CIE A-Level Music: Formula & Theorem Quick Reference | CIE A-Level 音乐：公式定理速查手册

📚 CIE A-Level Music: Formula & Theorem Quick Reference | CIE A-Level 音乐：公式定理速查手册

This guide compiles the essential ‘formulas’ and ‘theorems’ of A-Level Music for the CIE syllabus – the fundamental rules, structures, and terminology that underpin every composition, analysis, and performance task. Treat these elements like mathematical equations: once memorised and understood, they enable you to decode any musical texture, recognise stylistic fingerprints, and construct coherent arguments in both written and practical examinations.

本手册汇编了 CIE A-Level 音乐课程的核心“公式”与“定理”——即支撑所有作曲、分析和演奏任务的基本规则、结构及术语。将这些元素视为数学方程式：一旦熟记并理解，便能解读任何音乐织体、识别风格特征，并在笔试和实践考核中构建条理清晰的论证。

1. Note Values & Rests | 音符时值与休止符

In simple time, a semibreve (whole note) equals two minims, four crotchets, eight quavers, or sixteen semiquavers. Dotted notes add half of the original value; double dots add three-quarters. Rests follow the same durational hierarchy, with a whole-bar rest always written as a semibreve rest hanging from the fourth line, even in 3/4 time.

在单拍子中，全音符等于两个二分音符、四个四分音符、八个八分音符或十六个十六分音符。附点音符增加原时值的一半；双附点增加四分之三。休止符遵循相同的时值层级，整小节休止始终以悬挂在第四线上的全休止符表示，即使是在 3/4 拍中也不例外。

A triplet groups three notes into the time normally occupied by two, indicated by a bracketed ‘3’. Irregular groupings like duplets (two in the time of three) and quintuplets follow the same logic. In compound time, the beat naturally divides into three, so a dotted crotchet beat equals three quavers.

三连音将三个音符压缩进通常由两个音符占据的时值，用带“3”的弧线标示。二连音（两个音符代替三个）和五连音等不规则组合遵循相同逻辑。在复拍子中，拍点自然三等分，因此一个附点四分音符拍等于三个八分音符。

2. Time Signatures & Metre | 拍号与节拍

Simple time signatures (2/4, 3/4, 4/4) have an upper number indicating beats per bar and a lower number showing the note value of one beat (4 = crotchet). Compound time signatures (6/8, 9/8, 12/8) have a dotted note as the beat; the upper number divided by three gives the number of beats. Irregular metres like 5/4 or 7/8 combine simple and compound groupings, e.g., 7/8 often alternates 2+2+3 or 3+2+2 quavers.

单拍子（2/4, 3/4, 4/4）以上方数字表示每小节拍数，下方数字表示一拍所对应的音符时值（4 = 四分音符）。复拍子（6/8, 9/8, 12/8）以附点音符为一拍；上方数字除以 3 即得拍数。不规则节拍如 5/4 或 7/8 混合单拍子与复拍子的组合，例如 7/8 经常以 2+2+3 或 3+2+2 的八分音符分组交替出现。

Anacrusis (upbeat) is an incomplete bar at the start of a phrase, while syncopation shifts the accent off the strong beat. Hemiola, common in Baroque dance movements, superimposes two beats of three over three beats of two, creating a sense of metric cross-rhythm.

弱起（上拍）是乐句起始处的不完整小节，切分则将重音从强拍移开。赫米奥拉（Hemiola）常见于巴洛克舞曲乐章，在三拍子的结构中叠加两拍子，制造节拍交错感。

3. Key Signatures & Scale Patterns | 调号与音阶模式

The circle of fifths orders keys by their sharps or flats. Major keys: C (none), G (F♯), D (F♯ C♯) … up to C♯ major (seven sharps). Flat keys: F (B♭), B♭ (B♭ E♭) … to C♭ major (seven flats). Relative minors share the same key signature; the natural minor scale (Aeolian) lowers the 3rd, 6th, and 7th degrees compared to its parallel major. The harmonic minor raises the 7th, and the melodic minor raises the 6th and 7th ascending, reverting to natural minor descending.

五度圈按升号或降号数量排列调性。大调：C（无），G（F♯），D（F♯ C♯）……直至 C♯ 大调（七个升号）。降号调：F（B♭），B♭（B♭ E♭）……至 C♭ 大调（七个降号）。关系小调共享同一调号；自然小调（伊奥利亚）较其同主音大调降低第 3、6、7 级音。和声小调升高第 7 级，旋律小调上行升高第 6、7 级，下行还原为自然小调。

Modes provide alternative tonal colours: Dorian (white notes D–D) has a raised 6th compared to natural minor; Phrygian (E–E) a lowered 2nd; Lydian (F–F) a raised 4th; Mixolydian (G–G) a lowered 7th. Pentatonic scales (five notes) omit the 4th and 7th (major) or the 2nd and 6th (minor). Whole-tone scales are hexatonic and symmetrical; chromatic scales contain all twelve semitones.

调式提供不同的音色色彩：多利亚调式（白键 D–D）与自然小调相比有升高的第 6 级；弗里几亚（E–E）有降低的第 2 级；利底亚（F–F）有升高的第 4 级；混合利底亚（G–G）有降低的第 7 级。五声音阶（五个音）省略第 4、7 级（大调）或第 2、6 级（小调）。全音音阶为六音对称音阶；半音音阶包含全部十二个半音。

4. Intervals | 音程

Intervals are measured numerically by staff positions and qualitatively by semitone count. A perfect unison = 0 semitones, perfect 4th = 5 semitones, perfect 5th = 7 semitones, perfect octave = 12 semitones. Augmented intervals are one semitone wider than perfect or major; diminished intervals are one semitone narrower than perfect or minor. The tritone (augmented 4th / diminished 5th) spans 6 semitones and is a crucial element in dominant 7th chords and chromatic harmony.

音程的度数依谱表位置计算，性质按半音数确定。纯一度 = 0 个半音，纯四度 = 5 个半音，纯五度 = 7 个半音，纯八度 = 12 个半音。增音程比纯或大音程宽一个半音；减音程比纯或小音程窄一个半音。三全音（增四度 / 减五度）跨 6 个半音，是属七和弦与半音化和声中的关键元素。

Compound intervals exceed an octave: a 9th is a compound 2nd, a 10th a compound 3rd, etc. Consonant intervals (3rds, 6ths, perfect consonances) need no resolution; dissonant intervals (2nds, 7ths, all augmented/diminished) require resolution according to common-practice rules.

复音程超过八度：九度是复二度，十度是复三度，依此类推。协和音程（三度、六度、完全协和音程）无需解决；不协和音程（二度、七度、所有增减音程）按共性写作规则需解决。

5. Chord Construction & Harmonic Progressions | 和弦构成与和声进行

Triads are built by stacking thirds: major triad = major 3rd + minor 3rd (e.g., C–E–G); minor triad = minor 3rd + major 3rd (C–E♭–G); diminished triad = two minor 3rds (C–E♭–G♭); augmented triad = two major 3rds (C–E–G♯). Figured bass indicates inversions: root position (5/3, often unmarked), first inversion (6), second inversion (6/4). In a dominant 7th chord, the 7th is a minor 7th above the root; inversions are 6/5, 4/3, and 4/2.

三和弦由三度叠置构成：大三和弦 = 大三度 + 小三度（如 C–E–G）；小三和弦 = 小三度 + 大三度（C–E♭–G）；减三和弦 = 两个小三度（C–E♭–G♭）；增三和弦 = 两个大三度（C–E–G♯）。数字低音标示转位：原位（5/3，常省略），第一转位（6），第二转位（6/4）。在属七和弦中，七音与根音成小七度；转位标记为 6/5、4/3 和 4/2。

Functional harmony follows the order I–IV–V–I (tonic–subdominant–dominant–tonic). Common-practice rules govern voice-leading: avoid parallel fifths and octaves; double the root in root position, the soprano note (often the 3rd or root) in first inversion, and the bass note (5th) in second inversion. The leading note (7th degree) resolves upwards to the tonic.

功能和声遵循 I–IV–V–I（主–下属–属–主）的顺序。共性写作规则支配声部进行：避免平行五度和八度；原位时重复根音，第一转位重复旋律音（常为三音或根音），第二转位重复低音（五音）。导音（第 7 级音）上行解决到主音。

6. Cadences | 终止式

Perfect cadence (V–I, or V⁷–I) provides a strong full close; both chords are typically in root position, and the tonic is in the soprano of the final chord. Imperfect cadence (any chord to V) sounds unfinished, often ending on the dominant. Plagal cadence (IV–I) is the ‘Amen’ cadence and gives a softer close. Interrupted cadence (V–vi) deceives the ear by resolving to the submediant instead of the tonic.

完全终止（V–I 或 V⁷–I）给出强烈的完全收束；两和弦通常为原位，且主音位于终止和弦的旋律位置。不完全终止（任何和弦到 V）听感未结束，常收束于属和弦。变格终止（IV–I）即“阿门”终止，提供较柔和的收束。阻碍终止（V–vi）以解决至下中音而非主音，造成听觉上的意外。

In Baroque music, a Phrygian half-cadence (iv⁶–V) in minor keys is common, with the bass descending by a semitone (e.g., F–E in A minor). The Tierce de Picardie is a major tonic chord at the final cadence of a piece in a minor key, providing a brighter conclusion.

在巴洛克音乐中，小调的弗里几亚半终止（iv⁶–V）常见，低音下行半音（如 A 小调中 F–E）。辟卡迪三度（Tierce de Picardie）是在小调作品终止处使用大主和弦，赋予更明亮的结尾。

7. Melodic Construction & Motifs | 旋律构建与动机

A phrase is a musical sentence often built in two- or four-bar units, ending with a cadence. Period structure (antecedent + consequent) creates a question-answer relationship, commonly 4+4 bars. Sequences repeat a melodic pattern at higher or lower pitch levels; a real sequence exactly transposes intervals, while a tonal sequence adjusts intervals to stay within the key.

乐句是音乐的句子，常以二或四小节为单位，以终止式收束。乐段结构（前句 + 后句）形成问答关系，常见为 4+4 小节。模进将旋律模式在更高或更低的音高重复；完全模进精确移调音程，而守调模进调节音程以保持在调性内。

Motivic development techniques include augmentation (lengthening note values), diminution (shortening), inversion (mirroring intervals), retrograde (reversing order), and fragmentation (extracting part of a motif). In the Classical style, diatonic melodies predominate with regular phrasing, while Romantic melodies feature wider leaps, chromaticism, and longer spans.

动机发展技法包括时值扩大（加长音符）、时值缩小（缩短）、倒影（音程镜像）、逆行（顺序反转）和分裂（提取动机的一部分）。在古典风格中，自然音阶旋律占主导，分句规整；而浪漫派旋律则突出更大的跳进、半音化和更长的线条。

8. Texture & Part-Writing | 织体与声部写作

Monophony is a single unaccompanied line. Homophony involves a melody with chordal accompaniment; melody-dominated homophony places the main tune in the highest voice. Polyphony (counterpoint) involves two or more independent melodic lines; imitative counterpoint uses the same melodic material at staggered entries (e.g., canon, fugue). Antiphonal texture alternates between two groups of performers.

单声织体为单一无伴奏线条。主调织体包含旋律及其和弦伴奏；旋律支配的主调织体将主旋律置于最高声部。复调（对位）包含两条或以上独立旋律线；模仿式对位将相同旋律材料在不同时间点进入（如卡农、赋格）。应答轮唱织体在两组合奏者之间交替。

In four-part Bach chorale style, the soprano carries the melody, alto and tenor fill inner harmonies, and bass provides the harmonic foundation. Rules: no voice crossing (S>A>T>B ranges must be preserved), no overlapping of adjacent voices, and spacing within an octave between upper three voices in close position.

在四声部巴赫众赞歌风格中，女高音承载旋律，女中音和男高音填充内声部和声，男低音提供和声基础。规则：不得出现声部交叉（S>A>T>B 的音域需保持），相邻声部不重叠，且在密集排列中上三声部间距离保持在一个八度内。

9. Instrumentation & Timbre | 乐器法与音色

The standard Classical orchestra consists of strings (violins I/II, violas, cellos, double basses), woodwinds (flutes, oboes, clarinets, bassoons), brass (horns, trumpets, trombones—added later, tuba in Romantic), and percussion (timpani). Transposing instruments notate at a different pitch than sounding: clarinet in B♭ sounds a major 2nd lower; horn in F sounds a perfect 5th lower; trumpet in B♭ sounds a major 2nd lower. Alto saxophone in E♭ sounds a major 6th lower.

标准古典管弦乐团编制为弦乐（小提琴 I/II、中提琴、大提琴、低音提琴）、木管（长笛、双簧管、单簧管、大管）、铜管（圆号、小号、长号——后加入，浪漫派加入大号）及打击乐（定音鼓）。移调乐器记谱音高与实际音高不同：降 B 调单簧管发音低大二度；F 调圆号低纯五度；降 B 调小号低大二度。降 E 调中音萨克斯发音低大六度。

Articulation markings: legato (smooth, connected), staccato (short, detached), tenuto (held full value), accent (stressed), sforzando (sfz, sudden strong accent). Dynamic markings range from ppp to fff, with crescendo and diminuendo indicating gradual changes. String techniques include pizzicato (plucked), arco (bowed), con sordino (with mute), tremolo (rapid repetition), and double / triple stopping.

演奏法标记：连奏（legato，平滑连贯）、断奏（staccato，短促分离）、保持音（tenuto，奏足时值）、重音（accent，强调）、突强（sforzando，sfz，突然加强）。力度标记范围从 ppp 到 fff，渐强（crescendo）和渐弱（diminuendo）表示逐步变化。弦乐技法包括拨弦、弓奏、加弱音器、震音和双音/三音。

10. Form & Structure | 曲式与结构

Binary form (AB) consists of two complementary sections, each often repeated. Ternary form (ABA) returns to the opening material after a contrasting middle. Rondo form (ABACA or ABACABA) features a recurring A theme alternating with episodes. Sonata form, the staple of the Classical period, unfolds in exposition (thematic groups 1 and 2 in contrasting keys), development (modulatory, fragmented treatment), and recapitulation (both groups in the tonic).

二部曲式（AB）由两个互补段落构成，每段常重复。三部曲式（ABA）在对比较大的中段后回归开篇素材。回旋曲式（ABACA 或 ABACABA）以反复出现的 A 主题与各插部交替。奏鸣曲式是古典时期的核心结构，展开于呈示部（对比调性的两个主题组）、展开部（转调、碎片化处理）和再现部（两组主题均回归主调）。

Variation form (theme and variations) alters melody, harmony, rhythm, mode, or texture in successive statements. Through-composed structures avoid large-scale repetition, responding to a text or continuous narrative. Fugue, a pinnacle of Baroque counterpoint, is built on a subject (theme) stated by single voices in turn (answer at the dominant), woven with countersubjects and episodic passages.

变奏曲式（主题与变奏）在后续陈述中改变旋律、和声、节奏、调式或织体。通谱体结构避免大规模重复，响应文本或连续叙事。赋格是巴洛克对位法的巅峰，以主题在不同声部依次进入（答题在属调上）为基础，交织对题和插部段落。

11. Musical Periods & Style Characteristics | 音乐时期与风格特征

Baroque (c.1600–1750): basso continuo, terraced dynamics, ornamented melody, fugal and dance-suite forms, strong rhythmic drive. Representative composers: Bach, Handel, Vivaldi. Classical (c.1750–1820): homophonic texture, periodic phrasing, symmetrical structures, clear cadences, gradual dynamics. Composers: Haydn, Mozart, early Beethoven. Romantic (c.1820–1900): lyrical melodies, chromatic harmony, expanded orchestration, programme music, rubato. Composers: Schubert, Chopin, Brahms, Tchaikovsky.

巴洛克时期（约 1600–1750）：通奏低音、阶梯式力度、装饰性旋律、赋格与舞曲组曲形式、强烈的节奏驱动。代表作曲家：巴赫、亨德尔、维瓦尔第。古典时期（约 1750–1820）：主调织体、周期性分句、对称结构、明确终止式、渐进力度。作曲家：海顿、莫扎特、早期贝多芬。浪漫时期（约 1820–1900）：抒情旋律、半音化和声、扩展管弦配器、标题音乐、弹性速度。作曲家：舒伯特、肖邦、勃拉姆斯、柴可夫斯基。

20th-century styles include Impressionism (Debussy: whole-tone, pentatonic, parallel chords), Neo-classicism (Stravinsky: sparser textures, rhythmic innovation, pastiche of earlier forms), Expressionism (Schoenberg: atonal, twelve-tone serialism), and Minimalism (Reich, Glass: repetitive patterns, gradual transformation). CIE exams often require identification of period by stylistic clues in unseen extracts.

20 世纪风格包括印象主义（德彪西：全音阶、五声音阶、平行和弦）、新古典主义（斯特拉文斯基：更疏朗的织体、节奏创新、模仿早期形式）、表现主义（勋伯格：无调性、十二音序列）和简约主义（赖希、格拉斯：重复模式、渐变）。CIE 考试常要求通过未知选段中的风格线索识别时期。

12. Musical Analysis Terminology | 音乐分析术语速查

Anacrusis / 弱起: upbeat note(s) before the first strong beat / 第一个强拍前的上拍音符。
Cadenza / 华彩段: improvisatory solo passage showing virtuosity / 展示技巧的即兴独奏段落。
Chromaticism / 半音化: use of notes outside the prevailing key / 运用主调以外的音。
Counterpoint / 对位: combination of independent melodic lines / 独立旋律线的结合。
Dominant pedal / 属持续音: sustained or repeated dominant note beneath changing harmonies / 变化和声下持续或重复的属音。
Enharmonic / 等音: notes that sound identical but are spelled differently (F♯/G♭) / 音高相同但记谱不同的音。
Hemiola / 赫米奥拉: rhythmic ratio 3:2, often in Baroque dance / 节奏比 3:2，常见于巴洛克舞曲。
Ostinato / 固定音型: persistently repeated musical figure / 持续重复的音乐片段。
Rubato / 弹性速度: expressive flexibility in tempo / 速度上的表情性伸缩。
Sequence / 模进: repetition of a pattern at a different pitch / 在不同音高重复模式。

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CIE A-Level Music: Formula & Theorem Quick Reference | CIE A-Level 音乐：公式定理速查手册