📚 A-Level OCR Music Formula and Theorem Quick Reference Handbook | A-Level OCR 音乐公式定理速查手册
This handbook compiles essential ‘formulae’ and ‘theorems’ for the OCR A-Level Music course, translating musical grammar into clear, repeatable patterns. Whether you are analysing set works, composing in the Western Classical tradition, or delving into 20th-century innovations, these principles will accelerate your understanding and secure top marks. Every concept is presented as a concise statement, followed by its practical application, ensuring you can recall and deploy these rules under examination conditions.
本手册汇编了OCR A-Level音乐课程中必备的“公式”与“定理”，将音乐语法转化为清晰、可复制的模式。无论你是在分析指定作品、按照西方古典传统作曲，还是钻研二十世纪的创新技法，这些原则都将加速你的理解并确保高分。每个概念都以简洁陈述呈现，并附上实际应用，保证你在考试条件下能够回忆并运用这些规则。
1. Scale Formulas | 音阶公式
Music begins with scales. The major, natural minor, harmonic minor, and melodic minor scales each follow a rigid pattern of tones (T) and semitones (S). Memorising these intervals allows you to construct any scale from a given tonic without error, and to identify how composers exploit chromatic alterations for expressive effect.
音乐始于音阶。大调、自然小调、和声小调与旋律小调各自遵循全音（T）与半音（S）的固定模式。记忆这些音程关系能让你从任意主音无误地构建任何音阶，并识别作曲家如何利用半音变化达到表情效果。
Major: T – T – S – T – T – T – S
Natural minor: T – S – T – T – S – T – T
Harmonic minor: T – S – T – T – S – T+½ – S (raised 7th)
Melodic minor ascending: T – S – T – T – T – T – S
Melodic minor descending: natural minor
In Chinese: 大调: 全全半全全全半; 自然小调: 全半全全半全全; 和声小调: 全半全全半增二半 (升高第VII级); 旋律小调上行: 全半全全全全半, 下行同自然小调。Modes (church modes) are derived by rotating the major scale: Ionian (T-T-S-T-T-T-S), Dorian (T-S-T-T-T-S-T), Phrygian (S-T-T-T-S-T-T), Lydian (T-T-T-S-T-T-S), Mixolydian (T-T-S-T-T-S-T), Aeolian (T-S-T-T-S-T-T), Locrian (S-T-T-S-T-T-T).
教会调式由大调音阶轮转得出：伊奥尼亚、多利亚、弗里几亚、利底亚、混合利底亚、爱奥利亚、洛克利亚，各有独特色彩。
2. Chord Construction and Inversions | 和弦构建与转位
Triads are built by stacking thirds above a root. A major triad consists of a major third plus a minor third (R – 3 – 5), while a minor triad is minor third plus major third (R – ♭3 – 5). The diminished triad stacks two minor thirds (R – ♭3 – ♭5), and augmented triads two major thirds (R – 3 – ♯5). Seventh chords add another third: dominant 7th (major triad + minor seventh, R – 3 – 5 – ♭7), major 7th (major triad + major seventh, R – 3 – 5 – 7), minor 7th (minor triad + minor seventh, R – ♭3 – 5 – ♭7), etc.
三和弦由在根音上叠加三度构成。大三和弦=大三度+小三度（根-3-5），小三和弦=小三度+大三度（根-♭3-5），减三和弦=小三度+小三度（根-♭3-♭5），增三和弦=大三度+大三度（根-3-♯5）。七和弦再加一个三度：属七和弦=大三和弦+小七度（根-3-5-♭7），大七和弦=大三和弦+大七度（根-3-5-7），小七和弦=小三和弦+小七度（根-♭3-5-♭7）等。
Inversions occur when the lowest note is not the root. First inversion has the third in the bass (figured as 6, or 6_3), second inversion has the fifth in the bass (6_4), and for seventh chords, third inversion has the seventh in the bass (4_2). The stability of inversions decreases from root position to second inversion, which is often used as a passing or cadential 6_4 chord.
当最低音不是根音时即为转位。第一转位三音在低音（数字低音记作6或6₃），第二转位五音在低音（6₄）；七和弦第三转位七音在低音（4₂）。稳定性从原位到第二转位递减，第二转位常作为经过或终止四六和弦使用。
3. Cadences and Functional Harmony | 终止式与功能和声
Cadences are the musical equivalent of punctuation marks. The four primary cadences are: Perfect (V – I, both in root position, final I with tonic in top voice), Imperfect (any chord – V, ending on V), Plagal (IV – I, the ‘Amen’ cadence), and Interrupted/Deceptive (V – vi, or V – VI in minor). Each creates a different degree of closure and expectation.
终止式相当于音乐的标点符号。四种基本终止式：正格终止（V-I，均为原位，I最高音为主音）、半终止（任何和弦-属和弦，停留在V上）、变格终止（IV-I，“阿门”终止）、阻隔终止（V-vi，或小调V-VI）。每种创造不同的结束感和期待感。
Functional harmony classifies chords into tonic (I, iii, vi), subdominant (IV, ii), and dominant (V, vii°) functions. The archetypal progression is Tonic – Subdominant – Dominant – Tonic (I – IV – V – I). A cadential 6_4 chord (I 6_4) elongates the dominant approach: it is a second-inversion tonic that resolves to V, then to I, creating a double suspension.
功能和声将和弦分为主功能（I, iii, vi）、下属功能（IV, ii）和属功能（V, vii°）。原型进行为主-下属-属-主（I-IV-V-I）。终止四六和弦（I 6₄）延长了通往属和弦的路径：它是主和弦第二转位，解决到V再至I，产生双重延留效果。
4. Voice Leading Rules | 声部进行规则
Common-practice voice leading follows a set of ‘laws’ to ensure smooth, independent lines. Keep common tones in the same voice when possible. The leading note (7th degree) resolves up to tonic by step. In V7 – I, the chordal seventh (4th factor) resolves down by step. Avoid parallel perfect fifths and octaves between any two voices. Hidden (exposed) fifths and octaves in outer voices are acceptable only if the soprano moves by step.
共通实践时期的声部进行遵循一套“法则”以确保平滑且独立的线条。尽可能将共同音保持在同一声部。导音（第VII级）级进上行解决到主音。V7-I进行中，七和弦的七音（第四因子）级进下行解决。避免任何两声部之间的平行纯五度和平行八度。外声部的隐伏五度、八度仅在高音声部级进时才可接受。
When the root moves by step (e.g., IV – V), move the upper voices contrary to the bass. When roots move by fourth/fifth, keep the common tone and move the other two voices stepwise. Never double the leading note in a chord; in first-inversion triads, it is preferable to double the soprano or bass, not the third unless necessary. These rules ensure harmonic clarity and contrapuntal integrity.
当根音级进进行（如IV-V）时，上方声部与低音反向移动。当根音四度/五度跳进时，保留共同音并将另外两声部级进。切勿重复和弦中的导音；在第一转位三和弦中，最好重复高音或低音，除非必要不重复三音。这些规则保证了和声清晰与对位完整。
5. Counterpoint Principles | 对位法原理
Species counterpoint, as codified by Fux, provides a systematic method for studying melodic independence. First species (note against note) uses only consonant intervals: perfect unisons and octaves (used sparingly), perfect fifths, and imperfect thirds and sixths. Perfect consonances must be approached by contrary or oblique motion, never by similar motion to avoid parallels.
福克斯定型的分类对位法为学习旋律独立性提供了系统方法。第一类（一音对一音）仅使用协和音程：纯一度、纯八度（少用）、纯五度以及不完全协和的三度、六度。纯协和音程需以反向或斜向进入，绝不可用同向以避免平行。
Second species (two notes against one) introduces the passing tone dissonance: the second half-note on a weak beat must be a stepwise dissonance connecting two consonances, or a consonance. The downbeat must remain consonant. This establishes the principle that dissonances are prepared and resolved by step, a foundational concept for all later harmonic expansion.
第二类（二音对一音）引入经过音的不协和：弱拍上的第二个二分音符必须是连接两个协和音的级进不协和音，或本身为协和音。强拍须保持协和。这确定了不协和音需通过级进准备与解决的原则，这是日后所有和声扩张的基本概念。
6. Harmonic Progressions and Circle of Fifths | 和声进行与五度圈
The circle-of-fifths progression (I – IV – vii° – iii – vi – ii – V – I) is one of the most powerful sequence models. Each chord moves down by a perfect fifth (or up a fourth) to the next. This maximises tonal gravity and is frequently used in sequences, modulations, and development sections. In functional shorthand, it reads: Root motion by descending fifth is the strongest harmonic motion.
五度圈进行（I-IV-vii°-iii-vi-ii-V-I）是最强大的模进模型之一。每个和弦向下移动纯五度（或向上四度）到达下一个。这最大化了调性引力，常用于模进、转调和发展部。按功能简记：下行五度根音进行是最强的和声进行。
The descending thirds progression (I – vi – IV – ii – V – I) is another staple, known as the ‘Pachelbel progression’ in some contexts. Ascending second (stepwise) progressions (IV – V, ii – iii) also occur but are weaker. The half-diminished seventh chord (viiø7) in major and fully diminished vii°7 in minor resolve naturally to tonic. Understanding these prototypes enables you to recognise and exploit harmonic expectation in composition and analysis.
下行三度进行（I-vi-IV-ii-V-I）是另一常见模式，某些语境中称“帕赫贝尔进行”。上行二度（级进）进行（IV-V, ii-iii）也存在但力量较弱。大调中的半减七和弦（viiø7）与小调中的减七和弦（vii°7）自然解决到主音。理解这些原型能让你在创作与分析中识别并利用和声期待。
7. Non-Harmony Tones (Embellishments) | 和弦外音（装饰音）
Non-harmony tones add tension and colour. Passing tones (PT) move by step between two different chord tones. Neighbour tones (NT) move stepwise away from a chord tone and return to the same tone. Suspensions (SUS) hold a note over from the previous chord, creating a dissonance that resolves down by step: 4-3, 7-6, and 9-8 are the most common suspensions (bass suspension 2-3 is also found). Appoggiaturas (APP) are approached by leap and resolved by step.
和弦外音增加紧张度与色彩。经过音在两个不同和弦音之间级进移动。辅助音从和弦音级进离开并返回同音。延留音将前一和弦的音留住，产生不协和并级进下行解决：4-3、7-6、9-8最常见（低音延留2-3也存在）。倚音需跳进进入、级进解决。
Escape tones (ET) are approached by step and left by leap in the opposite direction. Anticipations (ANT) sound a chord tone early, before the rest of the chord arrives. The peddle point (pedal) sustains a note, usually tonic or dominant, through changing harmonies above. Recognising these ornamentations is critical for melodic and harmonic analysis in set works from Bach to Debussy.
逃音以级进进入并以反向跳进离开。先现音在所在和弦其他音出现前提前奏出和弦音。持续音（踏板音）在上方和声变换时持续保持，通常为主音或属音。识别这些装饰音对于从巴赫到德彪西指定作品的旋律与和声分析至关重要。
8. Figured Bass Realisation | 数字低音实现
For the OCR historical study component, figured bass is a core skill. The figures indicate intervals above the given bass note. A sharp or flat alone refers to the third. The common figures are: 6 = first inversion (third in bass), 7 = seventh chord root position, 6_5 = first inversion seventh, 4_3 = second inversion seventh, 4_2 = third inversion seventh. Chromaticism is shown by accidentals next to the numbers.
针对OCR历史研究部分，数字低音是核心技能。数字表示给定低音上方的音程。单独的升号或降号指代三音。常见数字为：6 = 第一转位（三音在低音），7 = 原位七和弦，6₅ = 七和弦第一转位，4₃ = 七和弦第二转位，4₂ = 七和弦第三转位。半音变化由数字旁边的临时记号显示。
When realising a figured bass, start by writing the bass line. Then fill in the inner parts to complete the harmony, attending to voice leading rules. The figures do not specify the disposition of upper voices, only which notes above the bass are required. Avoid parallel octaves and fifths; maintain independence. This skill directly connects to exercises in Baroque-style composition and analysis of Bach chorales.
在实现数字低音时，先写出低音谱。然后填充内声部以完成和声，并注意声部进行规则。数字不指定上方声部的排列方式，仅指出低音上方所需的音。避免平行八度与五度；保持声部独立性。这项技能直接关联巴洛克风格作曲练习与巴赫众赞歌分析。
9. Modulation Techniques | 转调技巧
Modulation is the process of changing key within a piece. Common-practice modulation relies on pivot chords, which are diatonic in both the old and new key. The most common targets are the dominant (V), the relative major/minor, and the subdominant. For example, in C major, a pivot chord like E minor (iii in C, vi in G) can initiate a move to the dominant G major.
转调是乐曲内调性转换的过程。共通实践转调依赖中介和弦，该和弦在原调和新调中均为自然音。最常见的转调目标是属调（V）、关系大小调和下属调。例如，在C大调中，中介和弦e小三和弦（C大调iii，G大调vi）可启动至属调G大调的转调。
Chromatic modulation introduces a chromatic alteration that acts as a pivot or as a direct new dominant preparation. An enharmonic modulation reinterprets a chord (typically a diminished seventh or German augmented sixth) to resolve in a remote key. The augmented sixth chords (Italian, French, German) are pivotal in chromatic harmony: they approach the dominant from a semitone above and often serve as modulation springboards.
变化音转调引入一个作为中介或直接属准备的变化音。等音转调重新解释一个和弦（常为减七和弦或德国增六和弦）以解决至远关系调。增六和弦（意大利、法国、德国）在变化音和声中至关重要：它们从上方半音逼近属和弦，常作为转调跳板。
10. Rhythmic and Metric Devices | 节奏与节拍手法
Rhythm and metre are manipulated through hemiola (shifting the perceived metre from 3/4 to 2/4 via accent patterns), syncopation (accenting weak beats or off-beats), cross-rhythm (simultaneous use of conflicting rhythmic patterns), and polyrhythm (e.g., 3 against 2). These devices create tension, drive, and forward momentum in music from Renaissance dance suites to 20th-century Stravinsky.
节奏与节拍通过赫米奥拉比例（通过重音将3/4感知变为2/4）、切分音（在弱拍或非拍点加重音）、交错节奏（同时使用冲突的节奏模式）和复节奏（如三对二）进行操控。这些手法从文艺复兴舞曲到二十世纪斯特拉文斯基，都能制造紧张度、推动力和向前动量。
Time signature changes (metric modulation) may occur where a note value from the old tempo becomes a new unit of beat. Additive rhythms (e.g., 3+3+2 eighth notes) appear in folk-inspired music and Messiaen’s works. Anacrusis (upbeat) and feminine endings (weak end) soften phrase contours. OCR set works often feature these rhythmic signatures, requiring identification and commentary.
拍号改变（节拍转调）可使旧速度中的某个音值成为新的拍单位。附加节奏（如3+3+2的八分音符）出现在民风作品与梅西安作品中。弱起（上拍）和阴性终止（弱收束）使乐句轮廓柔和。OCR指定作品常蕴含这些节奏特征，需要识别与评述。
11. 20th-Century Harmonic Techniques | 二十世纪和声技法
Atonality and extended tonality mark the 20th-century repertoire. Quartal and quintal harmony build chords from fourths and fifths rather than thirds, as found in Debussy and Bartók. Polychords superimpose two distinct triads (e.g., C major over D major). Pandiatonicism uses the notes of a diatonic scale freely, without functional resolutions. Clusters (adjacent notes) add percussive texture.
无调性与扩展调性标志着二十世纪曲目。四度叠置与五度叠置和弦以四度和五度而非三度构建，如德彪西和巴托克的作品。多和弦叠加两个不同的三和弦（如C大三和弦叠加D大三和弦）。泛自然音主义自由使用一个自然音阶的音，无功能解决。音簇（相邻音）增加敲击性织体。
The octatonic scale (alternating T-S, T-S) and whole-tone scale (T-T-T-T-T-T) eliminate traditional tonal hierarchy. Chordal parallelism (planing) moves identical chord shapes in parallel, defying voice leading norms. For OCR analysis, identify these techniques and link them to the composer’s expressive intent, especially in works like Debussy’s ‘Voiles’ or Stravinsky’s ‘The Rite of Spring’.
八声音阶（全半/半全交替）和全音音阶（全全全全全全）消除了传统调性层级。和弦平行进行（平面化）以相同结构和弦形态平行移动，打破声部进行常规。在OCR分析中，识别这些技法并将其与作曲家的表现意图相联系，尤其在德彪西《帆》或斯特拉文斯基《春之祭》等作品中。
12. Set Theory and Serialism Basics | 集合理论与序列主义基础
For the study of 20th-century music, basic set theory offers analytical tools. A pitch-class set is an unordered collection of notes reduced to a normal form (most compact ordering). The prime form begins with 0 and lists transposition levels in brackets. The interval vector counts interval classes (ic1–ic6) within the set, revealing its sound world. Common sets in Webern and Schoenberg include 3-3 (014) and 4-1 (0123).
针对二十世纪音乐研究，基础集合理论提供分析工具。音级集合是一种无序的音符集合，缩减为“标准序”（最紧凑排列）。原型以0开始，括号内列出移位级别。音程向量统计集合内的音程级（ic1-ic6），揭示其音响世界。韦伯恩和勋伯格作品中常见集合如3-3 (014) 和4-1 (0123)。
Twelve-tone serialism organises all 12 pitch classes into a row, which may be transposed, inverted, retrograded, and used in its retrograde-inversion forms. The matrix is a 12×12 grid ensuring systematic treatment. OCR expects awareness of how these structural principles generate cohesion in the absence of tonality, linking directly to set works by Schoenberg, Webern, or Berg.
十二音序列主义将全部12个音级安排成一个序列，可进行移位、倒影、逆行及逆行倒影。十二音矩阵是一个12×12的网格以保证系统化处理。OCR要求了解这些结构原则如何在无调性中产生统一性，直接关联勋伯格、韦伯恩或贝尔格的指定作品。
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