📚 Year 11 CCEA Music: Quick Reference Formula & Theorem Handbook | 音乐公式定理速查手册
This guide compiles the essential 'formulas' and 'theorems' of music theory that every Year 11 CCEA Music student needs at their fingertips. Just as mathematical equations provide structure in science, these patterns, rules and principles form the backbone of composition, performance and listening analysis. From scale construction to cadence recognition, each section offers a clear, bilingual reference to help you decode the language of music with confidence.
本手册汇集了每一位 Year 11 CCEA 音乐学生都需要熟练掌握的音乐理论核心“公式”与“定理”。正如数学方程赋予科学以结构一样，这些模式、规则与原理构成了作曲、表演与听觉分析的骨干。从音阶构建到终止式识别，每一节都提供清晰的双语速查参考，帮助你自信地解读音乐的语言。
1. Major Scale Formula | 大调音阶公式
The major scale is built using a fixed pattern of tones (T) and semitones (S). Starting from any tonic note, the sequence T-T-S-T-T-T-S produces a bright, familiar sound. In the key of C major, this gives C-D-E-F-G-A-B-C with semitones falling naturally between E-F and B-C.
大调音阶以一个固定的全音（T）与半音（S）模式构建。从任一主音出发，序列 T-T-S-T-T-T-S 即产生明亮而熟悉的音响。在 C 大调中，由此得出 C-D-E-F-G-A-B-C，半音自然落在 E-F 与 B-C 之间。
Major scale formula: T - T - S - T - T - T - S
大调音阶公式：全 - 全 - 半 - 全 - 全 - 全 - 半
- In solfège, a major scale is do-re-mi-fa-sol-la-ti-do'. The semitones occur between mi-fa and ti-do'.
- 在唱名法中，大调音阶为 do-re-mi-fa-sol-la-ti-do'。半音出现在 mi-fa 与 ti-do' 之间。
2. Natural Minor Scale Formula | 自然小调音阶公式
The natural minor scale uses the pattern T-S-T-T-S-T-T. Relative to its major counterpart (same key signature), it shares all notes but begins on the sixth degree. For A natural minor, the notes are A-B-C-D-E-F-G-A, with semitones between B-C and E-F.
自然小调音阶使用模式 T-S-T-T-S-T-T。相较于其关系大调（同调号），它使用完全相同的音，但始于第六级。以 A 自然小调为例，音符为 A-B-C-D-E-F-G-A，半音在 B-C 与 E-F 之间。
Natural minor formula: T - S - T - T - S - T - T
自然小调公式：全 - 半 - 全 - 全 - 半 - 全 - 全
- The relative minor is always found a minor third (three semitones) below the major tonic.
- 关系小调总是在大调主音下方小三度（三个半音）处找到。
3. Circle of Fifths and Key Signatures | 五度圈与调号
The circle of fifths maps key signatures. Moving clockwise from C major, each step adds one sharp: G (1♯), D (2♯), A (3♯), E (4♯), B (5♯), F♯ (6♯), C♯ (7♯). Moving anticlockwise adds flats: F (1♭), B♭ (2♭), E♭ (3♭), A♭ (4♭), D♭ (5♭), G♭ (6♭), C♭ (7♭). This is the fundamental 'theorem' linking key, tonic and accidentals.
五度圈标示了调号。从 C 大调顺时针出发，每一步增加一个升号：G（1♯）、D（2♯）、A（3♯）、E（4♯）、B（5♯）、F♯（6♯）、C♯（7♯）。逆时针则增加降号：F（1♭）、B♭（2♭）、E♭（3♭）、A♭（4♭）、D♭（5♭）、G♭（6♭）、C♭（7♭）。这是连接调、主音与变音记号的基本“定理”。
Order of sharps: F♯ C♯ G♯ D♯ A♯ E♯ B♯
升号次序：F♯ C♯ G♯ D♯ A♯ E♯ B♯
Order of flats: B♭ E♭ A♭ D♭ G♭ C♭ F♭
降号次序：B♭ E♭ A♭ D♭ G♭ C♭ F♭
4. Interval Number and Quality Rules | 音程度数与性质规则
An interval is the distance between two notes, defined by number (2nd, 3rd, 4th, etc.) and quality (perfect, major, minor, augmented, diminished). Count the letter names inclusive to get the number. Quality depends on the number of semitones: a perfect 5th equals 7 semitones, a major 3rd equals 4 semitones. The key formula: in a major scale, intervals from the tonic are either major or perfect (unison, 4th, 5th, octave are perfect; 2nd, 3rd, 6th, 7th are major).
音程是两个音之间的距离，由度数（二度、三度、四度等）与性质（纯、大、小、增、减）定义。从低音到高音包含计算字母名得到度数。性质取决于半音数：纯五度含 7 个半音，大三度含 4 个半音。核心公式：在大调音阶中，自主音开始的音程均为大音程或纯音程（同度、四度、五度、八度为纯；二度、三度、六度、七度为大）。
| Interval | 音程 | Semitones | 半音数 | Common example | 常见示例 |
|---|---|---|
| Minor 2nd | 小二度 | 1 | E-F |
| Major 2nd | 大二度 | 2 | C-D |
| Minor 3rd | 小三度 | 3 | A-C |
| Major 3rd | 大三度 | 4 | C-E |
| Perfect 4th | 纯四度 | 5 | C-F |
| Perfect 5th | 纯五度 | 7 | C-G |
| Octave | 八度 | 12 | C-C' |
5. Triad Construction Formulas | 三和弦构建公式
A triad is a three-note chord stacked in thirds. The quality depends on the intervals between the notes. A major triad consists of root + major 3rd + perfect 5th (4 + 3 semitones). A minor triad is root + minor 3rd + perfect 5th (3 + 4 semitones). Diminished triads have a minor 3rd and diminished 5th (3+3), while augmented triads have a major 3rd and augmented 5th (4+4). These formulas form the harmonic foundation of Western tonal music.
三和弦是由三度叠置而成的三个音组成的和弦。其性质取决于音与音之间的音程。大三和弦由根音 + 大三度 + 纯五度构成（4 + 3 个半音）。小三和弦为根音 + 小三度 + 纯五度（3 + 4 个半音）。减三和弦包含小三度与减五度（3 + 3），增三和弦则包含大三度与增五度（4 + 4）。这些公式构成了西方调性音乐的和声根基。
Major triad: Root + M3 + P5 (C-E-G)
大三和弦：根音 + 大三度 + 纯五度（C-E-G）
- ajor key: I, ii, iii, IV, V, vi, vii°. Capital = major, lowercase = minor, ° = diminished.
- 罗马数字标记中，大调音阶各级三和弦遵循：I（大）、ii（小）、iii（小）、IV（大）、V（大）、vi（小）、vii°（减）。大写为大调，小写为小调，° 为减。
6. Seventh Chord Formulas | 七和弦公式
Seventh chords add a fourth note—a seventh above the root—to a triad. The dominant 7th (V7) uses a major triad plus a minor 7th: root + M3 + P5 + m7. The major 7th chord has a major triad and a major 7th. The minor 7th uses a minor triad and a minor 7th. The half-diminished 7th (viiø7) is a diminished triad with a minor 7th, while the fully diminished 7th has a diminished triad and a diminished 7th. These formulas create tension and drive harmonic progressions.
七和弦在三和弦的基础上增加第四个音——高于根音的七度音。属七和弦（V7）使用大三和弦加小七度：根音 + 大三度 + 纯五度 + 小七度。大七和弦包含大三和弦与大七度。小七和弦由小三和弦与小七度构成。半减七和弦（viiø7）为减三和弦加小七度，而全减七和弦则为减三和弦加减七度。这些公式制造紧张感，推动和声进行。
Dominant 7th: Root + M3 + P5 + m7 (G-B-D-F in C major)
属七和弦：根音 + 大三度 + 纯五度 + 小七度（C大调中 G-B-D-F）
7. Cadence Recognition Theorems | 终止式识别定理
Cadences are harmonic punctuation marks that close phrases. The perfect cadence (V-I) sounds final and conclusive, like a full stop. The imperfect cadence (ending on V) feels unfinished, like a comma. The plagal cadence (IV-I) gives an 'Amen' effect. The interrupted cadence (V-vi) surprises the listener by moving to the submediant instead of the tonic. Recognising these 'theorems' by ear and score is a key Year 11 listening skill.
终止式是结束乐句的和声标点。正格终止（V-I）听感完满、终结，如同句号。不完全终止（结束于 V）听感未完成，如同逗号。变格终止（IV-I）带来“阿门”效果。阻碍终止（V-vi）通过进行到六级音而非主音，令听者意外。通过听觉与乐谱识别这些“定理”是 Year 11 关键听力技能。
| Cadence | 终止式 | Chords | 和弦 | Effect | 效果 |
|---|---|---|
| Perfect | 正格 | V - I | Final, conclusive | 完满、终结 |
| Imperfect | 不完全 | ? - V | Unfinished, pause | 未完成、停顿 |
| Plagal | 变格 | IV - I | Amen, gentle | 阿门、柔和 |
| Interrupted | 阻碍 | V - vi | Surprise, twist | 意外、转折 |
8. Rhythm and Time Signature Rules | 节奏与拍号规则
consist of two numbers: the top number indicates beats per bar, the bottom shows the beat' signatures (6/8, 9/8, 12/8) have dotted-crotchet beats that divide into three quavers. The 'theorem' e = total duration. Recognizing irregular metres such as 5/4 or 7/8 adds rhythmic variety.
拍号由两个数字组成：上方数字表示每小节的拍数，下方数字表示以何种音符为一拍。单拍子（2/4、3/4、4/4）的每一拍自然二分。复拍子（6/8、9/8、12/8）以附点四分音符为一拍，每拍分为三个八分音符。速度的“定理”：BPM（每分钟拍数）× 音符时值 = 总时长。识别 5/4 或 7/8 等不规则拍号，增加节奏多样性。
Compound duple: 6/8 = 2 dotted crotchet beats | 复二拍：6/8 = 2 个附点四分音符拍
- Dotted rhythms, syncopation (off-beat accents), and triplets (three notes in the time of two) are common devices.
- 附点节奏、切分音（重音落在弱拍）以及三连音（两拍内奏三个音）是常用手法。
9. Dynamics and Expression Terms | 力度与表情术语
Dynamics describe volume, expressed through Italian terms and their abbreviations. The 'formula' of gradual changes: crescendo (cresc., gradually louder) and diminuendo/dim. (gradually softer). Standard levels from softest to loudest: pp (pianissimo, very soft), p (piano, soft), mp (mezzo-piano, moderately soft), mf (mezzo-forte, moderately loud), f (forte, loud), ff (fortissimo, very loud). Articulation marks such as staccato, legato, accent and tenuto alter note attack and length.
力度描述音量，通过意大利术语及其缩写表达。渐变“公式”：crescendo（渐强）与 diminuendo/dim.（渐弱）。从最弱到最强的标准力度层次：pp（很弱）、p（弱）、mp（中弱）、mf（中强）、f（强）、ff（很强）。演奏法标记如断奏、连奏、重音与保持音改变音符的触键与长度。
| Term | 术语 | Abbreviation | 缩写 | Meaning | 含义 |
|---|---|---|
| pianissimo | pp | Very soft | 很弱 |
| mezzo-forte | mf | Moderately loud | 中强 |
| fortissimo | ff | Very loud | 很强 |
| staccato | dot above/below note | Short, detached | 短促、分离 |
| legato | slur | Smooth, connected | 圆滑、连贯 |
10. Ornamentation and Articulation Patterns | 装饰音与演奏法模式
Ornaments decorate the melodic line with added notes. The trill is a rapid alternation between the written note and the note above. The turn goes: note above, written note, note below, written note. The mordent is a quick alternation with the adjacent note and back, while the acciaccatura is a crushed grace note. These patterns act as melodic 'formulas' and are essential for accurate period-style performance.
装饰音以附加音符润饰旋律线条。颤音是书写音与上方相邻音的快速交替。回音进行为：上方音、书写音、下方音、书写音。波音为与相邻音快速交替并返回，而短倚音则为挤出的装饰音。这些模式充当旋律“公式”，对于准确再现时代风格至关重要。
Trill: note + upper auxiliary rapid alternation
颤音：书写音与上方辅助音的快速交替
- Appoggiatura is a non-chord tone that leans on the main note, taking half its value; suspension is a variation of the appoggiatura formula.
- 倚音为依靠在主音上的和弦外音，占用主音一半时值；延留音是倚音公式的变体。
11. Texture and Voicing Theorems | 织体与声部定理
Texture describes how musical lines interact. Monophonic texture is a single unaccompanied melody. Homophonic texture features a melody with chordal accompaniment, often melody-dominated. Polyphonic texture has two or more independent melodies woven together. Heterophonic texture involves simultaneous variations of a single melody. Understanding these 'theorems' helps in score analysis and describing the overall sound fabric of a piece.
织体描述音乐线条如何互动。单音织体为无伴奏的单条旋律。主调织体以一条旋律加和弦伴奏为特征，常为旋律主导型。复调织体包含两条或以上的独立旋律交织在一起。支声织体则是一条旋律的同步变奏。理解这些“定理”有助于总谱分析及描述作品的整体音响构造。
Texture Theorem: layers + relationship = texture type
织体定理：层次 + 关系 = 织体类型
- Common textures in CCEA set works: homorhythmic chords, imitative counterpoint, call and response, drone, and octave doubling.
- CCEA 指定作品中的常见织体：同节奏和弦、模仿对位、呼唤与回应、持续低音以及八度重叠。
12. Form and Structure Blueprints | 曲式与结构蓝图
Musical form is the 'architecture' of a composition, often following recurring patterns. Binary form (AABB) has two distinct sections, each repeated. Ternary form (ABA) returns to the opening material after a contrasting middle. Rondo form (ABACA) features a recurring A theme alternating with episodes. Theme and variations presents a theme followed by modified versions. Sonata form, crucial for CCEA analysis, uses exposition, development and recapitulation with key relationships.
曲式是音乐作品的“建筑蓝图”，常遵循重复模式。二段体（AABB）包含两个不同的乐段，每段重复。三段体（ABA）在对比性中段后返回开篇素材。回旋曲式（ABACA）以一个反复出现的 A 主题与插部交替。主题与变奏呈现一个主题及其变化版本。奏鸣曲式在 CCEA 分析中至关重要，包含呈示部、展开部与再现部，并涉及调性关系。
| Form | 曲式 | Structure | 结构 | Typical era | 典型时期 |
|---|---|---|
| Binary | AABB | Baroque dances | 巴洛克舞曲 |
| Ternary | ABA | Classical minuet & trio | 古典小步舞曲与三声中部 |
| Sonata | Expo - Dev - Recap | Classical, Romantic | 古典、浪漫 |
Sonata blueprint: I (tonic) - V (dominant) in exposition; modulation in development; all in tonic in recapitulation.
奏鸣曲蓝图：呈示部 I（主调） - V（属调）；展开部转调；再现部全部回归主调。
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