📚 Year 9 Cambridge Music Formula & Theorem Quick-Reference Handbook | 剑桥9年级音乐公式定理速查手册
This quick-reference handbook brings together the essential 'formulas' and rules for Year 9 Cambridge Music – from note values and scale structures to chord building and cadences. Use it to check intervals, key signatures, time signatures and musical terms whenever you need a fast reminder.
这本速查手册汇总了剑桥9年级音乐的核心“公式”与定理，涵盖音符时值、音阶结构、和弦构建、终止式等内容。当你需要快速查阅音程、调号、拍号和音乐术语时，随手翻看即可。
1. Note Values & Time Signatures | 音符时值与拍号
); an eighth note equals 2 sixteenth notes (semiquavers). A dot after a note adds half of its original value: dotted half note = 3 quarter notes.
全音符等于2个二分音符；二分音符等于2个四分音符；四分音符等于2个八分音符；八分音符等于2个十六分音符。附点增加原音符时值的一半：附点二分音符 = 3个四分音符。
Time signatures show how many beats are in each bar and which note value counts as one beat. The top number gives the number of beats per bar; the bottom number indicates the beat unit – 4 stands for a quarter note, 8 for an eighth note, 2 for a half note.
拍号显示每小节有几拍、以哪种音符为一拍。上方的数字表示每小节的拍数；下方的数字表示以几分音符为一拍 – 4代表四分音符，8代表八分音符，2代表二分音符。
In compound time (e.g. 6/8, 9/8, 12/8), the beat is a dotted note and each bar is divided into groups of three eighth notes. 6/8 has two dotted-quarter beats, 9/8 has three, 12/8 has four.
在复拍子中（如6/8、9/8、12/8），节拍单位为附点音符，每小节划分为若干组三个八分音符。6/8有两个附点四分音符的拍子，9/8有三个，12/8有四个。
Beat unit (simple time): 1/4 note, 1/8 note, 1/2 note. Dotted half = 3/4 note duration.
简单拍子的节拍单位：1/4音符，1/8音符，1/2音符。附点二分 = 3/4音符时值。
2. Major Scale Formula | 大调音阶公式
All major scales follow the same pattern of tones (whole steps) and semitones (half steps): Tone – Tone – Semitone – Tone – Tone – Tone – Semitone. This is often written as T T S T T T S.
所有大调音阶都遵循相同的全音和半音模式：全音 – 全音 – 半音 – 全音 – 全音 – 全音 – 半音。常记作 T T S T T T S。
Starting on any note and applying this formula gives the correct major scale. For example, C major uses only white keys, while G major requires an F♯ to maintain the pattern between the 7th and 8th degrees.
从任意音开始套用此公式即可得到正确的大调音阶。例如C大调只用白键，而G大调需要在第七级和第八级之间使用升F(♯)来保持模式。
Major scale formula: T T S T T T S (e.g. D: D–E–F♯–G–A–B–C♯–D)
大调音阶公式：T T S T T T S（例如D大调：D–E–升F–G–A–B–升C–D）
3. Minor Scale Types | 小调音阶类型
The natural minor scale uses the pattern: T S T T S T T. It shares the same key signature as its relative major but starts on the 6th degree of the major scale.
自然小调音阶的模式为：T S T T S T T。它与关系大调共用同一个调号，但起始音为大调的第六级音。
The harmonic minor scale raises the 7th degree by a semitone (compared to natural minor), creating a distinctive leap of a tone and a half (augmented 2nd) between the 6th and 7th degrees. Formula: T S T T S (T+½) S.
和声小调音阶将第七级音升高半音（与自然小调相比），在六级与七级之间产生一个半全音（增二度）的独特距离。公式：T S T T S (全音+半音) S。
The melodic minor scale raises the 6th and 7th degrees by a semitone when ascending only; the descending form is the same as the natural minor. Ascending pattern: T S T T T T S.
旋律小调音阶上行时升高第六和第七级半音，下行时还原，与自然小调相同。上行模式：T S T T T T S。
A harmonic minor: A–B–C–D–E–F–G♯–A. A melodic minor ascending: A–B–C–D–E–F♯–G♯–A.
A和声小调：A–B–C–D–E–F–升G–A。A旋律小调上行：A–B–C–D–E–升F–升G–A。
4. Interval Number & Quality | 音程的度数与性质
The number (size) of an interval is found by counting the letter names from the lower note to the higher note, including both notes. C to E is a 3rd (C,D,E – three letters).
音程的度数通过从较低音数到较高音的音名字母来得到，包含首尾两个音。C到E为三度（C, D, E – 三个字母）。
Intervals of a unison, 4th, 5th and octave can be perfect (P). Intervals of a 2nd, 3rd, 6th and 7th can be major (M) or minor (m). A major interval reduced by a semitone becomes minor; a perfect or major interval increased by a semitone becomes augmented; a perfect or minor interval reduced by a semitone becomes diminished.
同度、四度、五度和八度可以是纯音程。二度、三度、六度和七度可以是大音程或小音程。大音程减少半音变为小音程；纯音程或大音程增加半音变为增音程；纯音程或小音程减少半音变为减音程。
| Interval | Semitones | Example |
| Perfect Unison (P1) | 0 | C – C |
| Major 2nd (M2) | 2 | C – D |
| Major 3rd (M3) | 4 | C – E |
| Perfect 4th (P4) | 5 | C – F |
| Perfect 5th (P5) | 7 | C – G |
| Minor 6th (m6) | 8 | C – A♭ |
| Major 6th (M6) | 9 | C – A |
| Minor 7th (m7) | 10 | C – B♭ |
| Major 7th (M7) | 11 | C – B |
| Perfect Octave (P8) | 12 | C – C |
tones. Diminished 5th, which sounds the same, is also 6 semitones but spelled differently.
增四度（三全音）= 6个半音。减五度在音响上相同，也是6个半音，但音名字母拼写不同。
5. Circle of Fifths & Key Signatures | 五度圈与调号
The circle of fifths arranges the 12 major keys in a sequence where each step moves up a perfect fifth. Starting at C (no sharps/flats), G major has 1 sharp, D has 2 sharps, A has 3, etc. Going anticlockwise by perfect fourths gives the flat keys: F has 1 flat, B♭ has 2, E♭ has 3, and so on.
五度圈将12个大调按上行纯五度依次排列。从C大调（无升降号）开始，G大调有1个升号，D大调2个，A大调3个，以此类推。逆时针按纯四度下行得到降号调：F大调1个降号，降B大调2个，降E大调3个，依此类推。
The order of sharps in key signatures: F♯, C♯, G♯, D♯, A♯, E♯, B♯. The order of flats is the reverse: B♭, E♭, A♭, D♭, G♭, C♭, F♭. A useful mnemonic: Father Charles Goes Down And Ends Battle (sharps), and Battle Ends And Down Goes Charles' Father (flats).
调号中升号的顺序为：升F、升C、升G、升D、升A、升E、升B。降号的顺序与之相反：降B、降E、降A、降D、降G、降C、降F。记忆口诀：Father Charles Goes Down And Ends Battle（升号），反序则为降号。
To find the major key from a sharp signature, take the last sharp and go up a semitone. For a flat signature (except F major), the second-to-last flat is the tonic.
根据升号调号找大调：取最后一个升号并升高半音。对于降号调（F大调除外），倒数第二个降号就是主音。
Last sharp + semitone = major key. Second-to-last flat = major key.
最末升号 + 半音 = 大调主音。倒数第二个降号 = 大调主音。
6. Triad Chord Formulas | 三和弦公式
A triad is a three-note chord built by stacking two intervals of a third on top of a root note. The quality of the triad depends on the size of these thirds.
三和弦是由根音上方叠加两个三度音构成的三音和弦。三和弦的性质取决于这两个三度的音程大小。
ones) + perfect 5th (7 semitones from root). The outer interval from root to 5th is a perfect 5th, and the stacked thirds are M3 + m3.
大三和弦 = 根音 + 大三度（4个半音） + 纯五度（距离根音7个半音）。从根音到五音为纯五度，叠加的三度为大三度+小三度。
); stacked m3 + m3. Augmented triad = root + M3 + augmented 5th (8 semitones from root); stacked M3 + M3.
小三和弦 = 根音 + 小三度（3个半音） + 纯五度。叠加的三度：小三度+大三度。减三和弦 = 根音 + 小三度 + 减五度（距根音6个半音）；叠加小三度+小三度。增三和弦 = 根音 + 大三度 + 增五度（距根音8个半音）；叠加大三度+大三度。
C major: C–E–G. C minor: C–E♭–G. C diminished: C–E♭–G♭. C augmented: C–E–G♯.
C大三和弦：C–E–G。C小三和弦：C–降E–G。C减三和弦：C–降E–降G。C增三和弦：C–E–升G。
Inversions: root position (root in bass), 1st inversion (3rd in bass), 2nd inversion (5th in bass). The intervals above the bass change accordingly.
转位：原位（根音在低音），第一转位（三音在低音），第二转位（五音在低音）。低音上方的音程随之变化。
7. Seventh Chord Construction | 七和弦构建
Seventh chords add a 7th above the root to a triad. The most common types are major 7th, dominant 7th, minor 7th, half-diminished 7th and diminished 7th chords.
七和弦在三和弦基础上增加根音上方的七度音。常见类型有大大七和弦、大小七和弦（属七）、小小七和弦、半减七和弦和减七和弦。
Major 7th chord: major triad + major 7th (11 semitones from root). Stack: M3, m3, M3. Dominant 7th: major triad + minor 7th (10 semitones). Stack: M3, m3, m3. Minor 7th: minor triad + minor 7th (10 semitones). Stack: m3, M3, m3. Half-diminished 7th: diminished triad + minor 7th. Stack: m3, m3, M3. Diminished 7th: diminished triad + diminished 7th (9 semitones from root). Stack: m3, m3, m3.
大大七和弦：大三和弦 + 大七度（距根音11个半音）。叠加：大三度、小三度、大三度。属七和弦：大三和弦 + 小七度（10个半音）。叠加：大三度、小三度、小三度。小小七和弦：小三和弦 + 小七度（10个半音）。叠加：小三度、大三度、小三度。半减七和弦：减三和弦 + 小七度。叠加：小三度、小三度、大三度。减七和弦：减三和弦 + 减七度（距根音9个半音）。叠加：小三度、小三度、小三度。
Dom7 (C⁷): C–E–G–B♭. Maj7 (Cmaj⁷): C–E–G–B. Min7 (Cm⁷): C–E♭–G–B♭.
属七和弦(C⁷)：C–E–G–降B。大大七(Cmaj⁷)：C–E–G–B。小小七(Cm⁷)：C–降E–G–降B。
8. Cadences & Harmonic Progressions | 终止式与和声进行
Cadences are the musical equivalent of punctuation marks, closing phrases in specific harmonic ways. The four principal cadences are: perfect (V–I), plagal (IV–I), imperfect (I–V, or other chord moving to V) and interrupted (V–vi).
终止式相当于音乐中的标点符号，用特定的和声方式结束乐句。四种基本终止式为：正格终止（V–I），变格终止（IV–I），不完全终止（I–V或其它和弦进行到V属和弦）和阻碍终止（V–vi）。
A perfect cadence (V–I) sounds complete and final, with the leading tone resolving to the tonic. A plagal cadence (IV–I) is the "Amen" cadence. An imperfect cadence ends on V, creating a sense of expectation, while an interrupted cadence substitutes vi for the expected I, delaying the close.
正格终止（V–I）听感完满、终止感强，导音解决到主音。变格终止（IV–I）常被称为“阿们”终止。不完全终止停在V级，产生期待感；阻碍终止用vi代替预期的I，推迟了结束。
In C major: Perfect cadence G–C. Plagal F–C. Imperfect C–G or Dm–G. Interrupted G–Am.
C大调中：正格终止 G–C。变格终止 F–C。不完全终止 C–G 或 Dm–G。阻碍终止 G–Am。
9. Tempo & Expression Markings | 速度与表情术语
Tempo markings indicate the speed of the music. Common Italian terms: Largo (very slow and broad), Adagio (slow), Andante (walking pace), Moderato (moderate), Allegro (fast and lively), Vivace (lively and fast), Presto (very fast).
速度标记表明音乐的快慢。常用意大利术语：Largo（宽广而很慢），Adagio（慢板），Andante（如步行速度），Moderato（中板），Allegro（快而活泼），Vivace（活跃的快板），Presto（极快板）。
Metronome marks, e.g. ♩ er minute. Terms like ritardando (rit.) and accelerando (accel.) indicate gradual slowing down or speeding up.
节拍器标记，如♩=120，给出每分钟精确的拍数。ritardando (rit.) 意为渐慢，accelerando (accel.) 意为渐快。
Dynamics: pp (pianissimo, very soft), p (piano, soft), mp (mezzo-piano, moderately soft), mf (mezzo-forte, moderately loud), f (forte, loud), ff (fortissimo, very loud). Gradual changes: crescendo (cresc.) and diminuendo (dim.).
力度：pp（很弱），p（弱），mp（中弱），mf（中强），f（强），ff（很强）。渐强（cresc.）和渐弱（dim.）表示力度的逐步变化。
10. Articulation & Ornaments | 演奏法与装饰音
Articulation markings tell performers how to play or sing individual notes. Staccato (a dot above or below the note) means short and detached; legato (a slur) means smoothly connected; accent (>) means stressed; tenuto (–) means held for full value.
演奏法标记告诉表演者如何处理单个音符。断奏（音符上方或下方的点）表示短促分离；连奏（连线）表示圆滑连贯；重音（>）表示加重强调；保持音（–）表示奏足时值。
Ornaments add decoration to a melody. A trill (tr) is a rapid alternation between the written note and the note above. A mordent (short squiggle) is a quick alternation with the upper or lower neighbor. A turn rotates through the upper note, main note, lower note and back. An appoggiatura is a leaning note that takes half the value of the main note that follows.
装饰音为旋律增添花饰。颤音（tr）是书写音与其上邻音的快速交替。波音（短波浪线）是主音与上邻或下邻音的快速交替。回音围绕主音，上行经过上邻音、主音、下邻音再回到主音。倚音是靠在主音前、占用主音一半时值的装饰音。
Trill on C: rapidly alternate C–D–C–D–C. Mordent on C: C–D–C quickly.
C音颤音：快速交替C–D–C–D–C。C音波音：快速C–D–C。
11. Relative Minor & Key Relationships | 关系大小调与调性关系
Every major key has a relative minor sharing the same key signature. The relative minor starts on the 6th degree of the major scale, or a minor 3rd below the major tonic. For C major, the relative minor is A minor.
每个大调都有一个关系小调，两者共用同一调号。关系小调的主音是大调音阶的第六级音，即大调主音下方小三度。C大调的关系小调是a小调。
To find the relative major of a minor key, go up a minor 3rd from the minor tonic. A minor's relative major is C major. This relationship helps with modulation and understanding key changes.
找出小调的关系大调：从小调主音向上小三度。a小调的关系大调是C大调。这一关系有助于转调和理解调性变化。
The parallel minor shares the same tonic but uses a different key signature. C major and C minor are parallel keys. The parallel minor adds three flats (or removes three sharps) relative to the major.
同主音小调共享相同的主音，但使用不同的调号。C大调和c小调就是同主音调。同主音小调相对于大调增加三个降号（或减少三个升号）。
12. Form & Structure | 曲式与结构
Musical form describes how sections are organised. Binary form (AB) has two contrasting but related sections, often each repeated. Ternary form (ABA) presents a main idea, a contrasting middle section, and a return of the opening.
曲式描述音乐段落的组织结构。二部曲式（AB）有两个对比又相关的段落，通常各自反复。三部曲式（ABA）呈现主部、对比中段和再现首部。
Rondo form alternates a recurring main theme (A) with contrasting episodes: ABACA or ABACABA. Theme and variations takes a main theme and presents it in varied guises – changing rhythm, harmony, melody or texture each time.
回旋曲式让反复出现的主部（A）与对比插部交替：ABACA 或 ABACABA。主题变奏曲式以一个主部
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