📚 Year 8 Cambridge Music: Formula & Theorem Quick Reference | Year 8 Cambridge 音乐：公式定理速查手册
Music may be an art, but it is built on precise patterns and rules that act like 'formulas' and 'theorems'. This quick reference handbook gathers all the essential musical rules you need for Year 8 Cambridge Music, from note values and scales to chord construction and key signatures. Each rule is presented clearly so you can look it up in seconds and embed it into your listening, performing and composing.
音乐虽是一门艺术，但它建立在精确的模式和规则之上，这些规则就像“公式”和“定理”。这本速查手册汇集了 Year 8 Cambridge 音乐课程所需的所有核心规则，涵盖音符时值、音阶、和弦构建和调号等。每一条规则都清晰呈现，方便你随时查阅并运用在听赏、演奏和创作中。
1. The Musical Staff and Clefs | 五线谱与谱号
The five-line staff is the foundation of written music. Lines and spaces are counted from the bottom up.
五线谱是记谱法的基础。线和间都是从下往上数。
Formula: Treble clef lines (from bottom) spell E, G, B, D, F. Treble clef spaces spell F, A, C, E. Bass clef lines are G, B, D, F, A, and spaces are A, C, E, G.
公式：高音谱号从下往上的线依次是 E、G、B、D、F。高音谱号的间是 F、A、C、E。低音谱号的线是 G、B、D、F、A，间是 A、C、E、G。
Ledger lines extend the staff both above and below. Middle C sits on one ledger line below the treble staff or above the bass staff, acting as the central pivot of the grand staff.
加线将五线谱向上和向下延伸。中央 C 位于高音谱表下加一线或低音谱表上加一线，是大谱表的核心枢纽。
2. Note Values and Rest Formulas | 音符与休止符时值公式
Note durations follow precise mathematical relationships. The semibreve (whole note) is the largest unit in common use, and all other notes are fractions of it.
音符的时值遵循精确的数学关系。全音符是常用单位中最大的，所有其他音符都是它的等分。
erms: 1 whole note = 2 half notes = 4 quarter notes = 8 eighth notes = 16 sixteenth notes.
公式：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。
= 1½ crotchets or 3 quavers. Rests have equivalent values and follow the same arithmetic.
附点音符将原时值延长一半。附点二分音符 = 3 个四分音符；附点四分音符 = 1½ 个四分音符或 3 个八分音符。休止符的时值与对应音符相同，遵循同样的算式。
3. Time Signatures: The Metre Formula | 拍号：节拍公式
A time signature appears at the start of a piece. The top numeral tells how many beats are in each bar; the bottom numeral tells which note value equals one beat.
拍号出现在乐曲开头。上方的数字表示每小节有几拍；下方的数字表示以什么音符为一拍。
Common formula: 4/4 means 4 crotchet beats per bar. 3/4 means 3 crotchet beats. 2/4 means 2 crotchet beats. In 6/8, there are 6 quaver beats per bar, often grouped in two dotted-crotchet pulses (compound duple).
常见公式：4/4 表示每小节 4 个四分音符拍。3/4 表示 3 个四分音符拍。2/4 表示 2 个四分音符拍。6/8 拍表示每小节 6 个八分音符拍，通常组合成两个附点四分音符的脉动（复二拍子）。
The beat hierarchy rule: the first beat of a bar is the strongest (downbeat), helping to define the metre.
节拍强弱规则：每小节的第一拍最强（强拍），由此确立节拍的韵律。
4. Major Scale Formula | 大调音阶公式
All major scales share one pattern of tones (T) and semitones (S). This is the most fundamental 'theorem' in Western melody and harmony.
所有大调音阶共享同一个全音（T）与半音（S）的模式。这是西方旋律与和声中最基本的“定理”。
The formula in steps: T T S T T T S, or in words: Tone, Tone, Semitone, Tone, Tone, Tone, Semitone. For C major, this gives C D E F G A B C, with semitones occurring between E–F and B–C.
音级公式：全 全 半 全 全 全 半。以 C 大调为例，得出 C D E F G A B C，其中半音出现在 E–F 和 B–C 之间。
Apply the formula to any starting note to build a major scale. You must use each letter name once. Sharps or flats adjust pitches to match the pattern, never mixing sharps and flats in the same scale.
把这个公式应用在任何起始音上就能构建大调音阶。你必须使用每一个音名一次，用升号或降号来匹配音程模式，同一个音阶中不能混用升号和降号。
5. Minor Scale Patterns | 小调音阶模式
Year 8 Cambridge Music introduces natural, harmonic and melodic minors. Each has its own formula. The natural minor pattern (descending in the melodic minor) is T S T T S T T.
Year 8 Cambridge 音乐课会介绍自然小调、和声小调和旋律小调。每一种都有自己的公式。自然小调（同时也是旋律小调下行）的模式是 全 半 全 全 半 全 全。
Harmonic minor formula: T S T T S (T+S) S – meaning a step of one and a half tones (augmented second) between the 6th and 7th degrees. Example in A harmonic minor: A B C D E F G♯ A.
和声小调公式：全 半 全 全 半 增二度 半 —— 即第 6 级和第 7 级之间是一个增二度（一个全音加一个半音）。以 A 和声小调为例：A B C D E F G♯ A。
Melodic minor ascends: T S T T T T S; it descends as the natural minor. So A melodic minor ascends: A B C D E F♯ G♯ A, and descends: A G F E D C B A.
旋律小调上行：全 半 全 全 全 全 半；下行还原为自然小调。因此 A 旋律小调上行：A B C D E F♯ G♯ A，下行：A G F E D C B A。
6. Intervals: Counting Semitones | 音程：计算半音
An interval is the distance between two pitches. The size is measured in semitones (half steps). Use the formula: count the letter names for the interval number, then count semitones to determine quality (major, minor, perfect, etc.).
音程是两个音高之间的距离。大小以半音为单位计算。使用公式：先数字母名确定音程的度数，再数半音确定性质（大、小、纯等）。
| Interval | 音程 | Semitones |
|---|---|---|
| Perfect unison | 纯一度 | 0 |
| Major 2nd | 大二度 | 2 |
| Minor 3rd | 小三度 | 3 |
| Major 3rd | 大三度 | 4 |
| Perfect 4th | 纯四度 | 5 |
| Perfect 5th | 纯五度 | 7 |
| Minor 6th | 小六度 | 8 |
| Major 6th | 大六度 | 9 |
| Minor 7th | 小七度 | 10 |
| Major 7th | 大七度 | 11 |
| Perfect octave | 纯八度 | 12 |
erfect, and the numbers add up to 9. For example, a major 3rd becomes a minor 6th (3+6=9).
音程转位定理：音程转位后，大音程变为小音程，小音程变为大音程，纯音程保持纯音程，并且原来的度数与转位度数之和为 9。例如大三度转位后成为小六度（3+6=9）。
7. Chord Construction Rules | 和弦构建法则
Chords are built by stacking thirds. The formula for a major triad is root + 4 semitones (major third) + 3 semitones (minor third). The outer interval is a perfect fifth (7 semitones).
和弦是按照三度叠置构建的。大三和弦的公式是 根音 + 4 个半音（大三度）+ 3 个半音（小三度）。外框架为纯五度（7 个半音）。
Minor triad formula: root + 3 semitones + 4 semitones. Diminished triad: root + 3 + 3 (outer fifth is a tritone, 6 semitones). Augmented triad: root + 4 + 4 (outer fifth is an augmented fifth, 8 semitones).
小三和弦公式：根音 + 3 半音 + 4 半音。减三和弦：根音 + 3 + 3（外框架为三全音，6 个半音）。增三和弦：根音 + 4 + 4（外框架为增五度，8 个半音）。
Seventh chords extend the triad with an extra third. Dominant 7th formula: major triad + minor 3rd (root + 4 + 3 + 3). The chord on the 5th degree of a major scale is always a dominant seventh.
七和弦在三和弦基础上再叠一个三度。属七和弦公式：大三和弦 + 小三度（根音 + 4 + 3 + 3）。大调音阶第 V 级上构成的和弦必定是属七和弦。
8. Key Signatures and the Circle of Fifths | 调号与五度圈
Key signatures are the 'shorthand theorem' that sets the sharps or flats used throughout a piece. The order of sharps is F♯, C♯, G♯, D♯, A♯, E♯, B♯. The order of flats is the reverse: B♭, E♭, A♭, D♭, G♭, C♭, F♭.
调号是贯穿整首作品的“速记定理”，规定了升号或降号。升记号出现的顺序是 F♯、C♯、G♯、D♯、A♯、E♯、B♯。降记号出现的顺序是其逆行：B♭、E♭、A♭、D♭、G♭、C♭、F♭。
Circle of fifths formula: moving clockwise from C major, each new key adds one sharp (G–D–A–E–B–F♯–C♯). Moving anticlockwise adds one flat (F–B♭–E♭–A♭–D♭–G♭–C♭). Relative minor keys share the same key signature and lie a minor third below the major tonic.
五度圈公式：从 C 大调开始顺时针移动，每个新调增加一个升号（G–D–A–E–B–F♯–C♯）。逆时针移动则增加一个降号（F–B♭–E♭–A♭–D♭–G♭–C♭）。关系小调共享相同的调号，主音比大调主音低小三度。
9. Dynamic and Tempo Markings | 力度与速度标记
Dynamics and tempo markings are the performance formulas that shape expression. Dynamics follow a graduated scale from very soft to very loud.
力度与速度标记是塑造音乐表现的演奏公式。力度按照从极弱到极强的等级排列。
Dynamic formula: 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 include crescendo (getting louder) and diminuendo/decrescendo (getting softer).
力度公式：pp (很弱)、p (弱)、mp (中弱)、mf (中强)、f (强)、ff (很强)。逐渐变化包括 crescendo (渐强) 和 diminuendo/decrescendo (渐弱)。
ing pace), Moderato (moderate), Allegro (fast, lively), Presto (very fast). Metronome marks state exact BPM, e.g. ♩ = 120.
速度标记通常用意大利语表示节拍速度。从慢到快的常见术语：Largo (广板，非常慢)、Adagio (柔板，慢)、Andante (行板，步行速度)、Moderato (中板)、Allegro (快板，快速活泼)、Presto (急板，非常快)。节拍器标记给出精确的每分钟拍数，例如 ♩ = 120。
10. Articulation and Expression Formulas | 演奏法与表情公式
Articulation marks tell performers how to attack each note. Staccato (dot above or below the note) means short and detached; the note is typically played for half its written value.
演奏法记号告诉演奏者如何处理每个音。断奏 (音符上方或下方的点) 表示短促而有弹性的演奏，实际时长通常为所标时值的一半。
Legato (curved slur line) means smooth and connected, with no silence between notes. Accent (>) asks for a strong attack on the note. Tenuto (short horizontal line) means holding the note for its full value, often with slight weight.
连奏 (圆弧连线) 表示平滑连贯，音符之间没有空隙。重音记号 (>) 要求对那个音加以强调。保持音 (短横线) 表示弹足时值并稍加压力。
Ties join two notes of the same pitch, adding their durations together as one sustained sound. This is the 'tie addition theorem'.
延音线连接两个相同音高的音符，将它们的时值相加成为一个持续的音响。这就是“延音线加法定理”。
11. Simple Composition: Phrase Structure | 简单作曲：乐句结构
Musical phrases often follow formulaic structures. The most common structures in Year 8 are binary (AB), ternary (ABA), and rondo (ABACA). These act as large-scale 'architectural theorems'.
乐句常遵循公式化的结构。Year 8 最常见的曲式是二部曲式 (AB)、三部曲式 (ABA) 和回旋曲式 (ABACA)。它们就像大尺度的“建筑定理”。
Within a phrase, the 'question and answer' (call and response) formula creates balance. The antecedent (question) ends on an imperfect cadence, while the consequent (answer) ends on a perfect cadence, giving a sense of closure.
在乐句内部，“问与答” (呼应) 的公式营造了平衡感。前句 (提问) 结束于不完全终止，后句 (回答) 结束于完全终止，带来收束感。
Cadence formulas: perfect cadence V–I (full stop), imperfect cadence I–V or IV–V (comma), plagal cadence IV–I (Amen), interrupted cadence V–vi (surprise). These punctuation rules govern the flow of harmonic tension.
终止式公式：正格终止 V–I (句号)，半终止 I–V 或 IV–V (逗号)，变格终止 IV–I (阿门)，阻碍终止 V–vi (意外)。这些“标点规则”掌控着和声张力的流动。
12. Revision Checklist of Musical 'Theorems' | 音乐“定理”复习清单
Review these core formulas before your assessment. A solid grasp of these rules will support every part of the Cambridge Music curriculum, from score reading to creative composition.
考试前复习这些核心公式。牢牢掌握这些规则将为剑桥音乐课程的各个方面提供支持，从读谱到创意作曲。
- Staff-clef theorem: Lines and spaces assign fixed pitch names according to clef.
- 音符时值定理： 全音符、二分音符、四分音符及休止符之间的分数关系。
- Metre formula: Time signature dictates beat grouping and accent pattern.
- 大调公式： 全全半全全全半。
- 小调三种模式： 自然、和声、旋律小调各自的半音位置。
- Interval semitone map: Major, minor and perfect intervals defined by exact semitone counts.
- 和弦叠置定理： 三和弦由根、三、五音构成，七和弦再叠一个三度。
- Circle of fifths direction: Clockwise adds sharps, anticlockwise adds flats.
- Dynamics and tempo scale: pp – p – mp – mf – f – ff; Largo to Presto.
- 表演法记忆口诀： Staccato = 短，legato = 连，accent = 重。
- Cadence rules: V–I is perfect, IV–I is plagal, V–vi is interrupted.
- Structure formulas: Binary, ternary, rondo, and call–response phrase designs.
Keep this handbook with your manuscript paper. Every time you compose or analyse a piece, ask yourself which formula or theorem is at work. With practice, these rules will become automatic, freeing you to create more expressive and accurate music.
把这本手册与你的乐谱纸放在一起。每次作曲或分析作品时，问问自己哪个公式或定理在起作用。通过练习，这些规则将成为你的本能，让你能够创作出更富表现力且更准确的音乐。
Published by TutorHao | Music Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图