📚 Year 13 WJEC Music: Formula & Theorem Quick Reference Handbook | 音乐公式定理速查手册
This handbook translates the core concepts of Year 13 WJEC Music into ‘formulas’ and ‘theorems’ for quick memorisation and application. From scale construction and chord building to cadential patterns and modulation rules, each section presents a concise, exam-focused reference. Use these musical equations to decode analysis, guide composition, and strengthen your aural skills.
本手册将 Year 13 WJEC 音乐的核心概念转化为“公式”与“定理”，便于快速记忆与运用。从音阶构建、和弦构成到终止式模式与转调规则，每个部分都提供精炼的考试导向参考。运用这些音乐“方程式”，可帮助你解析作品、指导创作并提升听觉分析能力。
1. The Major Scale Formula | 大调音阶公式
The major scale follows a fixed pattern of whole steps (W) and half steps (H): W‑W‑H‑W‑W‑W‑H. Starting on any note, this sequence generates the correct key signature accidentals automatically.
大调音阶遵循固定的全音（W）与半音（H）模式：全‑全‑半‑全‑全‑全‑半。从任意音出发，该序列会自动生成正确的调号变音。
Converted into semitone steps: 2‑2‑1‑2‑2‑2‑1. For example, C major: C D (2) E (2) F (1) G (2) A (2) B (2) C (1).
转化为半音步进：2‑2‑1‑2‑2‑2‑1。例如 C 大调：C D (2) E (2) F (1) G (2) A (2) B (2) C (1)。
Scale degree numbering: 1 tonic, 2 supertonic, 3 mediant, 4 subdominant, 5 dominant, 6 submediant, 7 leading note. These labels function regardless of key.
音级编号：1 主音，2 上主音，3 中音，4 下属音，5 属音，6 下中音，7 导音。这些称谓在任意调中作用不变。
2. Minor Scale Variants | 小调音阶变体公式
Three minor scales share the same key signature but alter the 6th and 7th degrees differently. The natural minor applies the key signature literally: W‑H‑W‑W‑H‑W‑W (2‑1‑2‑2‑1‑2‑2).
三种小调音阶共享相同的调号，但对第6、第7级音的改动各不相同。自然小调直接使用调号：全‑半‑全‑全‑半‑全‑全（2‑1‑2‑2‑1‑2‑2）。
Harmonic minor formula: raise the 7th degree by a semitone from natural minor, creating an augmented 2nd between 6th and 7th. This gives the dominant chord a major quality.
和声小调公式：在自然小调基础上将第7级升高半音，形成第6与第7级间的增二度。这让属和弦具有大调色彩。
Melodic minor (ascending): raise both 6th and 7th degrees by a semitone from natural minor — W‑H‑W‑W‑W‑W‑H (2‑1‑2‑2‑2‑2‑1). Descending typically reverts to natural minor.
旋律小调（上行）：将第6与第7级同时升高半音——全‑半‑全‑全‑全‑全‑半（2‑1‑2‑2‑2‑2‑1）。下行通常回到自然小调。
3. Interval Theorems | 音程定理
Interval quality and number follow precise inversion rules. The inversion of a major interval is minor, perfect remains perfect, augmented becomes diminished — and the sum of the original and inverted numbers always equals 9.
音程的性质与度数遵循精确的转位规则。大音程转位后变为小音程，纯音程保持纯，增音程变为减音程——且原音程度数与转位音程度数之和恒为9。
Compound intervals beyond an octave: subtract 7 to find the simple equivalent. A major 9th reduces to a major 2nd; analysis can be done at the simple level first.
超过八度的复音程：减7可得到单音程等值。大九度减去7为大二度；可先以单音程进行分析。
Consonance and dissonance theorem: perfect unisons, octaves, 4ths and 5ths are perfect consonances; major and minor 3rds and 6ths are imperfect consonances; all 2nds, 7ths and augmented/diminished intervals are dissonant and require resolution.
协和与不协和定理：纯一度、纯八度、纯四度、纯五度为完全协和；大小三度、大小六度为不完全协和；所有二度、七度及增/减音程均为不协和，需要解决。
4. Triad Construction Formulas | 三和弦构建公式
Triads are built by stacking two 3rds above a root. Use semitone counting for precision: major triad = root + 4 semitones (major 3rd) + 3 semitones (minor 3rd) → total 7 semitones from root to 5th.
三和弦由根音上方叠加两个三度构成。用半音计算可精准构建：大三和弦 = 根音 + 4 半音（大三度） + 3 半音（小三度）→ 根音至五度为7个半音。
Formula table:
公式表：
| Triad | Structure (semitones above root) | Example in C |
| Major | 0, 4, 7 | C E G |
| Minor | 0, 3, 7 | C E♭ G |
| Augmented | 0, 4, 8 | C E G♯ |
| Diminished | 0, 3, 6 | C E♭ G♭ |
In Roman numeral analysis, major triads are shown with upper case (I, IV, V), minor with lower case (ii, iii, vi), diminished with lower case plus ° (vii°). Augmented triads appear as III⁺ in minor keys.
在罗马数字分析中，大三和弦用大写（I, IV, V），小三和弦用小写（ii, iii, vi），减三和弦用小写加 °（vii°）。增三和弦在小调中记为 III⁺。
5. Seventh Chord Formulas | 七和弦公式
Seventh chords add a 4th note a 7th above the root. The quality depends on the triad and the type of 7th. Formula in semitones above root:
七和弦是在三和弦基础上增加根音上方的七度音。其性质取决于三和弦与七度音的类型。半音公式（根音上方）：
- Major 7th: 0, 4, 7, 11 (major triad + major 7th)
- Dominant 7th: 0, 4, 7, 10 (major triad + minor 7th)
- Minor 7th: 0, 3, 7, 10 (minor triad + minor 7th)
- Half‑diminished 7th: 0, 3, 6, 10 (diminished triad + minor 7th)
- Diminished 7th: 0, 3, 6, 9 (diminished triad + diminished 7th)
大七和弦：0, 4, 7, 11（大三和弦 + 大七度）
属七和弦：0, 4, 7, 10（大三和弦 + 小七度）
小七和弦：0, 3, 7, 10（小三和弦 + 小七度）
半减七和弦：0, 3, 6, 10（减三和弦 + 小七度）
减七和弦：0, 3, 6, 9（减三和弦 + 减七度）
The dominant 7th chord contains a tritone between its 3rd and 7th, which drives resolution to the tonic. In 4‑part writing, the 7th of any seventh chord must resolve downwards by step.
属七和弦的三音与七音构成三全音，推动向主和弦解决。在四部和声中，任何七和弦的七音必须下行级进解决。
6. Chord Inversion Formulas | 和弦转位公式
A chord is inverted when a note other than the root is in the bass. The figured bass symbols indicate intervals above the bass note.
当和弦的根音不在低音声部时，即为转位。数字低音标记表示低音上方各音的音程。
Triad inversion theorem:
三和弦转位定理：
- Root position: 5/3 (often omitted)
- 1st inversion (third in bass): 6/3, commonly shortened to 6
- 2nd inversion (fifth in bass): 6/4
根音位置：5/3（常省略）
第一转位（三音在低音）：6/3，常简写为 6
第二转位（五音在低音）：6/4
Seventh chord inversions:
七和弦转位：
- Root position: 7
- 1st inversion (3rd in bass): 6/5
- 2nd inversion (5th in bass): 4/3
- 3rd inversion (7th in bass): 4/2 (or simply 2)
根音位置：7
第一转位（三音在低音）：6/5
第二转位（五音在低音）：4/3
第三转位（七音在低音）：4/2（或简写为 2）
The 6/4 chord is treated as a dissonance resolving onto a 5/3 on the same bass note (cadential 6/4), or used as a passing or pedal 6/4.
6/4 和弦被视为不协和和弦，需解决至同一低音的 5/3 和弦（终止 6/4），或用作经过 6/4、延留 6/4。
7. Cadence Formulas | 终止式公式
A cadence is a two‑chord progression that closes a phrase. Each type has a distinct harmonic formula and expressive function.
终止式是结束乐句的两个和弦进行。每种终止式都有独特的和声公式与表情功能。
| Cadence | Chords (major key) | Effect |
| Perfect (authentic) | V – I (both root position) | Strong close, finality |
| Imperfect | I – V, ii – V, IV – V, vi – V | Unfinished, expects continuation |
| Plagal | IV – I | Amen cadence, gentle resolution |
| Interrupted (deceptive) | V – vi (or V – IV6, V – ♭VI) | Surprise, avoids expected tonic |
正格终止（V‑I，均为根音位置）具有强烈的收束感；半终止（I‑V, ii‑V, IV‑V, vi‑V）期待继续；变格终止（IV‑I）常为“阿门”终止；阻碍终止（V‑vi 等）通过避开主和弦制造意外。
8. Diatonic Chord Function Theorems | 自然音和弦功能定理
Within a key, chords group into three functional families. This theorem underpins tonal harmony from Bach to film music.
在一个调内，所有和弦归入三个功能组。这一定理支撑着从巴赫到电影音乐的调性和声。
Tonic function (stable, rest): chords I, vi, and iii (iii is the weakest tonic substitute). Subdominant function (departing, gentle push away): chords IV, ii, and the supertonic 7th ii⁷. Dominant function (tension, drive to tonic): chords V, vii°, and vii⁷.
主功能（稳定，静止）：I, vi, iii（iii 是最弱的主功能替代）。下属功能（离开，温和推动）：IV, ii，以及上主七和弦 ii⁷。属功能（紧张，倾向主和弦）：V, vii°, vii⁷。
The predominant (subdominant) moves to dominant, which moves to tonic. The vi chord can substitute for I in deceptive progressions. The iii chord rarely progresses directly to IV in strict style.
下属功能和弦进行至属功能，属功能进行至主功能。vi 和弦可在阻碍进行中替代 I。严格风格中，iii 很少直接进行到 IV。
9. Modulation Rules | 转调规则
Modulation changes the tonal centre. The most reliable method uses a pivot chord — a chord that belongs to both the old and new keys.
转调改变调性中心。最可靠的方法是使用枢轴和弦——即同时属于原调与新调的和弦。
Pivot chord theorem: In moving from key A to key B, identify chords that are diatonic in both. For example, moving from C major to G major, the chords Am (vi in C, ii in G) and Em (iii in C, vi in G) are common pivots. The modulation is confirmed by a cadence in the new key.
枢轴和弦定理：在从 A 调转到 B 调时，找出同时在两调中为自然音的和弦。例如，从 C 大调转到 G 大调，Am（C 调 vi，G 调 ii）和 Em（C 调 iii，G 调 vi）是常见的枢轴。转调须由新调终止式加以确认。
Chromatic modulation uses an altered chord as a pivot, such as the Neapolitan 6th or an augmented 6th chord. Direct modulation (phrase modulation) changes key abruptly without pivot, common in Romantic and popular styles.
半音转调使用变音和弦作为枢轴，如拿波里六和弦或增六和弦。直接转调（乐句转调）不经过枢轴突然改变调性，在浪漫派与流行风格中常见。
10. Ornament Formulas | 装饰音公式
Ornaments are not random embellishments; each follows a precise pitch pattern. The WJEC exam expects recognition and realisation of these symbols.
装饰音并非随意的点缀；每一种都遵循精确的音高模式。WJEC 考试要求对其符号进行识别与完成实现。
- Trill (tr): rapid alternation between the written note and the upper diatonic note; may start on the upper note in Baroque practice.
- Turn (𝄐): four‑note figure: upper note – written note – lower note – written note.
- Mordent (𝄞, upper mordent): written note – upper note – written note, played quickly.
- Inverted mordent (𝄝, lower mordent): written note – lower neighbour – written note.
- Appoggiatura: a dissonant note that takes half the value of the main note (if the main note is not dotted) and resolves by step.
- Acciaccatura: a crushed note, played as quickly as possible before the main note.
颤音：快速交替本音与上方自然音；巴洛克实践中常从上助音开始。回音：四音列：上方音‑本音‑下方音‑本音。上波音：本音‑上方音‑本音，快速。下波音：本音‑下方音‑本音。倚音：占主音一半时值（若不附点）的不协和音，级进解决。碎音：尽可能快地奏出后随即进入主音。
11. Rhythm & Metre Theorems | 节奏与节拍定理
Time signatures convey both metric grouping and accent patterns. The top number indicates beats per bar; the bottom number shows the beat unit value.
拍号传达节拍分组与重音模式。上方数字表示每小节拍数；下方数字表示拍子的时值单位。
Simple time theorem: beats divide naturally into two equal parts. Examples: 2/4, 3/4, 4/4, 3/8. Compound time theorem: beats divide into three equal parts. Examples: 6/8 (two dotted‑crotchet beats), 9/8 (three), 12/8 (four).
单拍子定理：每拍自然分为两个均等部分。如 2/4, 3/4, 4/4, 3/8。复拍子定理：每拍分为三个均等部分。如 6/8（两个附点四分音符为一拍），9/8（三拍），12/8（四拍）。
Hemiola theorem: a temporary shift of accent, typically in triple metre, where two bars of 3/4 are articulated as three bars of 2/4. This creates cross‑rhythm tension often found in Baroque cadences and dance music.
赫米奥拉定理：临时重音移位，常见于三拍子中，将两小节 3/4 演绎为三组 2/4，产生交叉节奏张力，多见于巴洛克终止式与舞曲。
Syncopation: accenting a weak beat or off‑beat. The WJEC analysis should identify ties over barlines, rests on strong beats, and accented passing notes. The ‘back‑beat’ emphasis in pop and jazz stems from this principle.
切分音：强调弱拍或弱位。WJEC 分析需识别跨小节延音线、强拍休止、以及强拍上的经过音。流行与爵士中的“反拍”强调即源于此。
12. Form & Structure Theorems | 曲式与结构定理
Musical form is governed by thematic recurrence and key relationships. The most tested structures in WJEC include binary, ternary, sonata form, rondo, and theme & variations.
音乐曲式受主题再现与调性关系支配。WJEC 常考的结构包括二部曲式、三部曲式、奏鸣曲式、回旋曲式以及主题与变奏。
Binary form (AB): section A modulates to a related key (usually dominant if major, relative major if minor); section B begins in that new key and returns to the tonic. Rounded binary concludes with a partial return of A material.
二部曲式（AB）：A 段转至关系调（大调至属调，小调至关系大调）；B 段始于新调并返回主调。再现二部曲式在结尾部分再现 A 素材。
Ternary form (ABA): A closes in the tonic; B provides contrast in a new key, mood or texture; A returns complete. The return often features embellished melody or varied accompaniment (da capo aria form).
三部曲式（ABA）：A 段在主调结束；B 段在新调、情绪或织体上形成对比；A 段完整再现。再现时常带有装饰旋律或变化的伴奏（返始咏叹调式）。
Sonata form theorem: Exposition (first subject in tonic, bridge modulating, second subject in contrasting key, codetta) – Development (motivic fragmentation, sequence, harmonic instability) – Recapitulation (first subject, bridge altered to stay in tonic, second subject in tonic, coda).
奏鸣曲式定理：呈示部（第一主题主调，连接部转调，第二主题对比调性，小结尾）– 展开部（动机分裂、模进、和声不稳定）– 再现部（第一主题，连接部改写以停留在主调，第二主题主调，尾声）。
13. Chromatic Harmony Formulas | 半音和声公式
Chromatic chords introduce notes outside the key signature and are essential in the late Romantic and early 20th‑century repertoire studied at Year 13.
半音和弦引入调号以外的音，是 Year 13 学习的晚期浪漫派与 20 世纪早期曲目中的关键要素。
- Neapolitan 6th (♭II⁶): a major triad built on the flattened supertonic, typically in first inversion (hence the 6). It functions as a pre‑dominant and resolves to V or the cadential 6/4.
- Augmented 6th chords: three varieties — Italian (e.g. A♭, C, F♯), French (adds D), German (adds E♭). All contain the raised 4th (in minor) or the equivalent intervals resolving outward to an octave on the dominant.
- Secondary dominant: V of any diatonic chord other than I. Formula: a major triad (or dominant 7th) built on the root a 5th above the target chord. E.g., in C major, A major (V/ii) resolves to D minor.
- Diminished 7th modulation enharmonic theorem: any diminished 7th chord can be respelled enharmonically to resolve in at least four different keys. This makes it a powerful pivot for distant modulations.
拿波里六和弦（♭II⁶）：建立在降上主音上的大三和弦，通常为第一转位，起下属功能作用，解决至 V 或终止 6/4。增六和弦有三种——意大利增六、法国增六、德国增六——均包含升四级音（小调），向外解决至属音八度。副属和弦：任何自然音和弦（除 I 外）的属和弦，构建在目标和弦上方五度的大三和弦或属七。减七和弦等音转调定理：任一减七和弦可通过等音改写，在至少四个不同调中解决，成为远关系转调的强力枢轴。
14. Voice Leading ‘Laws’ | 声部进行“定律”
While not absolute, these conventions govern 4‑part writing and are examined in both harmony exercises and score analysis.
虽非绝对，但这些惯例支配着四部和声写作，在习题与乐谱分析中均有考查。
Law of the shortest way: keep common tones in the same voice when moving between chords that share notes. For chords a 3rd or 6th apart, move the remaining voices by step to the nearest chord tones.
最邻近进行定律：当和弦间有共同音时，将其保持在同一声部。相距三度或六度的和弦，其余声部级进至最近的和弦音。
Contrary motion law: when the bass moves, aim for upper voices to move in the opposite direction, especially between outer voices. This preserves independence and avoids objectionable parallels.
反向进行定律：当低音移动时，上声部尤其是外声部应尽可能朝反方向进行，以保持独立性并避免不当平行。
Parallel perfect interval prohibition: avoid parallel 5ths and octaves between any two voices. Also avoid exposed (hidden) 5ths and octaves: similar motion into a perfect interval with a leap in the soprano.
平行纯音程禁令：避免任何两声部间的平行五度与八度。同时避免暴露（隐伏）五度与八度：同向进行到达纯音程并伴有高音跳进。
Leading note theorem: the 7th degree of the scale, when present, must rise to the tonic by step — especially when it is in an outer voice or part of a dominant chord. The only exception is an internal descent in a melodic line that avoids parallelism.
导音定理：音阶第7级音出现时必须级进上行至主音——尤其在外声部或作为属和弦音时。唯一例外是旋律线内部为避开平行而做的下行。
15. Expression and Tempo Terminology | 音乐表情与速度术语速查
WJEC examining requires precise Italian, French and German terms linked to score markings. The following quick‑reference table lists high‑frequency terms categorised by function.
WJEC 考试要求精确掌握与乐谱标记相关的意、法、德术语。以下速查按功能分类列出高频术语。
| Category | Term | Meaning |
| Tempo | Largo, Adagio, Andante, Moderato, Allegro, Presto | Very slow, slow, walking pace, moderate, fast, very fast |
| Changes | ritardando, accelerando, rubato, a tempo | Gradually slower, faster, flexible tempo, return to original tempo |
| Dynamics | 更多咨询请联系16621398022（同微信）
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