度 | C – C |
| 1 | Minor 2nd (m2) / 小二度 | C – D♭ |
| 2 | Major 2nd (M2) / 大二度 | C – D |
| 3 | Minor 3rd (m3) / 小三度 | C – E♭ |
| 4 | Major 3rd (M3) / 大三度 | C – E |
| 5 | Perfect 4th (P4) / 纯四度 | C – F |
| 6 | Tritone (Augmented 4th / Diminished 5th) / 三全音 (增四度 / 减五度) | C – F♯ / G♭ |
| 7 | Perfect 5th (P5) / 纯五度 | C – G |
| 8 | Minor 6th (m6) / 小六度 | C – A♭ |
| 9 | Major 6th (M6) / 大六度 | C – A |
| 10 | Minor 7th (m7) / 小七度 | C – B♭ |
| 11 | Major 7th (M7) / 大七度 | C – B |
| 12 | Perfect Octave (P8) / 纯八度 | C – C |
To identify an interval, count the letter names to get the number (2nd, 3rd, etc.), then count the semitones to determine quality (major, minor, perfect, augmented, diminished).
要识别一个音程，先数音名字母得到度数（二度、三度等），然后数半音数确定性质（大、小、纯、增、减）。
4. Key Signatures & Circle of Fifths | 调号与五度圈
The circle of fifths arranges keys by the number of sharps or flats. Moving clockwise adds sharps: C (0♯), G (1♯: F♯), D (2♯: F♯, C♯), A (3♯: F♯, C♯, G♯), E (4♯), B (5♯), F♯ (6♯), C♯ (7♯). To find the major key from a sharp key signature, take the last sharp and go up a semitone.
五度圈将调性按升号或降号数量排列。顺时针方向增加升号：C (0♯)，G (1♯：F♯)，D (2♯：F♯、C♯)，A (3♯：F♯、C♯、G♯)，E (4♯)，B (5♯)，F♯ (6♯)，C♯ (7♯)。要从升号调识别大调，取最后一个升号再升一个半音即可。
Moving anticlockwise adds flats: C (0♭), F (1♭: B♭), B♭ (2♭: B♭, E♭), E♭ (3♭), A♭ (4♭), D♭ (5♭), G♭ (6♭), C♭ (7♭). The penultimate flat in the key signature gives the major key name (except F major with one flat). Relative minor keys share the same key signature and are found a minor 3rd below the major tonic.
逆时针方向增加降号：C (0♭)，F (1♭：B♭)，B♭ (2♭：B♭、E♭)，E♭ (3♭)，A♭ (4♭)，D♭ (5♭)，G♭ (6♭)，C♭ (7♭)。调号中倒数第二个降号即大调的主音（一个降号的 F 大调除外）。关系小调共享同一个调号，比大调主音低小三度。
A quick memory aid for sharp order: Father Charles Goes Down And Ends Battle (F♯, C♯, G♯, D♯, A♯, E♯, B♯). Flat order is the reverse: Battle Ends And Down Goes Charles’ Father (B♭, E♭, A♭, D♭, G♭, C♭, F♭).
升号顺序记忆法：Father Charles Goes Down And Ends Battle (F♯, C♯, G♯, D♯, A♯, E♯, B♯)。降号顺序与之相反：Battle Ends And Down Goes Charles’ Father (B♭, E♭, A♭, D♭, G♭, C♭, F♭)。
5. Time Signatures | 拍号公式
A time signature has two numbers. The upper number tells how many beats per bar; the lower number indicates the type of beat (4 = crotchet, 8 = quaver, 2 = minim).
拍号有两个数字。上方数字表示每小节的拍数；下方数字表示以哪种音符为一拍（4 = 四分音符，8 = 八分音符，2 = 二分音符）。
Simple time signatures have beats that divide naturally into two equal parts. Examples: 2/4 (two crotchet beats), 3/4, 4/4 (also written as C for common time).
单拍子的每拍可以自然地分为两个均等的部分。例如：2/4（两拍，每拍一拍四分音符），3/4，4/4（也可记为 C）。
Compound time signatures have beats that divide into three equal parts. The upper number is a multiple of 3 (6, 9, 12). To find the number of beats, divide the top number by 3. 6/8 = 2 dotted-crotchet beats per bar; 9/8 = 3 beats; 12/8 = 4 beats.
复拍子的每拍分为三个均等部分。上方数字为 3 的倍数（6、9、12）。要得到拍数，将上方数字除以 3。6/8 = 每小节两拍，每拍一个附点四分音符；9/8 = 三拍；12/8 = 四拍。
Irregular time signatures have 5, 7, or 11 beats grouped unevenly, e.g., 5/4 is often 3+2 or 2+3, 7/8 as 3+2+2 or 2+3+2.
不规则拍号有 5、7 或 11 拍，分成不均等的组合，例如 5/4 常为 3+2 或 2+3，7/8 为 3+2+2 或 2+3+2。
6. Note & Rest Relationships | 音符与休止符时值关系
Note values are based on a binary division system:
音符时值基于二分系统：
1 semibreve = 2 minims = 4 crotchets = 8 quavers = 16 semiquavers
1 个全音符 = 2 个二分音符 = 4 个四分音符 = 8 个八分音符 = 16 个十六分音符
A dotted note adds half of its original value. For example, a dotted crotchet (♩.) = 1½ beats (in simple time where a crotchet = 1 beat) and is equivalent to three quavers.
附点音符增加原时值的一半。例如，附点四分音符 (♩.) = 1½ 拍（在四分音符为一拍的单拍子中），相当于三个八分音符。
A triplet groups three notes in the time normally taken by two. For instance, a crotchet triplet in the time of two crotchets; a quaver triplet in the time of two quavers.
三连音表示用三个音符奏出常规两个音符的时值。例如，四分三连音原来为两个四分音符的时间，八分三连音为两个八分音符的时间。
Rests follow the same durations and their shapes are fixed: semibreve rest hangs from the 4th line, minim rest sits on the 3rd line, crotchet rest, quaver rest, etc.
休止符也遵循相同的时值，形状固定：全休止符挂在第四线下方，二分休止符坐在第三线上，还有四分休止符、八分休止符等。
7. Cadences | 终止式公式
A cadence is a progression of two chords at the end of a phrase. Four main types are tested in WJEC IGCSE Music:
终止式是乐句结尾处的两个和弦的进行。WJEC IGCSE 音乐中主要测试四种类型：
| Cadence / 终止式 | Chord Formula / 和弦公式 | Sound & Use / 听觉效果与用途 |
|---|---|---|
| Perfect (V–I) / 正格终止 | Dominant → Tonic | Strong, final; sounds complete. Both chords in root position for most conclusive effect. |
| Plagal (IV–I) / 变格终止 | Subdominant → Tonic | Amen cadence; softer, often used at end of hymns. |
| Imperfect (I–V, ii–V, IV–V) / 半终止 | Any chord → V | Unfinished, pauses on dominant; sounds like a question. |
| Interrupted (V–vi) / 阻碍终止 | V → vi (or VI) | Surprise; avoids expected tonic, moves to submediant (minor) instead. |
In a major key, V–I is dominant to tonic. In a minor key, the dominant chord is major (uses the raised 7th from harmonic minor), e.g., in A minor: E major to A minor.
在大调中，V–I 是属音到主音。在小调中，属和弦为大三和弦（使用和声小调中的升 7 级），例如 a 小调：E 大三和弦到 a 小三和弦。
8. Common Chord Progressions | 常见和声进行
The I – IV – V – I progression is the foundation of tonal harmony. In C major: C – F – G – C. This establishes the key clearly.
I – IV – V – I 进行是调性和声的基础。以 C 大调为例：C – F – G – C，清晰地确立了调性。
The 12-bar blues uses chords I, IV, V in a specific pattern, often with dominant 7ths: I – I – I – I – IV – IV – I – I – V – IV – I – V (or I). This formula is essential for improvisation and analysis.
12 小节布鲁斯使用 I、IV、V 和弦的特定模式，常搭配属七和弦：I – I – I – I – IV – IV – I – I – V – IV – I – V（或 I）。这一公式对即兴创作和分析都至关重要。
The circle progression (descending 5ths) is common in Baroque and Classical music: vi – ii – V – I (or iii – vi – ii – V – I). It provides strong root movement.
五度圈下行（下行五度）常见于巴洛克和古典音乐：vi – ii – V – I（或 iii – vi – ii – V – I）。其根音运动十分有力。
Cadential 6-4 progression (Ic – V – I) is a formula used to embellish the dominant. The tonic chord in second inversion resolves to the dominant, then to the tonic root position.
终止四六和弦进行（Ic – V – I）是用来装饰属功能的一种公式。主和弦第二转位解决到属和弦，再解决至原位主和弦。
9. Ornaments & Articulations | 装饰音与演奏法
Ornaments are melodic decorations written with specific symbols or small notes. Common formulas for performance:
装饰音是以特定符号或小音符写出的旋律装饰。常见的演奏公式如下：
| Ornament / 装饰音 | Symbol/Notation / 符号标记 | Performance Formula / 演奏公式 |
|---|---|---|
| Trill (颤音) | tr~~~~~ | Rapid alternation between the written note and the note a tone or semitone above, often starting on the upper note. |
| Mordent (波音) | Upper: zigzag line; Lower: zigzag with vertical line | Upper mordent: main note, upper neighbour, main note. Lower mordent: main note, lower neighbour, main note. |
| Turn (回音) | S-shaped symbol above note | Upper neighbour, main note, lower neighbour, main note. Can be inverted if symbol is
Published by TutorHao | IGCSE 音乐 Revision Series | aleveler.com 更多咨询请联系16621398022（同微信） CommentsMore posts |
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导