Year 12 CIE Music: Quick Reference Guide to Essential Formulas and Theorems | CIE 音乐公式定理速查手册

📚 Year 12 CIE Music: Quick Reference Guide to Essential Formulas and Theorems | CIE 音乐公式定理速查手册

Welcome to your essential quick-reference guide for CIE A-Level Music (Year 12). This handbook distils the core theoretical “formulas” and “theorems” you need to master — from interval construction and scale patterns to four-part harmony rules and cadential formulas. Keep these principles at your fingertips as you analyse scores and compose with confidence.

欢迎使用CIE A-Level音乐（12年级）核心理论速查手册。本手册提炼了你需要掌握的关键音乐“公式”与“定理”——从音程构建、音阶模式到四部和声规则及终止式公式。在分析乐谱和进行创作时，请将这些原则熟记于心并灵活运用。

1. Pitch and Note Names | 音高与音名

Pitches are named using the first seven letters of the alphabet (A–G) and can be altered by accidentals. The chromatic scale consists of twelve equally spaced semitones per octave. Each letter name may be raised by a sharp (♯), lowered by a flat (♭), or cancelled by a natural (♮). Enharmonic equivalents, such as C♯ and D♭, sound the same but are spelled differently depending on musical context.

音高用字母表前七个字母（A到G）命名，并可通过临时记号改变。半音阶在一个人度内包含十二个均等间隔的半音。每个音名可升高半音（♯，升号）、降低半音（♭，降号）或还原（♮，还原号）。等音如C♯和D♭在音响上相同，但根据音乐语境拼写不同。

Middle C is notated as C4 in Scientific Pitch Notation. The octave number changes at every C; the note immediately below middle C is B3. Understanding precise pitch location is crucial when transposing instruments are involved.

中央C在科学音高标记法中记为C4。每个C处八度数字变化；中央C下方紧邻的音是B3。当涉及移调乐器时，准确理解音高位置至关重要。

2. Intervals | 音程

An interval measures the distance between two pitches. Always count the lower note as ‘1’. The general size is determined by the letter name count (2nd, 3rd, 4th, etc.), then refined with quality: major (M), minor (m), perfect (P), augmented (A), or diminished (d). Unisons, 4ths, 5ths, and octaves are perfect; 2nds, 3rds, 6ths, and 7ths are major or minor.

音程衡量两个音高之间的距离。始终将下方音计为“1”。总体度数由音名数量决定（二度、三度、四度等），然后以性质细化：大（M）、小（m）、纯（P）、增（A）或减（d）。同度、四度、五度和八度为纯音程；二度、三度、六度和七度为大、小音程。

How to identify: count staff lines and spaces (including both notes), then consider semitones. For example, C to E is a 3rd (three letter names) with 4 semitones, thus a major 3rd. C to E♭ is a minor 3rd (3 semitones). A perfect 5th spans 7 semitones; C to G is perfect. If C to G♭, the semitone count is 6 — a diminished 5th (d5). Augmented intervals are one semitone wider than perfect or major; diminished intervals one semitone smaller than perfect or minor.

识别方法：数谱线和间（含两音），再考虑半音数。例如，C到E为三度（三个音名），含4个半音，因此是大三度。C到E♭是小三度（3个半音）。纯五度含7个半音；C到G为纯五度。若C到G♭，半音数为6——即减五度（d5）。增音程比纯或大宽一个半音；减音程比纯或小窄一个半音。

Inversion rule: Major ↔ minor, Augmented ↔ diminished, Perfect ↔ perfect. The sum of interval numbers before and after inversion is always 9. For instance, a major 3rd (C–E) inverts to a minor 6th (E–C).

转位规则：大↔小，增↔减，纯↔纯。转位前后音程度数之和恒为9。例如，大三度（C–E）转位为小六度（E–C）。

3. Scale Formulas | 音阶构成公式

Scales are built from fixed patterns of tones (T) and semitones (S). The major scale formula: T–T–S–T–T–T–S. For example, C major: C – T – D – T – E – S – F – T – G – T – A – T – B – S – C.

音阶由固定全音（T）与半音（S）模式构建。大调音阶公式：T–T–S–T–T–T–S。例如C大调：C–T–D–T–E–S–F–T–G–T–A–T–B–S–C。

Natural minor scale formula: T–S–T–T–S–T–T. Harmonic minor raises the 7th degree, creating an augmented 2nd between 6 and 7. Melodic minor raises the 6th and 7th ascending, and reverts to natural minor descending. The whole-tone scale uses T only; chromatic scale uses all S.

自然小调音阶公式：T–S–T–T–S–T–T。和声小调升高第VII级，在VI级与VII级之间形成增二度。旋律小调上行升高VI和VII级，下行还原为自然小调。全音阶仅用T；半音阶则用全部S。

The blues scale: 1, ♭3, 4, ♯4 (or ♭5), 5, ♭7. Pentatonic major: 1, 2, 3, 5, 6. Pentatonic minor: 1, ♭3, 4, 5, ♭7. These are the building blocks for endless melodies and improvisation.

布鲁斯音阶：1, ♭3, 4, ♯4（或♭5）, 5, ♭7。大五声音阶：1, 2, 3, 5, 6。小五声音阶：1, ♭3, 4, 5, ♭7。这些是无穷旋律与即兴创作的基石。

4. Chord Construction | 和弦构建

Chords are built by stacking thirds on a root. A triad consists of root, 3rd, and 5th. The formula for a major triad: root + M3 + P5. Minor triad: root + m3 + P5. Diminished: root + m3 + d5. Augmented: root + M3 + A5.

和弦通过根音叠加三度构成。三和弦由根音、三音和五音组成。大三和弦公式：根音 + M3 + P5。小三和弦：根音 + m3 + P5。减三和弦：根音 + m3 + d5。增三和弦：根音 + M3 + A5。

Seventh chords add a 7th. Dominant 7th: major triad + m7 (e.g., G–B–D–F). Major 7th: major triad + M7 (C–E–G–B). Minor 7th: minor triad + m7 (D–F–A–C). Half-diminished 7th: diminished triad + m7 (B–D–F–A). Fully diminished 7th: diminished triad + d7 (B–D–F–A♭).

七和弦附加七音。属七和弦：大三和弦 + m7（如G–B–D–F）。大七和弦：大三和弦 + M7（C–E–G–B）。小七和弦：小三和弦 + m7（D–F–A–C）。半减七和弦：减三和弦 + m7（B–D–F–A）。完全减七和弦：减三和弦 + d7（B–D–F–A♭）。

Roman numerals indicate chord function within a key, using upper case for major, lower case for minor, and ° for diminished. In C major: I (C), ii (Dm), iii (Em), IV (F), V (G), vi (Am), vii° (Bdim).

罗马数字表示调内和弦功能，大写为大三和弦，小写为小三和弦，°为减三和弦。C大调中：I(C), ii(Dm), iii(Em), IV(F), V(G), vi(Am), vii°(Bdim)。

5. Harmonic Functions and Progressions | 和声功能与和弦进行

The three primary harmonic functions are tonic (T), predominant (PD), and dominant (D). In major keys, I is tonic; IV and ii are predominant; V and vii° are dominant. The most fundamental progression is I–IV–V–I, creating a complete harmonic cycle: rest–departure–tension–resolution.

三大基本和声功能是主功能（T）、下属功能（PD）和属功能（D）。大调中，I是主；IV和ii是下属；V和vii°是属。最基础的进行是I–IV–V–I，构成完满的和声循环：静止–离开–紧张–解决。

The circle-of-fifths progression moves by descending perfect 5ths (or ascending 4ths): iii – vi – ii – V – I. This chain provides strong root movement. Avoid parallel fifths and octaves in part-writing; contrary motion is preferred.

五度圈进行通过下行纯五度（或上行纯四度）移动：iii–vi–ii–V–I。这一链条提供了强力的根音进行。在声部写作中避免平行五度和平行八度；反向进行更佳。

Cadential 6/4 (I⁶⁄₄) is frequently used before V. It is a second-inversion tonic chord that functions as a double suspension over the dominant bass, resolving to V. For example, in C major: G–C–E (I⁶⁄₄) moving to G–B–D (V). Always resolve the 6th down to 5th and the 4th down to 3rd.

终止四六和弦（I⁶⁄₄）常用于V之前。它是一个第二转位的主和弦，作为属低音上的双重延留，解决到V。例如C大调中：G–C–E（I⁶⁄₄）进行到G–B–D（V）。务必使六度音下行至五度音，四度音下行至三度音。

6. Four-Part Harmony Rules | 四部和声规则

In chorale-style writing, combine SATB (Soprano, Alto, Tenor, Bass) following strict conventions to maintain independence and smooth voice-leading. Spacing: no more than an octave between adjacent upper voices (alto–tenor can exceed an octave if necessary). Cover the full chord: include root, 3rd, and 5th; the 5th may be omitted if the root is doubled.

在众赞歌式写作中，组合SATB（女高音、女低音、男高音、男低音）并遵循严格惯例，以保持独立与平稳声部进行。间距：相邻高音声部之间不超过八度（必要时女低音与男高音之间可超八度）。覆盖完整和弦：包含根音、三音、五音；如果根音被重复，五音可省略。

Doubling: double the root in root-position triads; double the soprano note in first inversion; double the bass note in second inversion. Never double the leading tone (7th degree of the scale) as it creates parallel octaves when resolving. Avoid cross relations, and resolve seventh chords appropriately.

重复原则：原位三和弦重复根音；第一转位重复女高音；第二转位重复低音。切勿重复导音（音阶第七级），因为解决时会产生平行八度。避免交错关系，恰当解决七音。

7. Cadences | 终止式

Cadences are musical punctuation marks that articulate phrases. The four principal types:

Perfect (V–I): both chords in root position, soprano ends on tonic. Full close.
Imperfect (I–V, ii–V, etc.): ends on V; sounds incomplete.
Plagal (IV–I): ‘Amen’ cadence.
Interrupted (V–vi): deceptive; the expected I is replaced by vi.

终止式是表达乐句的音乐标点。四种主要类型：

正格终止（V–I）：两和弦皆为原位，女高音结束在主音。完满收束。
半终止（I–V, ii–V等）：结束在V上；听感未完成。
变格终止（IV–I）：“阿门”终止。
阻碍终止（V–vi）：进行具有欺骗性；预期的I被vi替代。

In CIE analysis, be able to identify these by Roman numeral and voice-leading characteristics. The perfect cadence is the strongest and most commonly used to end pieces.

在CIE分析中，需能通过罗马数字及声部进行特征识别这些终止式。正格终止最为有力，最常用于结束乐曲。

8. Melodic Ornamentation | 旋律装饰音

Ornaments are embellishments that add expressive detail. Common ornaments in Baroque and Classical styles include: trill (rapid alternation between principal note and upper auxiliary), mordent (single rapid alternation with upper or lower neighbour), turn (four-note figure: upper–principal–lower–principal), appoggiatura (leaning note that takes half the main note’s value, on the beat), and acciaccatura (crushed grace note, played very quickly before the beat in Classical period).

装饰音是添加表情细节的修饰。巴洛克与古典风格中的常见装饰音包括：颤音（主音与上辅助音快速交替）、波音（与上方或下方邻音快速交替一次）、回音（四音型：上辅助–主音–下辅助–主音）、倚音（占主音一半时值的倚靠音，在拍点上）和碎音（快速奏于拍点前的短倚音，在古典时期如此处理）。

Ornaments should be interpreted according to period performance practice. In Baroque music, a trill generally begins on the upper auxiliary; after 1800, the trill often starts on the principal note. Always check the context and treatises (e.g., C.P.E. Bach) for exact execution.

装饰音应根据时期演奏习惯解读。巴洛克音乐中的颤音通常从上辅助音开始；1800年后，颤音常从主音开始。始终检查语境及相关论著（如C.P.E. 巴赫）以获准确施行方式。

9. Rhythm and Meter | 节奏与节拍

Meter is the regular grouping of beats. Simple time: each beat divides into two equal parts (2/4, 3/4, 4/4). Compound time: each beat divides into three equal parts (6/8, 9/8, 12/8). The top number indicates beats per measure; bottom number indicates beat value. In 6/8 there are two dotted-quarter-note beats per bar.

节拍是有规律的拍子分组。单拍子：每拍分为两等份（2/4, 3/4, 4/4）。复拍子：每拍分为三等份（6/8, 9/8, 12/8）。上方数字指示每小节拍数；下方数字指示拍的时值。6/8中每小节有两个附点四分音符拍。

Rhythmic devices include syncopation (accent on a normally weak beat or off-beat), hemiola (shift of metric accent, e.g., three groups of two against two groups of three), and cross-rhythm. Triplets (3 notes in space of 2) and duplets (2 notes in space of 3) allow division across the expected beat.

节奏手法包括切分音（在通常弱拍或后半拍上加重音）、赫米奥拉 (hemiola)（节拍重音转移，例如三组二对二组三）和交错节奏。三连音（2拍空间内奏3音）和二连音（3拍空间内奏2音）可跨越预期的拍子分割。

10. Musical Forms | 曲式结构

Form is the blueprint of a composition. Binary (AB) consists of two roughly equal sections, each usually repeated. Ternary (ABA) has a contrasting middle section and a return of the opening material. Rondo (ABACA, ABACABA) features a recurring principal theme alternating with episodes. Sonata form (exposition–development–recapitulation) is the most significant structure in the Classical period, built on tonal conflict between primary (tonic) and secondary (dominant or relative major) key areas, resolved in the recapitulation where the secondary theme returns in the tonic.

曲式是乐曲的蓝图。二段体（AB）由两个大致相等的段落构成，每段通常重复。三段体（ABA）包含对比性中段和开头材料的回归。回旋曲式（ABACA，ABACABA）以重现的主要主题与交替的插部为特色。奏鸣曲式（呈示部–展开部–再现部）是古典时期最重要的结构，建立在主调与副调（属调或关系大调）之间的调性冲突上，并在再现部中由副部主题在主调上回归而得以解决。

In Year 12 analysis, be prepared to identify phrase structures: period (antecedent–consequent), sentence (presentation–continuation). Minuet and trio form (often ternary with each section binary) and theme and variations are also essential.

在12年级分析中，做好识别乐句结构的准备：乐段（前句–后句），乐句段（呈现–延续）。小步舞曲与三声中部（常为每部分二段体的三段体）及主题与变奏也同样重要。

11. Notation and Clefs | 记谱与谱号

The treble clef (middle C on a ledger line below staff) is standard for high instruments. The bass clef (middle C on a ledger line above) for low registers. The alto clef (middle C on the middle line) is used for viola. Tenor clef (middle C on the fourth line) appears for upper range of cello, bassoon, and trombone.

高音谱号（中央C在下加一线）是高音乐器的标准谱号。低音谱号（中央C在上加一线）用于低音区。中音谱号（中央C在第三线）用于中提琴。次中音谱号（中央C在第四线）用于大提琴、巴松管和长号的高音区。

Accidentals apply to the pitch they precede and all further occurrences of that pitch within the bar, unless cancelled. Key signatures indicate the prevailing key, raising or lowering specific notes throughout the piece. Transposing instruments (e.g., clarinet in B♭, horn in F) sound a different pitch than written — an essential formula when reading scores.

临时记号对其之后的同一音高及该小节内后续同音高有效，直至被取消。调号指示主调，全曲中升高或降低特定音。移调乐器（如降B调单簧管、F调圆号）的实际音高与记谱音高不同——阅读总谱时的关键公式。

12. Essential Musical Terms | 核心音乐术语

Tempo markings: Allegro (fast, cheerful), Andante (walking pace), Adagio (slow, stately), Presto (very fast), Largo (broad, slow). Dynamics: pianissimo (pp), piano (p), mezzo piano (mp), mezzo forte (mf), forte (f), fortissimo (ff). Gradual changes: crescendo (cresc.), diminuendo / decrescendo (dim. / decresc.).

速度标记：Allegro（快板，愉悦）、Andante（行板，步行速度）、Adagio（柔板，徐缓庄严）、Presto（急板，极快）、Largo（广板，宽广缓慢）。力度：pp（很弱）、p（弱）、mp（中弱）、mf（中强）、f（强）、ff（很强）。渐变：cresc.（渐强）、dim./decresc.（渐弱）。

Articulation: staccato (detached, short), legato (smooth, connected), tenuto (held, full value), accent (>), sforzando (sfz, strong sudden accent). Expression: dolce (sweetly), cantabile (singing style), agitato (agitated), maestoso (majestic).

演奏法：staccato（断奏，短促）、legato（连奏，流畅连接）、tenuto（持音，保持充足时值）、accent（重音，>）、sforzando（sfz，骤强）。表情术语：dolce（甜美地）、cantabile（如歌地）、agitato（激动地）、maestoso（庄严地）。

Memorise these as they frequently appear in score directions and examination commentary. Combined with the structural formulas above, they equip you to decode any CIE Music score with precision.

熟记这些术语，因为它们常出现在乐谱指示和考试评论中。结合上述结构公式，你就能精准解读任何CIE音乐考卷中的乐谱。

Published by TutorHao | Music Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）

Year 12 CIE Music: Quick Reference Guide to Essential Formulas and Theorems | CIE 音乐公式定理速查手册