Year 13 Edexcel Music Formula & Theorem Quick Reference Handbook | Year 13 Edexcel 音乐：公式定理速查手册

📚 Year 13 Edexcel Music Formula & Theorem Quick Reference Handbook | Year 13 Edexcel 音乐：公式定理速查手册

In Edexcel A Level Music, mastering the underlying ‘formulas’ of harmony, voice leading, structure, and rhythm is essential for both analysis and composition. This quick reference handbook collects the most important rules, patterns, and theoretical ‘theorems’ you need to apply confidently in the appraising paper and in your own composing. Think of it as your portable toolkit of musical logic – from cadence formulas and chord progressions to serial transformations and textural density rules.

在 Edexcel A Level 音乐课程中，掌握和声、声部进行、曲式结构和节奏的内在“公式”对于分析与作曲都至关重要。这本速查手册汇集了最关键的规则、模式与理论“定理”，帮你自信应对评赏试卷与自己的创作。把它当作随身携带的音乐逻辑工具箱——从终止式公式、和弦进行，到序列变换与织体密度法则。

1. Cadential Formulas | 终止式公式

Perfect Authentic Cadence (PAC): V–I with both chords in root position, soprano ending on the tonic. The leading tone must rise to the tonic. This is the strongest closing gesture in tonal music.

完美正格终止 (PAC)： V–I，两个和弦均为原位，高音部结束在主音上。导音必须上行解决到主音。这是调性音乐中最有力的收束方式。

Imperfect Authentic Cadence (IAC): Any V–I where one chord is inverted or the soprano does not end on the tonic. It provides a sense of closure but with less finality than a PAC.

不完全正格终止 (IAC)： 任何 V–I 进行中，若其中一个和弦转位或高音部不结束在主音上，即为 IAC。它带来收束感，但不如 PAC 强烈。

Plagal Cadence (PC): IV–I, often called the ‘Amen’ cadence. It is frequently used after a PAC to prolong the sense of rest.

变格终止 (PC)： IV–I，常被称为“阿门终止”。通常在 PAC 之后使用，以延长休止感。

Interrupted/Deceptive Cadence: V–vi (or V–♭VI in minor). It subverts the expected tonic, creating a surprise or momentary deflection.

阻碍终止/诈伪终止： V–vi（小调中可用 V–♭VI）。它打破对主和弦的期待，制造意外或短暂偏离。

Cadence Type	Formula (Major)	Effect
PAC	V → I (root, soprano tonic)	Complete closure
IAC	V → I (inverted, etc.)	Weaker closure
PC	IV → I	Amen, soft repose
Deceptive	V → vi	Surprise, deflection

C Major: V⁷ → I (G⁷ → C)

2. Chord Progression Patterns | 和弦进行模式

Certain root-movement patterns function as ‘progressional formulas’ in tonal music. The most fundamental is the I–IV–V–I progression, establishing the tonic–subdominant–dominant–tonic framework.

某些根音运动模式在调性音乐中充当“进行公式”。最基本的是 I–IV–V–I 进行，确立了主–下属–属–主的框架。

The circle-of-fifths progression (vi–ii–V–I or iii–vi–ii–V–I) creates a strong sense of forward drive by descending fifths. It is a staple of Baroque and Classical harmony.

五度圈进行（vi–ii–V–I 或 iii–vi–ii–V–I）通过下行五度产生强烈的推进感，是巴洛克与古典和声的核心素材。

The ii–V–I turn is especially common in Jazz and Romantic music, often enriched with sevenths: ii⁷–V⁷–Iᐞ⁷.

ii–V–I 周转在爵士与浪漫派音乐中极为常见，常加入七音形成 ii⁷–V⁷–Iᐞ⁷。

The Pachelbel progression (I–V–vi–iii–IV–I–IV–V) is a descending 5-3-1 bass pattern over which composers write countless variations. It can be analysed as a sequence of descending thirds.

帕赫贝尔进行（I–V–vi–iii–IV–I–IV–V）是一条下行 5-3-1 的低音线条，作曲家在此基础上发展出无数变奏；它可被视为下行三度的模进。

12-bar blues formula: I | I | I | I | IV | IV | I | I | V | IV | I | I (with variations). This pattern helps identify blues and blues-influenced styles in set works.

12 小节布鲁斯公式： I | I | I | I | IV | IV | I | I | V | IV | I | I（可有变形）。这一模式有助于在指定作品中识别布鲁斯及受布鲁斯影响的风格。

3. Voice Leading Rules | 声部进行规则

Four-part texture (SATB) follows strict voice-leading formulas that prevent awkward leaps, parallels, and hidden intervals. The most critical rules are:

四声部织体（SATB）遵循严格的声部进行规则，以避免生硬的跳进、平行进行和隐伏音程。最关键的规则如下：

No parallel perfect fifths or octaves: Two voices must not move in similar motion into a perfect fifth or octave.

禁止平行五度与八度： 任意两个声部不可同向进行到纯五度或纯八度。

Contrary motion preferred: Whenever possible, upper voices should move opposite to the bass to maintain independence.

提倡反向进行： 只要可能，上方声部应与低音部反向运动以保持声部独立。

Common tone retention: When two chords share a pitch, keep that pitch in the same voice. For example, in I–IV progressions, retain the tonic note.

共同音保持： 当两个和弦共有同一音高时，将该音保持在同一声部。例如 I–IV 进行中保持主音。

Leading-tone resolution: The leading tone (⁷) must rise by step to the tonic, except when it appears in an inner voice and moves to the fifth of the tonic chord (allowed but weaker).

导音解决： 导音（⁷）必须级进上行到主音，除非在内声部并移至主和弦的五音（允许但较弱）。

Leap compensation: A leap larger than a fourth should be followed by stepwise motion in the opposite direction.

跳进补偿： 超过四度的跳进后应跟随反向的级进进行。

4. Harmonic Function & Cycle | 和声功能与循环

Harmonic function categorises chords into three families: Tonic (T) – stable, home; Predominant (P) – prepares dominant; Dominant (D) – tension demanding resolution. The functional cycle is the ‘grammar’ of tonal music:

和声功能将和弦分为三个家族：主功能 (T)——稳定、归处；下属功能 (P)——预备属功能；属功能 (D)——紧张感要求解决。功能循环是调性音乐的“语法”：

Tonic → Predominant → Dominant → Tonic

Typical functional progressions: I can move to any chord. ii and IV usually act as predominants and lead to V. V most often resolves to I, but can also move to vi (deceptive). vi can go to IV or ii. iii is the weakest chord and typically moves to vi or IV.

典型功能进行：I 可进行到任何和弦。ii 与 IV 通常作为下属功能，导向 V。V 最常解决到 I，但也可移至 vi（阻碍）。vi 可前往 IV 或 ii。iii 是最弱的和弦，通常移至 vi 或 IV。

Function	Typical Chords (Major)	Resolves to
Tonic	I, vi (false tonic)	Any
Predominant	ii, IV, ♭II (Neapolitan)	V, vii°
Dominant	V, V⁷, vii°	I, vi

5. Modal Scales and Formulas | 调式音阶公式

Beyond major and minor, the seven diatonic modes provide colouristic alternatives. Each mode is defined by a specific pattern of whole (W) and half (H) steps:

在大、小调之外，七种自然调式提供色彩性的选择。每种调式由特定的全音 (W) 和半音 (H) 组合决定：

Ionian (Major): W W H W W W H. Happy, stable.

伊奥尼亚（大调）： W W H W W W H。明亮、稳定。

Dorian: W H W W W H W. Minor with raised 6th; jazzy, soulful.

多利亚： W H W W W H W。小调升六级；爵士风、深情。

Phrygian: H W W W H W W. Minor with lowered 2nd; Spanish, dark.

弗里几亚： H W W W H W W。小调降二级；西班牙风格、阴暗。

Lydian: W W W H W W H. Major with raised 4th; dreamy, bright.

利底亚： W W W H W W H。大调升四级；梦幻、明亮。

Mixolydian: W W H W W H W. Major with lowered 7th; bluesy, folk.

混合利底亚： W W H W W H W。大调降七级；布鲁斯感、民谣风。

Aeolian (Natural Minor): W H W W H W W. Soft minor.

爱奥利亚（自然小调）： W H W W H W W。柔和的小调。

Locrian: H W W H W W W. Diminished fifth, unstable; rare.

洛克里亚： H W W H W W W。减五度，不稳定；罕见。

Formula check: D Dorian = D E F G A B C D (W H W W W H W)

6. Intervallic Relationships | 音程关系定理

Intervals are the building blocks of melody and harmony. Recognising their quality and size by formula is vital, especially when transposing or analysing 20th-century works.

音程是旋律与和声的基石。通过公式识别其性质与大小至关重要，尤其是在移调或分析 20 世纪作品时。

Number of semitones + quality: Unison (0), minor 2nd (1), Major 2nd (2), minor 3rd (3), Major 3rd (4), Perfect 4th (5), Tritone (6), Perfect 5th (7), minor 6th (8), Major 6th (9), minor 7th (10), Major 7th (11), Octave (12).

半音数 + 性质： 同度 (0)、小二度 (1)、大二度 (2)、小三度 (3)、大三度 (4)、纯四度 (5)、三全音 (6)、纯五度 (7)、小六度 (8)、大六度 (9)、小七度 (10)、大七度 (11)、八度 (12)。

Inversion theorem: The sum of an interval and its inversion always equals 9. A Major 3rd (M3) inverts to a minor 6th (m6); a Perfect 4th (P4) inverts to a Perfect 5th (P5).

转位定理： 音程与其转位的度数之和永远为 9。大三度 (M3) 转位为小六度 (m6)；纯四度 (P4) 转位为纯五度 (P5)。

Compound intervals: Add 7 to the simple interval number. A M2 becomes a M9, etc. The quality remains unchanged.

复音程： 将单音程度数加 7。大二度变为大九度，性质不变。

Consonance vs dissonance: Perfect intervals and 3rds/6ths are consonant; 2nds, 7ths, and all augmented/diminished intervals are dissonant and require resolution.

协和与不协和： 纯音程与三度/六度为协和；二度、七度及所有增、减音程为不协和，需要解决。

7. Rhythmic Grouping & Meter Rules | 节奏分组与节拍规则

Correct rhythmic notation follows clear beaming and grouping conventions that reflect the metre. These ‘rules’ ensure readability and stylistic accuracy.

正确的节奏记谱遵循清晰的符杠与分拍惯例，反映节拍结构。这些“规则”确保可读性与风格准确性。

Simple meter (2/4, 3/4, 4/4): Beam beats to show each crotchet beat. In 4/4, group quavers as four pairs of two; do not beam across the middle of the bar.

单拍子 (2/4, 3/4, 4/4)： 符杠组合显示每个四分音符拍点。4/4 中将八分音符组合为四对，不要将符杠跨过小节中间。

Compound meter (6/8, 9/8, 12/8): Beam to show dotted-crotchet beats. In 6/8, two groups of three quavers; in 9/8, three groups; in 12/8, four groups.

复拍子 (6/8, 9/8, 12/8)： 符杠组合显示附点四分音符拍点。6/8 有两大组（每组三个八分音符），9/8 三大组，12/8 四大组。

Syncopation theorem: Accents on weak beats or weak parts of beats create rhythmic displacement. Common patterns: tied notes across bar lines, rests on strong beats, offbeat accents.

切分音定理： 重音落在弱拍或弱部分产生节奏位移。常见模式：跨小节连音线、强拍休止、弱拍重音。

Duplets and triplets: A triplet divides a beat into three equal parts in simple meter (3:2 ratio). A duplet divides a dotted beat into two in compound meter.

二连音与三连音： 三连音在单拍子中将一拍分为三等分（3:2 比）。二连音在复拍子中将附点拍分为二等分。

8. Structural Forms | 曲式结构

Large-scale musical forms function as architectural ‘theorems’ that govern tonal trajectory and thematic recurrence. Memorise these formulas to analyse set works effectively.

大型曲式结构是有如建筑“定理”，支配着调性轨迹与主题再现。记住这些公式以高效分析指定作品。

Sonata form (Sonata-allegro): Exposition (First subject in tonic, transition, Second subject in dominant/relative, codetta) → Development (fragmentation, modulation through distant keys) → Recapitulation (First subject in tonic, Second subject in tonic, coda).

奏鸣曲式（奏鸣快板）： 呈示部（主部主题在主场，连接部，副部主题在属调/关系调，小结尾）→ 展开部（碎片化、远关系转调）→ 再现部（主部主题在主调，副部主题在主调，尾声）。

Ternary form (ABA): A section in tonic, contrasting B section in new key, return of A in tonic. Often found in Romantic character pieces and arias.

三段式 (ABA)： A 段在主调，对比性 B 段在新调，A 段在主调回归。常见于浪漫派特性小品和咏叹调。

Rondo form (ABACA, ABACABA): The recurring refrain (A) in tonic alternates with contrasting episodes (B, C) in related keys. The final A provides closure.

回旋曲式 (ABACA, ABACABA)： 回旋主题 (A) 在主调反复出现，与在关系调上的对比插部 (B, C) 交替。最后的 A 提供收束。

Theme and variations: Statement of a theme followed by several variations altering melody, harmony, rhythm, mode, or texture while retaining the structural outline.

主题与变奏： 主题陈述后跟随多个变奏，在保持结构框架的前提下改变旋律、和声、节奏、调式或织体。

9. Counterpoint Guidelines | 对位法指导

Counterpoint (species) provides a rigorous set of formulas for combining independent melodic lines. The five species systematise rhythmic relationships.

对位法（分类对位）提供一套严密的公式来结合独立旋律线。五种分类将节奏关系系统化。

First species (note against note): Use only consonant intervals (perfect, 3rds, 6ths). Begin and end on perfect unisons or octaves. Avoid parallel perfect intervals.

第一类（一音对一音）： 只使用协和音程（纯、三度、六度）。开头与结尾用纯一度或纯八度。避免平行纯音程。

Second species (two notes against one): The second minim may be dissonant only if passing on an unaccented beat. The downbeat must be consonant.

第二类（二音对一音）： 第二个二分音符若为不协和，只能作为弱拍上的经过音。强拍必须协和。

Fourth species (suspensions): Prepare the suspension as a consonant note, tie over the barline, and resolve downwards

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Year 13 Edexcel Music Formula & Theorem Quick Reference Handbook | Year 13 Edexcel 音乐：公式定理速查手册