📚 GCSE Edexcel Music: Quick Reference Handbook of Formulas & Theorems | GCSE Edexcel 音乐：公式定理速查手册
This reference handbook distills the essential ‘formulas’ and ‘theorems’ required for the GCSE Edexcel Music specification. From scale construction and interval logic to chord spelling, cadential patterns, and structural blueprints, every core theoretical principle is presented as a clear, repeatable rule. Use these pages as a rapid revision tool to build fluency in the musical language that underpins performance, composition, and appraisal.
本速查手册提炼了 GCSE Edexcel 音乐课程所必需的核心“公式”与“定理”。从音阶构建、音程逻辑到和弦拼写、终止模式以及结构蓝图，每一个关键理论原则都以清晰、可复用的规则呈现。可以将这些页面作为快速复习工具，帮助你熟练掌握支撑表演、作曲与评价的音乐语言。
1. Note‑Value Equations and Time Signature Rules | 音符时值公式与拍号法则
Every time signature defines a mathematical relationship between beats and bars. The upper numeral shows the number of beats per bar; the lower numeral gives the beat unit as a fraction of a semibreve. Thus 4/4 means four crotchet beats, 6/8 means six quaver beats grouped in two dotted‑crotchet pulses.
每个拍号都定义了拍子与小节之间的数学关系。上方数字表示每小节的拍数；下方数字则表示以全音符为基准的拍子单位。因此 4/4 表示四个四分音符拍，6/8 表示六个八分音符拍但以两个附点四分音符为一组。
Common note‑value equations: 1 semibreve = 2 minims = 4 crotchets = 8 quavers = 16 semiquavers. A dot increases duration by half; a double dot adds a further quarter. Triplets fit three notes into the time of two, and duplets fit two into the time of three.
常见音符时值等式：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。附点增加原有时值的一半；复附点再增加一半的一半。三连音将三个音塞进两个音的时间里，二连音将两个音塞进三个音的时间里。
| Time Signature | Beat Unit | Strong Beats | Type |
|---|---|---|---|
| 2/4 | Crotchet | 1 | Simple duple |
| 3/4 | Crotchet | 1 | Simple triple |
| 4/4 | Crotchet | 1 and 3 | Simple quadruple |
| 6/8 | Dotted crotchet (group of 3 quavers) | 1 and 4 | Compound duple |
2. Major Scale Formula | 大调音阶公式
The major scale follows an invariable pattern of tones (T) and semitones (S): T – T – S – T – T – T – S. Starting from any note and applying this step sequence yields the diatonic major scale. For example, C major uses only white keys and confirms the pattern: C–D (T), D–E (T), E–F (S), F–G (T), G–A (T), A–B (T), B–C (S).
大调音阶遵循固定的全音（T）与半音（S）模式：全 – 全 – 半 – 全 – 全 – 全 – 半。从任意音符出发并运用这个步进序列，即可得到自然大调音阶。例如，C 大调只使用白键，并印证了这一模式：C–D（全），D–E（全），E–F（半），F–G（全），G–A（全），A–B（全），B–C（半）。
To build a major scale on any tonic, write the seven letter names in order, then adjust accidentals so that the semitones fall exactly between steps 3–4 and 7–8. The formula also governs key‑signature construction: the order of sharps is F♯ C♯ G♯ D♯ A♯ E♯ B♯, and the order of flats is B♭ E♭ A♭ D♭ G♭ C♭ F♭, derived from the circle of fifths.
在任何主音上构建大调音阶时，先按顺序写出七个音名，再通过变音记号调整，使半音恰好位于第 3–4 级和第 7–8 级之间。该公式也支配着调号的构建：升号调的顺序为 F♯ C♯ G♯ D♯ A♯ E♯ B♯，降号调的顺序为 B♭ E♭ A♭ D♭ G♭ C♭ F♭，这两者都源于五度圈。
3. Minor Scale Recipes (Natural, Harmonic, Melodic) | 小调音阶配方（自然、和声、旋律）
All minor scales share a tonic triad of root, minor third, and perfect fifth. The natural minor applies the same tone–semitone pattern as its relative major but starting on the sixth degree: T – S – T – T – S – T – T. Thus A natural minor is A–B–C–D–E–F–G–A.
所有小调音阶共享由根音、小三度和纯五度构成的主三和弦。自然小调采用的音程模式与其关系大调相同，但从第六级开始：全 – 半 – 全 – 全 – 半 – 全 – 全。因此，a 自然小调为 A–B–C–D–E–F–G–A。
The harmonic minor raises the seventh degree to create a semitone leading note and an augmented second between degrees 6 and 7. Pattern: T – S – T – T – S – A2 – S (where A2 = augmented 2nd, three semitones). Example in A minor: A–B–C–D–E–F–G♯–A.
和声小调升高第七级，从而形成一个半音导音，并在第六级与第七级之间形成一个增二度。模式：全 – 半 – 全 – 全 – 半 – 增二度 – 半。以 a 小调为例：A–B–C–D–E–F–G♯–A。
The melodic minor raises both the sixth and seventh degrees when ascending, smoothing the augmented second, and reverts to the natural minor form when descending. Ascending pattern: T – S – T – T – T – T – S. Descending: same as natural minor. A minor ascending: A–B–C–D–E–F♯–G♯–A.
旋律小调在上行时升高第六和第七级，使增二度变得平滑；下行时则恢复为自然小调形式。上行模式：全 – 半 – 全 – 全 – 全 – 全 – 半。下行：与自然小调相同。a 小调上行：A–B–C–D–E–F♯–G♯–A。
4. Interval Calculation | 音程计算公式
An interval is defined by two parameters: the numeric distance (2nd, 3rd, 4th, etc.) determined by counting letter names from the lower note to the higher, and the quality (perfect, major, minor, augmented, diminished) determined by the number of semitones. Unisons, 4ths, 5ths, and octaves are perfect; 2nds, 3rds, 6ths, and 7ths can be major or minor.
音程由两个参数定义：一是根据从低音到高音的音名字母数得出的度（如二度、三度、四度等），二是根据半音数确定的性质（纯、大、小、增、减）。同度、四度、五度和八度是纯音程；二度、三度、六度和七度可以是大音程或小音程。
To work out an interval quickly: (1) count the letter names inclusive of both notes; (2) count the semitones; (3) compare with the standard semitone counts for that numeric size. For example, a major 3rd is 4 semitones, a minor 3rd is 3 semitones; a perfect 5th is 7 semitones. An augmented interval is one semitone larger than perfect/major; a diminished interval is one semitone smaller than perfect/minor.
快速计算音程的方法：（1）数出包含两个音在内的音名字母数；（2）数出半音数；（3）与该度数的标准半音数进行对比。例如，大三度为 4 个半音，小三度为 3 个半音；纯五度为 7 个半音。增音程比纯/大音程多一个半音；减音程比纯/小音程少一个半音。
| Interval | Semitones (standard) | Example |
|---|---|---|
| Minor 2nd | 1 | E–F |
| Major 2nd | 2 | C–D |
| Minor 3rd | 3 | A–C |
| Major 3rd | 4 | C–E |
| Perfect 4th | 5 | G–C |
| Perfect 5th | 7 | C–G |
| Octave | 12 | C–C’ |
5. Triad and Seventh‑Chord Spelling | 三和弦与七和弦的拼写公式
A triad is built by stacking two thirds on a root. The formula for a major triad is root + major 3rd (4 semitones) + perfect 5th (7 semitones). A minor triad: root + minor 3rd (3 semitones) + perfect 5th. A diminished triad: root + minor 3rd + diminished 5th (6 semitones). An augmented triad: root + major 3rd + augmented 5th (8 semitones).
三和弦由在根音上叠置两个三度构成。大三和弦的公式为：根音 + 大三度（4 个半音）+ 纯五度（7 个半音）。小三和弦：根音 + 小三度（3 个半音）+ 纯五度。减三和弦：根音 + 小三度 + 减五度（6 个半音）。增三和弦：根音 + 大三度 + 增五度（8 个半音）。
Seventh chords add a third above the triad. The dominant 7th (e.g., G⁷) consists of a major triad plus a minor 7th (10 semitones above the root). The major 7th (Cmaj⁷) has a major triad plus a major 7th (11 semitones). The minor 7th (Am⁷) is a minor triad plus a minor 7th. The half‑diminished 7th (Bm⁷♭⁵ or B∅) is a diminished triad plus a minor 7th, and the fully diminished 7th (B°⁷) is a diminished triad plus a diminished 7th (9 semitones).
七和弦在三和弦上方再增加一个三度。属七和弦（如 G⁷）由大三和弦加上小七度（根音上方 10 个半音）构成。大七和弦（Cmaj⁷）是大三和弦加大七度（11 个半音）。小七和弦（Am⁷）是小三和弦加小七度。半减七和弦（Bm⁷♭⁵ 或 B∅）是减三和弦加小七度，而全减七和弦（B°⁷）是减三和弦加减七度（9 个半音）。
In GCSE Edexcel, chord symbols use Roman numerals: uppercase for major (I, IV, V), lowercase for minor (ii, vi), with ° for diminished (vii°) and + for augmented. The roman numeral reflects the scale-degree root.
在 GCSE Edexcel 中，和弦符号采用罗马数字：大写表示大三和弦（I、IV、V），小写表示小三和弦（ii、vi），° 表示减三和弦（vii°），+ 表示增三和弦。罗马数字反映了音级根音。
6. Circle of Fifths and Key‑Signature Logic | 五度圈与调号逻辑
The circle of fifths maps key relationships by ascending perfect 5ths. Moving clockwise from C major (no sharps/flats) adds one sharp each step; moving anticlockwise adds one flat. The new sharp is always the leading note (7th degree) of the new key, and the new flat is the subdominant (4th degree) of the new key.
五度圈通过上行纯五度来描绘调性关系。从 C 大调（无升降号）开始，顺时针每步增加一个升号；逆时针每步增加一个降号。新的升号总是新调的导音（第七级），新的降号则是新调的下属音（第四级）。
To determine the major key from a sharp key signature, take the last sharp and raise it by a semitone; that note is the tonic. For flat keys, the penultimate flat in the key signature is the tonic (except F major with one flat). The relative minor is always a minor 3rd below the major tonic.
从升号调号确定大调时，取最后一个升号并升高半音，该音即为主音。降号调则取倒数第二个降号即为主音（单降号的 F 大调除外）。关系小调总是位于大调主音下方小三度。
| Major Key | Key Signature | Relative Minor |
|---|---|---|
| C | None | A minor |
| G | F♯ | E minor |
| D | F♯, C♯ | B minor |
| A | F♯, C♯, G♯ | F♯ minor |
| F | B♭ | D minor |
| B♭ | B♭, E♭ | G minor |
7. Cadential Formulas and Common Chord Progressions | 终止式公式与常见和弦进行
A cadence is the musical punctuation that closes a phrase. The four main cadential formulas are: perfect (V–I) which sounds final and complete; plagal (IV–I) often associated with ‘Amen’; imperfect (I–V, ii–V, IV–V) which sounds unfinished; and interrupted (V–vi) where the expected tonic is replaced by the submediant, creating surprise.
终止式是乐句结尾的音乐标点。四种主要终止式公式为：正格终止（V–I）听感完满而确定；变格终止（IV–I）常与“阿门”相关联；不完全终止（I–V、ii–V、IV–V）听感未完成；阻碍终止（V–vi）以六级和弦替代预期的主和弦，制造意外感。
Beyond cadences, functional harmony relies on chord‑progression patterns: the primary triads I, IV, and V (and their inversions) provide harmonic skeleton. Strong root motion by descending 5th (or ascending 4th) dominates: I–IV–vii°–iii–vi–ii–V–I. In the GCSE set works candidates will encounter these patterns repeatedly, alongside pedal notes, suspensions, and perfect cadences at structural moments.
在终止式之外，功能和声依赖于和弦进行的模式：主三和弦 I、IV、V（及其转位）提供了和声骨架。以下行五度（或上行四度）进行的强根音进行为主导：I–IV–vii°–iii–vi–ii–V–I。在 GCSE 指定作品中，考生会反复遇到这些模式，以及持续音、延留音和结构节点上的正格终止。
8. Rhythmic Devices and Metre Transformations | 节奏手法与拍子转换公式
Rhythmic interest arises from syncopation (emphasis on normally weak beats or off‑beats), hemiola (two bars of simple triple metre articulated as three groups of two), cross‑rhythms, and irregular groupings such as quintuplets. The formula for a tresillo rhythm, common in Latin genres, is 3+3+2 quaver groupings within a bar of 8 quavers.
节奏趣味来自切分（在通常的弱拍或拍点之间加重音）、赫米奥拉比例（将两个简单三拍子小节表现为三组两拍）、交叉节奏以及五连音等不规则音群。拉丁体裁中常见的三连二节奏公式是在一个八分音符小节内采用 3+3+2 的分组模式。
Metric modulation occurs when a note value from the old tempo becomes a different note value in the new tempo (e.g., old crotchet = new dotted crotchet). While not a heavy focus at GCSE, candidates need to recognise tempo changes, ritardando, accelerando, and the mathematical shift from simple to compound time when the beat divides from two into three subdivisions.
当旧速度中的某个音符时值变为新速度中的另一种时值时，即发生节拍转调（例如旧四分音符 = 新附点四分音符）。虽然 GCSE 对此要求不深，但考生需辨认速度变化、渐慢、渐快，以及当拍子细分从二等分变为三等分时产生的简单拍子到复合拍子的数学转换。
9. Melodic and Harmonic Devices | 旋律与和声手法公式
A stepwise melody moves by seconds; a leap moves by a third or more. Sequence is the immediate repetition of a melodic idea at a higher or lower pitch (real sequence preserves intervals exactly; tonal sequence adjusts to stay within the key). Other important devices: passing notes (stepwise unessential notes between two chord tones), auxiliary (neighbour) notes, appoggiaturas (leaning notes), anticipations, and suspensions (prepared, suspended, resolved).
级进旋律以二度进行；跳进则以三度或以上进行。模进是旋律素材在更高或更低音高上的即时重复（完全模进精确保持音程；守调模进在保持调性范围内进行微调）。其他重要手法包括：经过音（两个和弦音之间的级进非本质音）、辅助音（邻音）、倚音、先现音以及延留音（准备、延留、解决三阶段）。
Harmonic devices include pedal notes (tonic or dominant sustained while chords change above), harmonic rhythm (rate of chord change), consonance vs dissonance, and chromaticism. The formula for a chromatic scale is 12 successive semitones, often filling melodic or harmonic gaps with colouristic effect.
和声手法包括持续音（主音或属音在变化和弦之上持续）、和声节奏（和弦变化速率）、协和与不协和、以及半音化。半音音阶的公式是连续 12 个半音，常用于以色彩性效果填充旋律或和声间隙。
10. Texture, Dynamics, and Articulation Map | 织体、力度与演奏法术语图谱
Texture describes how musical layers interact. Monophony is a single unaccompanied line; homophony features melody with chordal accompaniment moving in the same rhythm; polyphony combines two or more independent melodic lines; heterophony presents simultaneous variants of a single melody. A fugal texture begins imitatively.
织体描述音乐层次的互动方式。单声织体是单一无伴奏声部；主调织体以旋律加和弦伴奏且节奏一致为特征；复调织体结合两个或以上独立旋律线条；支声织体呈现同一旋律的同时变体。赋格织体则以模仿开始。
Dynamics range from pianissimo (pp) to fortissimo (ff) with gradual change markings (crescendo, diminuendo). Articulation defines attack and release: staccato (detached), legato (smooth), accent (>), tenuto (–), sforzando (sfz). For GCSE, accurate Italian terms must be learned, e.g., dolce, agitato, cantabile, marcato.
力度范围从很弱（pp）到很强（ff），还有逐渐变化的标记（crescendo 渐强、diminuendo 渐弱）。演奏法定义了音头的起音与释放：断奏（staccato，短促）、连奏（legato，平滑）、重音（>）、保持音（–）、突强（sfz）。GCSE 要求准确掌握意大利术语，例如 dolce（柔美）、agitato（激动的）、cantabile（如歌的）、marcato（着重的）。
For instrumental techniques, ‘arco’ means bowed, ‘pizzicato’ plucked; ‘con sordino’ indicates mute. Vocal writing may demand syllabic (one note per syllable) or melismatic (many notes per syllable) setting. These are not formulas as such, but they follow standardised interpretive ‘rules’ you must recall in the appraisal paper.
对于器乐技巧，“arco” 意为拉弓，“pizzicato” 为拨弦；“con sordino” 表示加弱音器。声乐创作可能采用一字一音的音节式，或一字多音的装饰式。这些虽然不是公式，但遵循标准的诠释“规则”，必须在评价试卷中忆起。
11. Structure and Form Blueprints | 结构与曲式蓝图
Musical form follows repeated or contrasting sections. Binary form (AB) often modulates to a related key then returns; ternary form (ABA) features a contrasting middle section followed by a repeat of the opening. Rondo form (ABACADA) alternates a recurring A theme with contrasting episodes.
音乐曲式遵循重复或对比的段落。二部曲式（AB）通常转至关系调后回归；三部曲式（ABA）具有对比性的中间段落，随后重复开头部分。回旋曲式（ABACADA）在反复出现的 A 主题与对比插部之间交替。
Theme and variations presents a theme (A) then varied versions (A¹, A², A³…). Strophic form repeats the same music for each verse (AAA); through‑composed has no large‑scale repetition. Sonata form (exposition, development, recapitulation) appears in GCSE set works such as Beethoven, with its internal key relationships: exposition moves from tonic to dominant (or relative major), development explores distant keys, recapitulation returns all material to the tonic.
主题与变奏呈现一个主题（A），随后是其变体（A¹、A²、A³……）。分节歌形式为每段歌词重复相同的音乐（AAA）；通谱歌则没有大规模重复。奏鸣曲式（呈示部、展开部、再现部）出现在如贝多芬等 GCSE 指定作品中，其内部调性关系为：呈示部从主调转至属调（或关系大调），展开部探索远关系调，再现部将所有材料回归主调。
Popular song form often uses verse–chorus structures with a bridge and an instrumental solo. The 12‑bar blues formula is a fixed harmonic progression: I – I – I – I – IV – IV – I – I – V – IV – I – I (or variations thereof). This pattern underpins countless GCSE case studies from Delta blues to rock.
流行歌曲常用主歌–副歌结构，包含桥段和乐器独奏。12 小节蓝调公式是一个固定的和声进行：I – I – I – I – IV – IV – I – I – V – IV – I – I（或它的变体）。这一模式支撑了无数从三角洲蓝调到摇滚的 GCSE 案例研究。
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