📚 AS Eduqas Music: Formula & Theorem Quick Reference Handbook | AS Eduqas 音乐：公式定理速查手册
In AS Eduqas Music, a deep understanding of the "formulas" behind harmony, melody, and structure is essential for both analysis and composition. This handbook condenses the core theoretical principles into a set of memorable rules, patterns, and quick-reference tables covering intervals, chords, cadences, harmonic progressions, scales, rhythm, melodic construction, and form. Use it as a daily revision tool to sharpen your aural skills and written responses.
在 AS Eduqas 音乐课程中，深入理解隐藏在和谐、旋律和结构背后的“公式”对分析与作曲都至关重要。本手册将核心理论原理浓缩为一套易记的规则、模式和速查表，涵盖音程、和弦、终止式、和声进行、音阶、节奏、旋律建构和曲式。将其作为日常复习工具，提升你的听觉能力和书面作答水平。
1. Interval Construction Rules | 音程构建规则
An interval is the distance between two notes, measured in semitones and scale degrees. The quality (major, minor, perfect, augmented, diminished) depends on the number of semitones and the letter names involved.
音程是两个音符之间的距离，以半音和音级来度量。其性质（大、小、纯、增、减）取决于半音数量及所涉及的字母名称。
Perfect intervals (unison, 4th, 5th, octave) become augmented when increased by a semitone, and diminished when decreased by a semitone. Major intervals (2nd, 3rd, 6th, 7th) become minor when lowered by a semitone, diminished when lowered by two semitones, and augmented when raised by a semitone.
纯音程（一度、四度、五度、八度）扩大一个半音变为增音程，缩小一个半音变为减音程。大音程（二度、三度、六度、七度）降低一个半音变为小音程，降低两个半音变为减音程，升高一个半音变为增音程。
| Interval | Semitones | Example from C |
|---|---|---|
| Minor 2nd | 1 | C-Db |
| Major 2nd | 2 | C-D |
| Minor 3rd | 3 | C-Eb |
| Major 3rd | 4 | C-E |
| Perfect 4th | 5 | C-F |
| Augmented 4th / Diminished 5th | 6 | C-F# / C-Gb |
| Perfect 5th | 7 | C-G |
| Minor 6th | 8 | C-Ab |
| Major 6th | 9 | C-A |
| Minor 7th | 10 | C-Bb |
| Major 7th | 11 | C-B |
| Perfect Octave | 12 | C-C' |
2. Chord Spelling Formulas | 和弦拼写公式
Chords are built by stacking thirds above a root. The quality of the third and fifth intervals determines the chord type. Major chord formula: root + major 3rd (4 semitones) + perfect 5th (7 semitones). Minor chord: root + minor 3rd (3 semitones) + perfect 5th. Diminished chord: root + minor 3rd + diminished 5th (6 semitones). Augmented chord: root + major 3rd + augmented 5th (8 semitones).
和弦通过在根音上方叠加三度构成。三度和五度音程的性质决定了和弦类型。大三和弦公式：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 another third. Dominant 7th: major triad + minor 7th (10 semitones above root). Major 7th: major triad + major 7th (11 semitones). Minor 7th: minor triad + minor 7th. Half-diminished 7th: diminished triad + minor 7th. Fully diminished 7th: diminished triad + diminished 7th (9 semitones).
七和弦再加入一个三度。属七和弦：大三和弦 + 小七度（根音上方10个半音）。大七和弦：大三和弦 + 大七度（11个半音）。小七和弦：小三和弦 + 小七度。半减七和弦：减三和弦 + 小七度。全减七和弦：减三和弦 + 减七度（9个半音）。
| Chord Type | Formula (intervals above root) |
|---|---|
| Major | M3 + P5 |
| Minor | m3 + P5 |
| Diminished | m3 + d5 |
| Augmented | M3 + A5 |
| Dominant 7th | M3 + P5 + m7 |
| Major 7th | M3 + P5 + M7 |
| Minor 7th | m3 + P5 + m7 |
3. Key Signature Circle of Fifths | 五度循环调号定理
Key signatures follow the circle of fifths. Moving clockwise (up a perfect 5th) adds a sharp; moving counterclockwise (down a perfect 5th) adds a flat. The order of sharps: F# C# G# D# A# E# B#. The order of flats: Bb Eb Ab Db Gb Cb Fb.
调号遵循五度循环圈。顺时针移动（上行纯五度）增加一个升号；逆时针移动（下行纯五度）增加一个降号。升号顺序：F# C# G# D# A# E# B#。降号顺序：Bb Eb Ab Db Gb Cb Fb。
To identify a major key from sharps: the last sharp is the leading note — go up a semitone. For flats: the penultimate flat is the tonic (except F major with one flat). Relative minor is a minor 3rd below the major tonic.
从升号调找大调主音：最后一个升号是导音——上行一个半音即为主音。降号调：倒数第二个降号是主音（F大调只有一个降号例外）。关系小调在大调主音下方小三度。
| Major Key | Key Signature | Relative Minor |
|---|---|---|
| C major | 0 sharps/flats | A minor |
| G major | 1# (F#) | E minor |
| D major | 2# (F#, C#) | B minor |
| A major | 3# (F#, C#, G#) | F# minor |
| F major | 1b (Bb) | D minor |
| Bb major | 2b (Bb, Eb) | G minor |
4. Cadence Identification Theorems | 终止式识别定理
A cadence is a harmonic formula that closes a phrase. Perfect cadence: V–I (or V7–I) in major or minor; sounds final. Imperfect cadence: any chord moving to V; ends on the dominant, sounds incomplete. Plagal cadence: IV–I; the "Amen" cadence. Interrupted cadence: V–vi (or V–VI in minor); the deceptive move away from the expected tonic.
终止式是收束乐句的和声公式。正格终止：V–I（或 V7–I），用于大调或小调，听感完结。半终止：任何和弦进行到 V，停在属和弦上，听感未完。变格终止：IV–I，“阿们”终止。阻碍终止：V–vi（小调中 V–VI），期待的主和弦被替代产生的意外效果。
In chorale-style harmony, the leading note in V must rise to the tonic in I, except when the texture forces a descent to the 5th of the tonic chord. The bass typically moves from dominant to tonic by leap of a 4th or 5th.
在众赞歌式和声中，V 和弦的导音必须上行至 I 和弦的主音，除非织体迫使它下行到主和弦的五音。低音通常以四度或五度跳进从属音进行到主音。
- Perfect: V – I (authentic)
- Imperfect: ? – V
- Plagal: IV – I
- Interrupted: V – vi / VI
5. Functional Harmony Flowchart | 功能性和声流向定理
Diatonic chords in a major key follow a hierarchy of function: Tonic (I, vi), Predominant (IV, ii), Dominant (V, vii°). The typical progression moves from tonic to predominant to dominant and back to tonic. I can move to any chord. IV and ii usually move to V or vii°. V resolves to I or vi (deceptive). vii° resolves to I or moves to V.
大调自然音和弦遵循功能层级：主功能（I, vi）、下属功能（IV, ii）、属功能（V, vii°）。典型进行由主功能到下属功能再到属功能，最后回到主功能。I 可以连接到任何和弦。IV 和 ii 通常进行到 V 或 vii°。V 解决到 I 或 vi（阻碍）。vii° 解决到 I 或进行到 V。
The chord chart below shows the most common root movements. Strong progressions move down by 5th (or up by 4th), down by 3rd, or stepwise. Avoid retrogressions like V–IV in strict common-practice style unless used sequentially.
下面的和弦表展示了最常见的根音进行。强有力的进行向下五度（或向上四度），向下三度，或级进。在严格的共性写作风格中避免如 V–IV 这样的逆功能进行，除非作为模进使用。
| From | Typical Moves To |
|---|---|
| I | IV, ii, V, vi |
| ii | V, vii° |
| IV | V, I, ii |
| V | I, vi |
| vi | IV, ii, V |
6. Scale Degree Tendency Theorems | 调式音级倾向定理
Each scale degree has an inherent melodic tendency within tonal music. The leading note (7) resolves upward by semitone to the tonic. The subdominant (4) often resolves downward to the mediant (3). The supertonic (2) can move either to 1 or 3, but in a V–I cadence it typically rises to 3 if doubled in the alto or tenor.
在调性音乐中，每个音级都具有内在的旋律倾向。导音（7）以半音上行解决到主音。下属音（4）常下行解决到中音（3）。上主音（2）可进行到 1 或 3，但在 V–I 终止式中若在中音部或次中音部重复，通常上行至 3。
Avoid augmented intervals melodically. The augmented 4th (between 4 and 7) is resolved by 7 going up to 1 and 4 going down to 3. Chromatic alterations follow the same directional principle: sharps tend to rise, flats tend to fall.
旋律上避免增音程。增四度（4 与 7 之间）通过 7 上行至 1 且 4 下行至 3 来解决。变化音遵循同样的方向原则：升号倾向上升，降号倾向下降。
7. Rhythmic and Metric Formulas | 节奏与节拍公式
Simple time signatures have beats divisible by 2 (e.g., 2/4, 3/4, 4/4). Compound time signatures have beats divisible by 3 (e.g., 6/8, 9/8, 12/8). The top number in compound meters indicates the number of divisions, not beats; divide by 3 to get the number of beats.
单拍子每拍可分为2等份（如 2/4、3/4、4/4）。复拍子每拍可分为3等份（如 6/8、9/8、12/8）。复拍子谱号的上方数字表示等分的数量而非拍数，除以3即得拍数。
Dotted rhythms, syncopation, and hemiola are essential devices. A dotted quarter note in compound time equals one full beat. Syncopation shifts accent to a weak beat or offbeat. Hemiola creates a temporary shift from compound to simple feel (3 groups of 2 in 6/8).
附点节奏、切分音和希米奥拉是核心手法。复拍子中的附点四分音符等于一个完整拍。切分音将重音转移到弱拍或拍子后半部。希米奥拉在复拍子中临时造成单拍子的感觉（6/8中形成3组2拍）。
- Simple duple: 2/4, 2/2; Simple triple: 3/4, 3/2; Simple quadruple: 4/4
- Compound duple: 6/8; Compound triple: 9/8; Compound quadruple: 12/8
8. Melodic Construction Rules | 旋律构建规则
Melodies in the Common Practice style balance stepwise motion (conjunct) with leaps (disjunct). After a leap larger than a 3rd, the melody usually changes direction and fills the gap by step. Avoid augmented intervals and leaps of a major 7th or more. The leading note rises to the tonic unless part of a descending scale line.
共性写作时期的旋律平衡级进（连贯）与跳进（分离）。大于三度的跳进后，旋律通常反向级进填补空隙。避免增音程以及大七度或更大的跳进。导音上行至主音，除非是下行音阶的一部分。
The overall contour should have a single high point (climax) and clear shape. Motifs are developed by repetition, sequence, inversion, and rhythmic augmentation/diminution.
整体轮廓应有一个高点（高潮）和清晰的形态。动机通过重复、模进、倒影和节奏增值/减值来发展。
9. Non-Harmony Tone Formulas | 非和弦音公式
Non-chord tones (NCTs) are classified by their approach and departure. Passing tone: connects two chord tones by step. Neighbour tone: moves stepwise from a chord tone and returns. Suspension: held over from a previous chord, then resolves down (4-3, 7-6, 9-8, 2-3 in bass). Appoggiatura: leaps to a dissonance that resolves by step in the opposite direction. Escape tone: stepwise into dissonance, then leaps away. Anticipation: sounds a note early before the chord changes.
非和弦音按其进入和离开的方式分类。经过音：级进连接两个和弦音。邻音：从和弦音级进并返回。挂留音：从前一和弦延留，然后下行解决（4-3, 7-6, 9-8, 低音 2-3）。倚音：跳进至不协和音，反向级进解决。跳离音：级进进入不协和音，然后跳离。先现音：在和弦改变前提早出现该音。
| NCT Type | Approach | Departure |
|---|---|---|
| Passing tone | Step | Step (same direction) |
| Neighbour tone | Step | Step (return) |
| Suspension | Same note (held) | Step down |
| Appoggiatura | Leap | Step (opposite direction) |
| Anticipation | Step or same note | Remains (becomes chord tone) |
10. Binary and Ternary Form Theorems | 二部曲式与三部曲式定理
Binary form (AB) consists of two sections, each usually repeated. Section A modulates to the dominant (or relative major if minor). Section B begins in the new key and returns to the tonic. Rounded binary returns the opening material in the tonic near the end, creating an ABA' feel without full ternary structure.
二部曲式（AB）由两个乐段组成，每段通常反复。A段转调到属调（小调则为关系大调）。B段从新调开始并返回主调。复二部曲式在结尾附近再现开头的材料，造成 ABA' 的感觉，但并非完整的三部结构。
Ternary form (ABA) has a contrasting middle section that is harmonically closed or exploratory, followed by a complete return of the A section (often with ornamentation or a coda). The B section typically contrasts in key, texture, or thematic material.
三部曲式（ABA）有一个对比性的中段，和声封闭或展开，随后完全再现 A 段（常加装饰或尾声）。B 段通常在调性、织体或主题材料上形成对比。
In Eduqas set works analysis, always identify the overall form and explain how the composer manipulates tonal relationships and thematic material within the chosen framework.
在 Eduqas 固定作品分析中，务必识别整体曲式，并说明作曲家如何在所选框架内处理调性关系和主题材料。
11. Texture Density Equations | 织体密度公式
Texture refers to the layers of sound and how they interact. Monophonic: single unaccompanied line (1). Homophonic: melody with chordal accompaniment (melody + harmonic support). Polyphonic/contrapuntal: two or more independent melodic lines (2+ independent lines). Heterophonic: simultaneous variations of a single line. Thickening texture by adding doubling (octaves, thirds) increases density; thinning by reducing parts decreases it.
织体指声音的层次及其互动方式。单声部：单一无伴奏线条（1）。主调：旋律加和弦伴奏（旋律 + 和声支持）。复调/对位：两个或以上独立旋律线条（2+ 独立线条）。支声：同一条旋律的同步变体。通过加倍（八度、三度）加厚织体可增加密度；减少声部则降低密度。
Antiphonal texture alternates between groups of instruments or voices. Imitative texture features entries of the same melodic idea in different voices at different times (fugal). A common exam question asks you to describe and compare textures in excerpts; use precise terminology.
交替对唱织体在乐器组或声部组之间轮换。模仿织体以不同声部在不同时间进入相同的旋律乐思（赋格式）。常见考题要求描述并比较选段中的织体，需使用精确术语。
12. Quick Reference for Musical Periods and Stylistic Traits | 音乐时期与风格特征速查
AS Eduqas music covers the Western Classical Tradition and one optional area of study. Key periods: Baroque (1600–1750) — terraced dynamics, contrapuntal textures, basso continuo. Classical (1750–1820) — balanced phrases, homophonic textures, functional harmony. Romantic (1820–1900) — expressive chromaticism, expanded forms, programmatic elements. 20th Century — exploration of tonality, atonality, impressionism, serialism, and new textures.
AS Eduqas 音乐涵盖西方古典传统及一个可选研究领域。关键时期：巴洛克（1600–1750）——阶梯式力度、对位织体、通奏低音。古典（1750–1820）——均衡乐句、主调织体、功能性和声。浪漫（1820–1900）——表情性变音、扩展曲式、标题性元素。20世纪——调性探索、无调性、印象主义、序列主义和新的织体。
For each set work, memorize the key structural points, harmonic features, and stylistic fingerprints. Apply the formulas from this handbook to articulate your analysis precisely.
对每部固定作品，熟记其关键结构点、和声特点和风格印记。应用本手册中的公式来精确阐述你的分析。
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