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

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

This handbook distils the essential ‘formulas’ of music theory and composition for Year 13 CIE Music students. Think of harmonic progressions, structural blueprints, contrapuntal rules, and serial procedures as your musical equations – once internalised, they unlock analytical precision and creative fluency. Use this reference to reinforce your aural perception, written work, and performance insights.

本手册为 Year 13 CIE 音乐学生提炼音乐理论与创作的核心“公式”。把和声进行、结构蓝图、对位规则和序列程序视为你的音乐方程式——一旦内化，它们将解锁分析精度与创作流畅度。借助本参考指南强化你的听觉感知、书面作答和演奏洞察。

1. Harmonic Progressions & Cadences | 和声进行与终止式

A harmonic progression is the backbone of tonal music, moving from tension to resolution. The most fundamental progression is I–IV–V–I, often extended with inversions and seventh chords. Cadences act as punctuation: perfect (V–I), imperfect (I–V, etc.), plagal (IV–I), and interrupted (V–vi). In CIE analysis, identify cadence types by root movement and outer-voice motion, especially in chorale-style excerpts.

和声进行是调性音乐的骨架，从紧张走向解决。最基本的是 I–IV–V–I 进行，常通过转位与七和弦加以扩展。终止式充当标点：正格终止 (V–I)、半终止 (I–V等)、变格终止 (IV–I) 和阻碍终止 (V–vi)。在 CIE 分析中，应依据根音进行与外声部运动辨识终止式类型，尤其在众赞歌式片段中。

2. Figured Bass & Realisation | 数字低音与实现

Figured bass encodes intervals above a given bass note using numbers and accidentals. For example, a ‘6’ indicates a first-inversion triad, ‘6/4’ a second inversion, and ‘7’ a root-position seventh chord. When realising a figured bass in four-part harmony, double the bass (root position) or soprano as appropriate, resolve leading tones upward, and avoid parallel fifths and octaves. Chromatic figures (e.g. #, b) affect the third above the bass.

数字低音用数字与变音记号标明给定低音上方的音程。例如“6”表示原位和弦第一转位，“6/4”表示第二转位，“7”表示原位七和弦。在四部和声中实现数字低音时，应根据需要重复低音（原位）或女高音声部，将导音上行解决，避免平行五八度。半音数字（如 #、b）作用于低音上方三度音。

3. Counterpoint Rules | 对位法规则

Species counterpoint governs the combination of independent melodic lines. Key rules include: begin and end on perfect consonances (unison, octave, fifth); use contrary motion where possible; avoid parallel perfect intervals; resolve dissonances by stepwise descent (e.g. suspensions 4–3, 7–6). In CIE two-part textures, apply these principles to melodic dictation and embellishment exercises, treating each line as a self-sufficient melody.

分类对位法支配独立旋律线条的结合。关键规则包括：起始与结束采用完全协和音程（同度、八度、五度）；尽可能使用反向进行；避免平行完全音程；不协和音级进下行解决（例如留音 4–3、7–6）。在 CIE 二声部织体中，将这些原则应用于旋律听写与装饰练习，把每一声部视作自足的旋律。

4. Chord Functions & Roman Numeral Analysis | 和弦功能与罗马数字分析

Chords carry syntactic functions: tonic (I, vi) provide stability; dominant (V, vii°) create tension; subdominant (IV, ii) prepare for dominants. In major keys, the functional map I – IV – V – I is foundational. In minor, the raised leading tone in V must be reflected in analysis (e.g. V in harmonic minor). Use roman numerals with inversion figures (e.g. I⁶, V⁶₅) to label chords in CIE score extracts, noting modulations and applied dominants.

和弦具有句法功能：主功能（I、vi）提供稳定；属功能（V、vii°）制造紧张；下属功能（IV、ii）为属做准备。大调中 I–IV–V–I 的功能图是基础。小调中，属和弦的升高导音须在分析中体现（如和声小调的 V）。运用罗马数字与转位符号（如 I⁶、V⁶₅）为 CIE 乐谱选段标记和弦，并标注转调与副属和弦。

中文译文：和弦功能表：主功能（I, vi）→ 下属功能（IV, ii, ii⁶）→ 属功能（V, vii°, V⁷）→ 主或中断。

5. Musical Forms & Structures | 曲式结构

Common structures in CIE set works and analysis include binary (AB), ternary (ABA), rondo (ABACA), sonata form (exposition – development – recapitulation), and theme and variations. Know the key relationships in sonata form: first subject in tonic, second subject in dominant (major) or relative major (minor). Minuet and trio features compound ternary form with da capo. For each work, map repeats, transitions, and coda.

CIE 规定作品与分析中常见曲式包括二部曲式 (AB)、三部曲式 (ABA)、回旋曲式 (ABACA)、奏鸣曲式（呈示部—发展部—再现部）以及主题与变奏。须掌握奏鸣曲式的调性关系：第一主题在主调，第二主题在属调（大调）或关系大调（小调）。小步舞曲与三声中部呈现复三部曲式，带有返始记号。为每部作品标出反复、过渡与尾声。

6. Intervals & Scale Degrees | 音程与音级

Intervals are the distance between two pitches, measured in semitones. Learn perfect (P4, P5, P8), major/minor (M2, m3, M6, m7), augmented (A4, A5) and diminished (d5, d7) qualities. Scale degrees have functional names: tonic (1̂), supertonic (2̂), mediant (3̂), subdominant (4̂), dominant (5̂), submediant (6̂), leading tone (7̂). Identifying intervals by ear and score is vital for dictation and error-detection questions.

音程是两音高的距离，以半音计量。掌握纯音程（P4、P5、P8）、大小音程（M2、m3、M6、m7）、增音程（A4、A5）与减音程（d5、d7）。音级有功能名称：主音 (1̂)、上主音 (2̂)、中音 (3̂)、下属音 (4̂)、属音 (5̂)、下中音 (6̂)、导音 (7̂)。通过听觉与乐谱识别音程对听写与纠错题目至关重要。

7. Modulation Techniques | 转调技巧

Tonal music shifts key through pivot chords, chromatic inflection, or enharmonic reinterpretation. A pivot chord is diatonic in both the old and new key, often ii, IV or vi. Direct modulation (phrase modulation) jumps without pivot. In Romantic works, remote modulations exploit diminished seventh chords (enharmonic to multiple keys). Analyse CIE excerpts by identifying the new key via leading-tone resolution, then trace pivot function.

调性音乐通过共同和弦、半音变化或等音重解来转换调性。共同和弦是同时属于新旧两调的自然音和弦，常见于 ii、IV 或 vi。直接转调（乐句转调）无共同和弦跳转。浪漫派作品利用减七和弦作远关系转调（等音解至多调）。分析 CIE 选段时，先通过导音解决找出新调，再追溯共同和弦功能。

8. Rhythm & Metre | 节奏与节拍

Metric hierarchy is crucial: simple (2/4, 3/4, 4/4) vs compound (6/8, 9/8, 12/8) time, and irregular metres (5/4, 7/8). Syncopation displaces natural accents, hemiola creates cross-rhythm (e.g. three against two). In CIE rhythmic dictation and composition, notate rests and ties accurately; recognise augmentation, diminution, and rhythmic motifs. The harmonic rhythm (rate of chord change) underpins phrase structure.

节拍层次至关重要：单拍子 (2/4、3/4、4/4) 对比复拍子 (6/8、9/8、12/8)，以及不规则节拍 (5/4、7/8)。切分音移位自然重音，赫米奥拉比例制造交错节奏（如三对二）。在 CIE 节奏听写与创作中，准确记写休止符与延音线；识别增值、减值与节奏动机。和声节奏（和弦变化速率）支撑乐句结构。

9. Twentieth-Century Techniques: Serialism & Atonality | 二十世纪技法：序列主义与无调性

Serialism organises pitch through a tone row: an ordered series of all twelve chromatic pitches, used in original (P), retrograde (R), inversion (I), and retrograde-inversion (RI) forms. Transpose rows maintaining interval content. Atonal analysis uses pitch-class set theory: name sets by prime form (e.g. [0,1,4]) and interval vectors. CIE requires recognising row transformations and set classes in score extracts, and understanding how serial structure replaces tonality.

序列主义通过音列组织音高：十二个半音的有序系列，以原型 (P)、逆行 (R)、倒影 (I)、逆行倒影 (RI) 形式使用。移调保持音程内容。无调性分析运用音级集合理论：以原型（如 [0,1,4]）与音程向量命名集合。CIE 要求在乐谱选段中辨认音列变形与集合类别，理解序列结构如何取代调性。

10. Ornamentation & Performance Practice | 装饰音与演奏实践

Ornaments vary by period: Baroque trills start on the upper auxiliary note, appoggiaturas emphasise dissonance on the beat, mordents and turns add quick oscillations. Classical grace notes are played on the beat. In Romantic music, rubato and dynamic extremes are expressive formulas. For CIE, connect ornament realisation to performance context (e.g. harpsichord vs piano) and editorial interpretative marks, and apply them in melody completion tasks.

装饰音因时期而异：巴洛克颤音由上辅助音开始，倚音强调拍点上的不协和，波音与回音增加快速回旋。古典装饰音在拍上演奏。浪漫派音乐中，伸缩节奏与极端力度为表情公式。在 CIE 中，需将装饰音实现与表演语境（如羽管键琴 vs 钢琴）及编订诠释记号相联系，并运用于旋律补全任务。

Published by TutorHao | Music Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）