📚 Year 9 CIE Music: Quick Reference to Music Theory Formulas & Theorems | CIE 音乐：乐理公式定理速查手册
This quick-reference handbook compiles the essential 'formulas' and 'theorems' of music theory that every Year 9 CIE Music student needs to master. Think of these as the building blocks you carry into every listening, performing, and composing task. From note values and scale patterns to interval shortcuts and chord recipes, each rule is presented clearly with its English and Chinese explanation so you can revise efficiently.
这本速查手册汇编了每位 Year 9 CIE 音乐学生必须掌握的乐理核心“公式”与“定理”。你可以把它们当作走进每一节聆听、演奏和创作课堂的基本构件。从音符时值和音阶模式，到音程速算口诀与和弦构成方法，每条规则都配有中英双语解释，帮助你高效复习。
1. Note Values & Rest Formulas | 音符时值与休止符公式
crotchets = 8 quavers = 16 semiquavers. Each rest mirrors the duration of its matching note exactly.
在常规四四拍中，全音符等于 4 拍。时值关系可以用简单的倍增链表示：1 个全音符 = 2 个二分音符 = 4 个四分音符 = 8 个八分音符 = 16 个十六分音符。每种休止符的时值都与其对应音符完全一致。
| Note / 音符 | Rest / 休止符 | Beats (4/4) / 拍数 |
|---|---|---|
| Semibreve / 全音符 | Whole-bar rest / 全休止符 | 4 |
| Minim / 二分音符 | Minim rest / 二分休止符 | 2 |
| Crotchet / 四分音符 | Crotchet rest / 四分休止符 | 1 |
| Quaver / 八分音符 | Quaver rest / 八分休止符 | 1/2 |
| Semiquaver / 十六分音符 | Semiquaver rest / 十六分休止符 | 1/4 |
te it follows. Thus dotted minim = 2 + 1 = 3 beats; dotted crotchet = 1 + 1/2 = 1.5 beats.
附点音符公式：附点增加其前面音符时值的一半。因此，附点二分音符 = 2 + 1 = 3 拍；附点四分音符 = 1 + 1/2 = 1.5 拍。
2. Time Signature & Beat Grouping Theorems | 拍号与节拍组合定理
The upper number tells how many beats per bar; the lower number tells which note value counts as one beat. Simple time (2/4, 3/4, 4/4) divides each beat into two equal parts. Compound time (6/8, 9/8, 12/8) divides each beat into three equal parts, where the beat is a dotted note.
上方数字表示每小节有多少拍；下方数字表示以何种音符为一拍。单拍子（2/4、3/4、4/4）将每一拍分为二等份。复拍子（6/8、9/8、12/8）将每一拍分为三等份，其拍子单位为附点音符。
Beaming rule: in simple time, beam quavers and semiquavers to show complete beats. In 6/8, beam in groups of three quavers to show the dotted-crotchet beat. In 3/4, never beam across the middle of the bar.
符尾连接规则：单拍子中，八分音符与十六分音符的符尾应按拍子组合，显示完整的拍子单元。6/8 拍中，应每三个八分音符连为一组，以体现附点四分音符的单位拍。3/4 拍中，切勿横跨小节中间进行连接。
3. Clefs & Pitch Position Formulas | 谱号与音高定位公式
Treble clef (G clef) circles the second line, fixing it as G above middle C. Bass clef (F clef) places its two dots either side of the fourth line, fixing it as F below middle C. Middle C sits on one ledger line below the treble staff and one ledger line above the bass staff.
高音谱号（G 谱号）围绕第二线画圈，将其固定为中央 C 上方的 G。低音谱号（F 谱号）的两个点夹住第四线，将其固定为中央 C 下方的 F。中央 C 位于高音谱表下方加一线，也位于低音谱表上方加一线。
Pitch naming pattern: notes move stepwise through the musical alphabet A–G, then the pattern repeats. Ledger lines extend the staff in the same stepwise fashion.
音名排列规律：音高按音乐字母 A–G 级进循环。加线以同样的级进规律扩展谱表范围。
4. Major Scale Construction Formula | 大调音阶构成公式
Every major scale follows the step-pattern formula: Tone, Tone, Semitone, Tone, Tone, Tone, Semitone (T–T–S–T–T–T–S). A tone equals 2 semitones; a semitone is the smallest step on a keyboard. Starting on C gives: C – D (T) – E (T) – F (S) – G (T) – A (T) – B (T) – C (S).
每个大调音阶都遵循相同的音阶级进公式：全音、全音、半音、全音、全音、全音、半音（全-全-半-全-全-全-半）。一个全音等于 2 个半音；半音是键盘上最小的音级距离。从 C 开始得到：C – D（全）– E（全）– F（半）– G（全）– A（全）– B（全）– C（半）。
Applying the same formula to G major requires F♯ to preserve the pattern. To D major requires F♯ and C♯. Each new sharp is added a perfect fifth above the previous key note.
将同一个公式应用到 G 大调时，必须使用 F♯ 以保持音级模式。D 大调则需要 F♯ 和 C♯。每一个新升号都出现在前一调性主音的上方纯五度。
5. Minor Scale Patterns & Transformations | 小调音阶模式与变形
The natural minor scale uses the formula: T–S–T–T–S–T–T, which is the same as a major scale starting on the 6th degree. A natural minor: A – B – C – D – E – F – G – A.
自然小调音阶使用公式：全-半-全-全-半-全-全，也就是从大调第六级开始的音阶模式。a 自然小调：A – B – C – D – E – F – G – A。
- Harmonic minor / 和声小调: Raise the 7th degree by a semitone. A harmonic minor: A – B – C – D – E – F – G♯ – A. Creates a gap of 1½ tones between 6th and 7th.
- Melodic minor ascending / 旋律小调上行: Raise both the 6th and 7th degrees (A – B – C – D – E – F♯ – G♯ – A). Descending it reverts to natural minor.
和声小调：升高第七级半音。a 和声小调：A – B – C – D – E – F – G♯ – A。在六级与七级之间产生增二度（1½ 全音）。旋律小调上行：升高第六与第七级（A – B – C – D – E – F♯ – G♯ – A）；下行则还原为自然小调。
6. Key Signature Formula & Circle of Fifths | 调号公式与五度圈
The order of sharps: F♯ C♯ G♯ D♯ A♯ E♯ B♯. Flats order: B♭ E♭ A♭ D♭ G♭ C♭ F♭. To find the major key from a sharp signature, go one semitone above the last sharp. For flats (except F), the penultimate flat names the key.
升号调顺序：F♯ C♯ G♯ D♯ A♯ E♯ B♯。降号调顺序：B♭ E♭ A♭ D♭ G♭ C♭ F♭。从升号调号推算大调：最后一个升号升高半音即为调性。对于降号调（F 大调除外），倒数第二个降号即调名。
| Key Signature / 调号 | Major Key / 大调 | Relative Minor / 关系小调 |
|---|---|---|
| 0 sharps/flats / 无升降号 | C major / C 大调 | A minor / a 小调 |
| 1 sharp / 升号 | G major / G 大调 | E minor / e 小调 |
| 2 flats / 降号 | B♭ major / B♭ 大调 | G minor / g 小调 |
s from the major tonic to find the relative minor. For instance, C major to A minor (C→B→B♭→A).
关系大小调定理：从大调主音向下三半音即关系小调主音。例如，C 大调到 a 小调（C→B→B♭→A）。
7. Interval Recognition Shortcuts | 音程识别速算公式
An interval is named by its number (2nd, 3rd, 4th…) and quality (perfect, major, minor, augmented, diminished). Count the semitones between two notes to check quality. Key semitone counts:
音程由度数（二度、三度、四度……）和性质（纯、大、小、增、减）命名。计算两个音之间的半音数以确定性质。核心半音数如下：
| Interval / 音程 | Semitones / 半音 | Example in C / C 调示例 |
|---|---|---|
| Minor 2nd / 小二度 | 1 | C – D♭ |
| Major 2nd / 大二度 | 2 | C – D |
| Perfect 4th / 纯四度 | 5 | C – F |
| Perfect 5th / 纯五度 | 7 | C – G |
| Major 3rd / 大三度 | 4 | C – E |
| Octave / 纯八度 | 12 | C – C' |
Inversion theorem: the sum of an interval and its inversion always equals 9. Perfect stays perfect; major becomes minor; augmented becomes diminished.
音程转位定理：原位音程与其转位音程的度数之和恒为 9。纯音程转位仍为纯；大音程转位变小；增音程转位变减。
8. Triad & Chord-Building Formulas | 三和弦及和弦构成公式
A triad is a three-note chord built by stacking two 3rds on a root. The type depends on the semitone spacings. Basic formulas:
三和弦是由根音上叠加两个三度音构成的三音和弦。其类型取决于半音距离。基本公式：
- Major triad / 大三和弦: Root + 4 semitones + 3 semitones. Example: C – E (4) – G (3).
- Minor triad / 小三和弦: Root + 3 semitones + 4 semitones. Example: C – E♭ (3) – G (4).
- Diminished triad / 减三和弦: Root + 3 semitones + 3 semitones. Example: C – E♭ – G♭.
- Augmented triad / 增三和弦: Root + 4 semitones + 4 semitones. Example: C – E – G♯.
Each degree of a major scale generates a specific chord type: I major, II minor, III minor, IV major, V major (dominant), VI minor, VII diminished.
大调音阶的每个音级产生特定的和弦性质：I 级大三，II 级小三，III 级小三，IV 级大三，V 级大三（属和弦），VI 级小三，VII 级减三。
9. Cadence Formulas & Voice-Leading | 终止式公式与声部进行
Cadences are chord progressions that close a musical phrase. The four principal cadence formulas:
终止式是结束乐句的和弦进行。四种基本终止式公式：
| Cadence / 终止式 | Chords / 和弦 | Effect / 效果 |
|---|---|---|
| Perfect / 正格终止 | V – I (both in root position, top note is tonic) / V – I（均为原位，高音为主音） | Strong, final / 强收束，完满结束 |
| Plagal / 变格终止 | IV – I / IV – I | 'Amen' ending / '阿们' 式结束 |
| Imperfect / 非完满终止 | I – V, IV – V, or any – V / I – V、IV – V 或其他到 V | Paused, expects continuation / 暂停，期待继续 |
| Interrupted / 阻碍终止 | V – VI (surprise) / V – VI（意外） | Deceptive break / 欺骗性断开 |
Smooth voice-leading rule: keep common tones in the same voice when possible, and move the other voices stepwise.
平稳声部进行规则：尽可能将共同音保持在同一声部，其余声部级进移动。
10. Tempo, Dynamics & Articulation Markings | 速度、力度与演奏法记号
Moderato (moderate), Allegro (fast), Presto (very fast). A metronome mark gives exact BPM: ♩ = 120 means 120 crotchet beats per minute.
这些记号是控制表情的演奏公式。速度：Largo（广板，很慢），Adagio（柔板，慢），Andante（行板，步行速度），Moderato（中板），Allegro（快板），Presto（急板）。节拍器标记给出精确 BPM：♩ = 120 代表每分钟 120 个四分音符拍。
Dynamics range from pianissimo (pp, very soft) to fortissimo (ff, very loud). Gradual changes use crescendo (cresc., getting louder) and diminuendo (dim., getting softer).
力度范围从 pianissimo（pp，很弱）到 fortissimo（ff，很强）。渐强用 cresc.，渐弱用 dim. 或 decresc.。
Articulation marks: staccato (dot, detached), legato (slur, smooth), accent (> , stressed), tenuto (line, held full length).
奏法记号：staccato（点，断奏），legato（连线，连奏），重音记号 (>，强调)，tenuto（横线，充分保持）。
11. Form & Structure Recognition Rules | 曲式与结构识别规则
Binary form (AB) consists of two contrasting sections, each often repeated. Ternary form (ABA) returns to the opening material after a contrasting middle section. Rondo form layers a recurring A section between episodes: ABACA or ABACABA. Theme and variations takes a main idea and alters it through changes in melody, rhythm, harmony, or instrumentation.
二段体（AB）由两个对比乐段组成，每段常各自反复。三段体（ABA）在对比性中段后重现首段。回旋曲式在插部之间循环叠入 A 段：ABACA 或 ABACABA。主题与变奏则将主要乐思通过旋律、节奏、和声或配器的变化加以发展。
Phrase period theorem: a balanced phrase typically includes a 4-bar question (antecedent) ending on V or an imperfect cadence, followed by a 4-bar answer (consequent) resolving to I. Symmetry is the default formula in Classical period melodies.
乐句乐段定理：一个平衡的乐段通常包含一个 4 小节的问句（前乐句），终止于 V 级或非完满终止，随后是一个 4 小节的答句（后乐句），解决到 I 级。对称是古典时期旋律的默认公式。
12. Ornaments & Symbolic Abbreviations | 装饰音与符号缩编公式
Ornaments are small additional notes that add expression. Main types: trill (tr, rapid alternation with upper note), mordent (quick note – written note – note below/above and back), turn (note above – note – note below – note), grace note (acciaccatura – crushed note; appoggiatura – leaning note that takes half the main note's value).
装饰音是为旋律添加表情的小音符。主要类型：颤音（tr，与本音上方音快速交替），波音（快速弹出本音–邻音–本音），回音（上方音–本音–下方音–本音），倚音（短倚音–挤入式装饰；长倚音–占据主要音符一半时值）。
Repeat signs and 1st/2nd-time bars serve as structural shortcuts, telling performers to return to the beginning or a segno. Da Capo al Fine (D.C. al Fine) means repeat from the start up to the word Fine; Dal Segno (D.S.) returns to the sign 𝄋.
反复记号和第一、第二结尾是结构的速记公式，指示演奏者返回开头或 S 符号。Da Capo al Fine（D.C. al Fine）表示从头反复至 Fine 处；Dal Segno（D.S.）则返回到 𝄋 符号处。
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