Year 11 CAIE Music: Quick Reference Handbook of Formulas and Rules | Year 11 CAIE 音乐：公式定理速查手册

📚 Year 11 CAIE Music: Quick Reference Handbook of Formulas and Rules | Year 11 CAIE 音乐：公式定理速查手册

This rapid-reference guide summarises the essential ‘formulas’ and theoretical rules for Year 11 CAIE IGCSE Music. Use it to revise pitch notation, scales, intervals, chords, rhythm, key signatures, musical terms, forms, textures and compositional devices.

本速查手册总结了 Year 11 CAIE IGCSE 音乐最核心的理论“公式”与规则，涵盖音高记谱、音阶、音程、和弦、节拍、调号、音乐术语、曲式、织体和作曲技法，是考前快速回顾的理想材料。

1. Pitch and Notation | 音高与记谱法

The staff consists of five lines and four spaces. Notes are placed on lines or in spaces to indicate pitch. Ledger lines extend the staff upwards or downwards.

五线谱由五条线和四个间组成。音符放在线上或间内以表示音高。加线用于向上或向下扩展谱表。

A clef assigns fixed pitches to the lines and spaces. The treble clef (𝄞) fixes G above middle C on the second line; the bass clef (𝄢) fixes F below middle C on the fourth line. The alto clef fixes middle C on the third line and is used mainly by the viola.

谱号赋予线和间固定的音高。高音谱号 (𝄞) 将中央C上方的G定在第二线；低音谱号 (𝄢) 将中央C下方的F定在第四线。中音谱号将中央C定在第三线，主要用于中提琴。

Accidentals alter pitch for a note: a sharp ♯ raises it by a semitone; a flat ♭ lowers it by a semitone; a natural ♮ cancels any previous accidental. Double sharp (𝄪) and double flat (𝄫) raise or lower by two semitones respectively.

变音记号改变音符的音高：升号 ♯ 升高半音；降号 ♭ 降低半音；还原号 ♮ 取消先前的变音记号。重升号 (𝄪) 和重降号 (𝄫) 分别升高或降低两个半音。

2. Scale Formulas | 音阶公式

Scales are stepwise patterns of whole tones (W) and semitones (H). The octave is divided into twelve equal semitones in modern equal temperament.

音阶是按级进排列的全音(W)与半音(H)模式。在当今平均律中，一个八度被分为十二个相等的半音。

Major scale: W – W – H – W – W – W – H

大调音阶：全 – 全 – 半 – 全 – 全 – 全 – 半

Natural minor: W – H – W – W – H – W – W

自然小调：全 – 半 – 全 – 全 – 半 – 全 – 全

Harmonic minor: W – H – W – W – H – A2 – H
(A2 = augmented 2nd, e.g. F to G♯ in A harmonic minor)

和声小调：全 – 半 – 全 – 全 – 半 – 增二度 – 半
(增二度，如a和声小调中的F到G♯)

Melodic minor (ascending): W – H – W – W – W – W – H
(descending uses natural minor)

旋律小调（上行）：全 – 半 – 全 – 全 – 全 – 全 – 半
(下行用自然小调)

The chromatic scale moves entirely by semitones. Pentatonic scales use five notes (e.g. C–D–E–G–A): W–W–m3–W–m3.

半音阶全部由半音构成。五声音阶使用五个音（如 C–D–E–G–A），其音程模式为全–全–小三度–全–小三度。

3. Intervals | 音程

An interval is the distance in pitch between two notes. It consists of a number (2nd, 3rd, 4th, etc.) and a quality (major, minor, perfect, augmented, diminished).

音程是两个音在音高上的距离，由度数（二度、三度、四度等）和性质（大、小、纯、增、减）构成。

To find interval quality:
Count the letter names to get the number. Then count semitones to determine quality. Inversion reverses intervals: a 3rd becomes a 6th, major becomes minor, augmented becomes diminished, and perfect stays perfect.

确定音程性质：先数音名得出度数，再数半音确定性质。转位会翻转音程：三度变六度，大音程变小音程，增变减，纯音程仍为纯。

Common interval formulas in semitones:
Perfect unison: 0 · Minor 2nd: 1 · Major 2nd: 2 · Minor 3rd: 3 · Major 3rd: 4 · Perfect 4th: 5 · Augmented 4th/Diminished 5th: 6 · Perfect 5th: 7 · Minor 6th: 8 · Major 6th: 9 · Minor 7th: 10 · Major 7th: 11 · Octave: 12.

常用音程半音数：纯一度 0 · 小二度 1 · 大二度 2 · 小三度 3 · 大三度 4 · 纯四度 5 · 增四度/减五度 6 · 纯五度 7 · 小六度 8 · 大六度 9 · 小七度 10 · 大七度 11 · 八度 12。

4. Chord Formulas | 和弦公式

A triad consists of a root, a third and a fifth. The quality is determined by the intervals above the root.

三和弦由根音、三音和五音构成，其性质取决于根音上方的音程。

Major triad = Root + Major 3rd (4 semitones) + Perfect 5th (7 semitones)

大三和弦 = 根音 + 大三度（4半音）+ 纯五度（7半音）

Minor triad = Root + Minor 3rd (3 semitones) + Perfect 5th (7 semitones)

小三和弦 = 根音 + 小三度（3半音）+ 纯五度（7半音）

Diminished triad = Root + Minor 3rd + Diminished 5th (6 semitones)

减三和弦 = 根音 + 小三度 + 减五度（6半音）

Augmented triad = Root + Major 3rd + Augmented 5th (8 semitones)

增三和弦 = 根音 + 大三度 + 增五度（8半音）

Seventh chords add a fourth note above the root. The dominant 7th chord formula: Root + Major 3rd + Perfect 5th + Minor 7th. Common inversions: root position (5/3), first inversion (6/3), second inversion (6/4); for seventh chords, the third inversion adds (4/2).

七和弦在根音上方再加上第四个音。属七和弦公式：根音 + 大三度 + 纯五度 + 小七度。常见转位：原位（5/3）、第一转位（6/3）、第二转位（6/4）；七和弦还有第三转位（4/2）。

5. Rhythm and Time Signatures | 节奏与拍号

A time signature tells how many beats are in a bar (top number) and what note value counts as one beat (bottom number). Simple time divides the beat into two equal parts; compound time divides the beat into three.

拍号表示每小节有几拍（上方数字）以及以何种音符为一拍（下方数字）。单拍子将一拍平分为二，复拍子将一拍平分为三。

Simple duple: 2/4, 2/2 · Simple triple: 3/4, 3/2 · Simple quadruple: 4/4 (C), 4/2
单二拍子：2/4, 2/2 · 单三拍子：3/4, 3/2 · 单四拍子：4/4 (C), 4/2
Compound duple: 6/8 · Compound triple: 9/8 · Compound quadruple: 12/8
复二拍子：6/8 · 复三拍子：9/8 · 复四拍子：12/8

Note value relationships (British terms): semibreve = 4 beats, minim = 2, crotchet = 1, quaver = ½, semiquaver = ¼. Dots add half the value of the preceding note. A tie joins two notes of the same pitch, adding their durations.

音符时值关系：全音符 4拍，二分音符 2拍，四分音符 1拍，八分音符 ½拍，十六分音符 ¼拍。附点增加前面音符时值的一半。延音线连接两个相同音高的音符，将时值相加。

Syncopation shifts the accent to a weak beat or off-beat. Triplets fit three notes in the time normally taken by two.

切分音将重音移到弱拍或弱位。三连音在通常两拍的时值内均匀演奏三个音。

6. Key Signatures and the Circle of Fifths | 调号与五度循环

A key signature shows which notes are to be consistently played sharp or flat. Major and minor keys share key signatures (relative pairs), but the tonic differs. The circle of fifths organises keys by ascending fifths.

调号表示哪些音需持续升高或降低。大调与其关系小调共用调号，但主音不同。五度循环按上行五度排列调性。

Sharp major keys (order of sharps: F♯ C♯ G♯ D♯ A♯ E♯ B♯): C – 0; G – 1♯ (F♯); D – 2♯ (F♯ C♯); A – 3♯; E – 4♯; B – 5♯; F♯ – 6♯; C♯ – 7♯.

升号大调（升号顺序：F♯ C♯ G♯ D♯ A♯ E♯ B♯）：C调 0升；G调 1升（F♯）；D调 2升（F♯ C♯）；A调 3升；E调 4升；B调 5升；F♯调 6升；C♯调 7升。

Flat major keys (order of flats: B♭ E♭ A♭ D♭ G♭ C♭ F♭): C – 0; F – 1♭ (B♭); B♭ – 2♭ (B♭ E♭); E♭ – 3♭; A♭ – 4♭; D♭ – 5♭; G♭ – 6♭; C♭ – 7♭.

降号大调（降号顺序：B♭ E♭ A♭ D♭ G♭ C♭ F♭）：C调 0降；F调 1降（B♭）；B♭调 2降（B♭ E♭）；E♭调 3降；A♭调 4降；D♭调 5降；G♭调 6降；C♭调 7降。

Relative minors lie a minor third below the major tonic. For example, A minor is the relative of C major. To find the tonic of a major flat key: the penultimate flat is the tonic. For sharp keys: the last sharp is the leading note (semitone below tonic).

关系小调的主音在大调主音下方小三度。例如，a小调是C大调的关系小调。识别降号大调主音：倒数第二个降号即主音。升号大调：最后一个升号是导音（主音下方半音）。

7. Musical Terms and Directions | 音乐术语与表情记号

Understanding Italian terms is essential for interpreting tempo, dynamics and expression. The following table lists common terms.

理解意大利术语对解读速度、力度和表情至关重要。下表列出常见术语。

Term	中文	Meaning
Largo	广板	Very slow, broad
Adagio	柔板	Slow and stately
Andante	行板	At a walking pace
Moderato	中板	Moderate speed
Allegro	快板	Fast, cheerful
Vivace	活板	Lively and fast
Presto	急板	Very fast
Ritardando (rit.)	渐慢	Gradually slower
Accelerando (accel.)	渐快	Gradually faster
A tempo	回原速	Return to original speed

Dynamics abbreviations: pp (pianissimo, very soft), p (piano, soft), mp (mezzo-piano, moderately soft), mf (mezzo-forte, moderately loud), f (forte, loud), ff (fortissimo, very loud). Crescendo (cresc.) means gradually louder; diminuendo (dim.) or decrescendo means gradually softer.

力度记号缩写：pp (很弱), p (弱), mp (中弱), mf (中强), f (强), ff (很强)。Crescendo (渐强) 表示逐渐变强；diminuendo 或 decrescendo (渐弱) 表示逐渐减弱。

8. Forms and Structure | 曲式与结构

Binary form (AB) has two contrasting sections, each usually repeated. Ternary form (ABA) returns to the opening material after a contrasting middle section. Minuet and trio often follow an AABB structure with ternary design.

二段体 (AB) 包含两个对比乐段，各段通常重复。三段体 (ABA) 在对比中段后回归开头素材。小步舞曲与三声中部常为AABB结构，但具有三段体框架。

Rondo form alternates a main theme (A) with contrasting episodes: ABACA or ABACABA. Theme and variations presents a main theme followed by several altered versions (changes in rhythm, harmony, texture, modality, etc.).

回旋曲式是主部主题(A)与对比插部交替出现，如ABACA 或 ABACABA。主题与变奏先呈示主题，随后呈现多个改变的版本（变化节奏、和声、织体、调式等）。

Sonata form (often used in first movements of classical symphonies) has three main sections: exposition (first subject in tonic, second subject in dominant or relative major), development, and recapitulation (subjects in tonic).

奏鸣曲式（常见于古典交响曲第一乐章）包含呈示部（第一主题在主调，第二主题在属调或关系大调）、展开部和再现部（主题均回归主调）。

Strophic form uses the same music for every verse (AAA), common in folk songs. Through-composed music has no large-scale repetition.

分节歌 (AAA) 每段歌词用相同旋律，常见于民歌。通体歌没有大型重复，音乐持续发展。

9. Texture and Ensemble | 织体与合奏

Monophonic texture consists of a single unaccompanied melodic line. Homophonic texture features a dominant melody supported by chordal accompaniment (hymns, most pop songs).

单音织体由单一无伴奏的旋律线条构成。主调织体有一个主旋律，配以和弦伴奏（如赞美诗、多数流行歌曲）。

Polyphonic (contrapuntal) texture combines two or more independent melodic lines of equal or near-equal importance. Imitative polyphony includes canon and fugue. Heterophonic texture happens when two parts play the same melody with slight variations simultaneously (common in some world music traditions).

复调织体结合两条或以上相对独立的旋律线条。模仿式复调包括卡农和赋格。支声织体指两个声部同时演奏同一旋律但有细微变化，常见于某些世界音乐传统。

Common ensemble types: string quartet (2 violins, viola, cello), piano trio (violin, cello, piano), wind quintet (flute, oboe, clarinet, bassoon, horn), orchestra (strings, woodwind, brass, percussion).

常见合奏形式：弦乐四重奏（两把小提琴、中提琴、大提琴），钢琴三重奏（小提琴、大提琴、钢琴），木管五重奏（长笛、双簧管、单簧管、大管、圆号），管弦乐队（弦乐、木管、铜管、打击乐）。

10. Compositional Devices | 作曲技法

A sequence is the repetition of a melodic phrase at a higher or lower pitch. If the intervals are exactly maintained it is a real sequence; a tonal sequence stays within the key.

模进是将一个旋律片段在更高或更低的音高上重复。严格模进精确保持音程关系；调性模进保持在调内，音程大小可能变化。

Imitation is the overlapping repetition of a melody in a different voice, often at the unison or octave. Inversion flips the melody upside-down (ascending intervals become descending and vice versa). Retrograde plays the melody backwards.

模仿是旋律在另一个声部叠入重复，常在同度或八度。倒影将旋律上下翻转（上行音程变下行，反之亦然）。逆行将旋律逆向演奏。

An ostinato is a persistently repeated melodic, rhythmic or harmonic figure. A pedal (or drone) is a sustained or repeated note, usually in the bass, above which harmonies change.

固定音型是持续重复的旋律、节奏或和声片段。持续音（或长音）是保持或重复的音，通常在低音部，其上方的和声不断变化。

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Year 11 CAIE Music: Quick Reference Handbook of Formulas and Rules | Year 11 CAIE 音乐：公式定理速查手册