📚 Year 7 CAIE Music: Quick Reference to Formulas and Theorems | Year 7 CAIE 音乐：公式定理速查手册
Music, like any other discipline, has its own set of rules and structures that can be thought of as ‘formulas’ or ‘theorems’. For Year 7 students following the CAIE Music curriculum, mastering these foundational patterns is essential for reading, writing, and understanding music. This quick reference handbook compiles the essential formulas and theorems you will encounter, from note values and scale constructions to chord building and key signatures. Use it as a handy guide to reinforce your learning and boost your confidence in music theory.
音乐和其他学科一样，也有自己的一套规则和结构，这些规则可以看作是’公式’或’定理’。对于学习 CAIE 音乐课程的 Year 7 学生来说，掌握这些基础模式是读谱、记谱和理解音乐的关键。这本速查手册汇编了你将遇到的核心公式与定理，涵盖音符时值、音阶构成、和弦构建以及调号等。把它当作一个便捷指南，用来巩固所学知识、增强你在音乐理论方面的信心。
1. Note Values and Time Signatures | 音符时值与拍号
The duration of a note is defined by its shape and the context of the time signature. The most common note values in Year 7 are the semibreve, minim, crotchet, quaver, and their corresponding rests. The time signature appears at the beginning of a piece and sets the number of beats per bar and the type of beat that receives one count.
音符的时值由其形状和拍号的环境决定。Year 7 最常见的音符时值包括全音符、二分音符、四分音符、八分音符及其对应的休止符。拍号出现在乐曲开头，规定了每小节有多少拍，以及以何种音符为一拍。
Note Value Tree (Common Time):
| English Name | 中文名称 | Symbol | Relative Duration (in 4/4) |
|---|---|---|---|
| Semibreve | 全音符 | 𝅝 | 4 beats |
| Minim | 二分音符 | 𝅗𝅥 | 2 beats |
| Crotchet | 四分音符 | 𝅘𝅥 | 1 beat |
| Quaver | 八分音符 | 𝅘𝅥𝅮 | 1/2 beat |
The time signature formula is expressed as top number divided by bottom number. The top number indicates how many beats are in each bar, while the bottom number indicates the type of note that equals one beat (4 = crotchet, 8 = quaver, 2 = minim). For example, 4/4 means four crotchet beats per bar.
拍号公式用上方数字除以下方数字来表示。上方数字表示每小节有几拍，下方数字表示以哪种音符为一拍（4 代表四分音符，8 代表八分音符，2 代表二分音符）。例如，4/4 表示每小节有四个四分音符拍。
2. Major Scale Formula | 大调音阶公式
Every major scale follows the same series of tones (whole steps) and semitones (half steps). This pattern is the fundamental ‘formula’ behind the bright, happy sound of major keys. By applying this formula starting on any note, you create the correct major scale.
每个大调音阶都遵循相同的全音与半音序列。这个模式就是大调明亮、愉快音色背后的基本’公式’。从任何音符开始应用这一公式，你就能构建出正确的大调音阶。
Major Scale Formula: W – W – H – W – W – W – H
(W = Whole tone, H = Half tone/semitone). For example, C major: C [W] D [W] E [H] F [W] G [W] A [W] B [H] C. No sharps or flats are needed. If you start on G, you must raise the seventh note (F to F#) to maintain the formula.
（W 代表全音，H 代表半音）。以 C 大调为例：C [W] D [W] E [H] F [W] G [W] A [W] B [H] C，不需要任何升降号。如果从 G 开始，为了让公式成立，必须升高第七级音（F 到 F#）。
3. Minor Scale Formulas | 小调音阶公式
Year 7 students typically explore the natural minor scale, but it is helpful to know there are three common forms. The natural minor uses a specific pattern of whole and half steps, giving it a sadder or more serious character. The formula can be derived from the major scale by lowering the 3rd, 6th, and 7th degrees.
Year 7 学生主要会接触到自然小调，但了解三种常见形式也很有帮助。自然小调有一套特定的全音半音模式，使它听起来更悲伤或更严肃。该公式可以从大调音阶通过降低第 3、第 6、第 7 级音推导出来。
Natural Minor Scale Formula: W – H – W – W – H – W – W
Using A minor (the relative minor of C major) as an example: A [W] B [H] C [W] D [W] E [H] F [W] G [W] A. No sharps or flats. Harmonic minor raises the 7th note by a semitone compared to natural minor, creating a distinctive step and a half between the 6th and 7th degrees.
以 A 小调（C 大调的关系小调）为例：A [W] B [H] C [W] D [W] E [H] F [W] G [W] A，没有升降号。和声小调在自然小调的基础上将第 7 级音升高半音，在 6 级和 7 级之间产生了一个标志性的增二度。
Harmonic Minor: WHWWH (Aug. 2nd) H
Melodic minor ascends with raised 6th and 7th degrees (only the 7th is raised compared to major: W H W W W W H), but for Year 7, the natural minor is the core theorem.
旋律小调上行时升高第 6 和第 7 级音（相对于大调只升高第 7 级音：W H W W W W H），但 Year 7 阶段，自然小调是核心定理。
4. Interval Formulas | 音程公式
An interval is the distance between two notes. Understanding intervals is crucial for building chords and recognising melodies. The size of an interval is counted by the number of letter names involved, and the quality is determined by the number of semitones. This table presents the formulas for intervals up to an octave.
音程是两个音符之间的距离。理解音程对于构建和弦以及识别旋律至关重要。音程的大小根据包含的音名个数来计算，性质则由半音数量决定。下表列出了八度以内音程的公式。
| Interval Name | 中文名称 | Semitones | Example (C to..) |
|---|---|---|---|
| Perfect Unison | 纯一度 | 0 | C |
| Major 2nd | 大二度 | 2 | D |
| Major 3rd | 大三度 | 4 | E |
| Perfect 4th | 纯四度 | 5 | F |
| Perfect 5th | 纯五度 | 7 | G |
| Minor 6th | 小六度 | 8 | Ab |
| Major 6th | 大六度 | 9 | A |
| Minor 7th | 小七度 | 10 | Bb |
| Major 7th | 大七度 | 11 | B |
| Perfect Octave | 纯八度 | 12 | C |
The formula for a major interval can be turned into a minor interval by reducing the distance by one semitone. A perfect interval reduced by a semitone becomes diminished; increased by a semitone, it becomes augmented. These transformations are key theorems for analysis.
大音程减少一个半音就变成了小音程。纯音程减少一个半音变成减音程，增加一个半音变成增音程。这些变换是音程分析中的关键定理。
5. Triad Chord Formulas | 三和弦公式
A triad is a three-note chord built by stacking two thirds on top of a root note. The quality of a triad depends on the combination of major and minor thirds. These formulas are essential for harmonising melodies and understanding tonal music.
三和弦是由根音上方叠加两个三度音构成的三个音的和弦。三和弦的性质取决于大三度和小三度的组合方式。这些公式是旋律配和声以及理解调性音乐的基础。
Major Triad = Root + Major 3rd + Perfect 5th (i.e., major 3rd + minor 3rd)
Minor Triad = Root + Minor 3rd + Perfect 5th (i.e., minor 3rd + major 3rd)
Diminished Triad = Root + Minor 3rd + Diminished 5th (minor 3rd + minor 3rd)
Augmented Triad = Root + Major 3rd + Augmented 5th (major 3rd + major 3rd)
For example, C major triad: C (root), E (major 3rd, 4 semitones above C), G (perfect 5th, 7 semitones above C). A minor triad: A-C-E. These triads are the building blocks of harmony and the Roman numeral system used in CAIE music analysis.
例如，C 大三和弦：C（根音）、E（大三度，在C上方4个半音）、G（纯五度，在C上方7个半音）。A 小三和弦：A-C-E。这些三和弦是和声的基石，也是 CAIE 音乐分析中所用罗马数字体系的基础。
6. Key Signatures and the Circle of 5ths | 调号与五度圈
Key signatures are a shorthand that tells us which notes are consistently sharp or flat in a piece. The theorem for major keys with sharps: the last sharp in the key signature is the leading note (7th degree), and the tonic is a semitone above it. The theorem for flat keys: the penultimate flat in the key signature is the tonic.
调号是一种速记方式，告诉我们乐曲中哪些音要一直升或一直降。升号大调的定理：调号中最后一个升号是导音（第7级），主音就是它上方半音。降号大调的定理：调号中倒数第二个降号就是主音。
Sharp major keys: Father Charles Goes Down And Ends Battle (F#, C#, G#, D#, A#, E#, B#)
Flat major keys: Battle Ends And Down Goes Charles Father (Bb, Eb, Ab, Db, Gb, Cb, Fb)
Relative minor keys share the same key signature. To find the relative minor of a major key, count down three semitones from the major tonic. For example, C major’s relative minor is A minor (C → B → Bb → A = 3 semitones down). This pairing is a fundamental relationship in the Circle of 5ths.
关系小调与大调共用同一个调号。要找到某个大调的关系小调，从大调主音向下数三个半音。例如，C 大调的关系小调是 A 小调（C → B → Bb → A，下降3个半音）。这种配对是五度圈中的基本关系。
7. Dynamics and Articulation Marks | 力度标记与演奏法
Dynamics indicate how loud or soft the music should be played, while articulation defines how individual notes are performed. These symbols form a vocabulary that every performer must know, and they can be treated as ‘transformative formulas’ that change the character of a passage.
力度标记表示音乐应当演奏得多强或多弱，演奏法则规定了单个音符如何演绎。这些符号构成了一套每个演奏者都必须掌握的词汇，它们可以被视作改变乐段性质的’变换公式’。
| Symbol | Italian Term | 中文 | Meaning |
|---|---|---|---|
| pp | pianissimo | 极弱 | very soft |
| p | piano | 弱 | soft |
| mp | mezzo-piano | 中弱 | moderately soft |
| mf | mezzo-forte | 中强 | moderately loud |
| f | forte | 强 | loud |
| ff | fortissimo | 极强 | very loud |
| cresc. / < | crescendo | 渐强 | gradually louder |
| dim. / > | diminuendo | 渐弱 | gradually softer |
Articulation marks such as staccato (dot above or below the note, meaning short and detached) and legato (curved line, meaning smooth and connected) are equally important. An accent mark (>) over a note means play that note with extra force. These marks are like mathematical modifiers that alter the ‘equation’ of the note’s duration and attack.
演奏法标记如断奏（音符上方或下方的圆点，表示短促而分离地演奏）和连奏（弧线，表示平滑连贯地演奏）同样重要。重音记号（>）放在音符上方时，表示要用力强调这个音。这些标记就像数学中的修饰符，改变了音符时值和起音的’方程式’。
8. Tempo Markings and Metronome Formulas | 速度标记与节拍器公式
Tempo is measured in beats per minute (BPM). Italian terms are traditionally used to describe the speed and character of a piece. Understanding these terms and their approximate BPM ranges is essential for performing with the correct stylistic feel.
速度以每分钟拍数（BPM）来衡量。传统上使用意大利术语来描述乐曲的速度和性格。理解这些术语及其大致的 BPM 范围，对于用正确的风格感觉来演奏至关重要。
| Term | 中文 | Meaning | Approx. BPM |
|---|---|---|---|
| Largo | 广板 | very slow and broad | 40–60 |
| Adagio | 柔板 | slow and stately | 66–76 |
| Andante | 行板 | walking pace | 76–108 |
| Moderato | 中板 | moderately | 108–120 |
| Allegro | 快板 | fast, lively | 120–168 |
| Presto | 急板 | very fast | 168–200 |
The metronome mark, often given as ‘M.M. ♩ = 120’, directly states the BPM for a crotchet beat. To convert between note values, use the proportion: if ♩ = 120, then ♪ = 240 (because a quaver is half a crotchet). This proportional thinking is a vital formula for tempo changes.
节拍器标记常常写成 ‘M.M. ♩ = 120’，直接说明了四分音符的 BPM。在不同音符时值之间换算时，利用比例关系：如果 ♩ = 120，那么 ♪ = 240（因为八分音符是四分音符的一半）。这种比例思维是速度变化中的重要公式。
9. Common Rhythmic Patterns and Grouping Rules | 常见节奏型与音群组合规则
Rhythms are built from combinations of note lengths, and their notation must follow strict grouping rules to be clearly readable. In simple time (2/4, 3/4, 4/4), notes and rests should be grouped to show the individual beats clearly. The use of ties and dotted notes follows logical theorems based on beat division.
节奏由不同时值的音符组合而成，记谱时必须遵循严格的音群组合规则，以确保清晰可读。在单拍子（2/4, 3/4, 4/4）中，音符和休止符的组合要明确显示每一拍的分隔。延音线和附点音符的使用遵循基于拍子划分的逻辑定理。
Dotted Note Theorem: A dot after a note increases its duration by half of its original value.
For example, a dotted crotchet (♩.) = 1 + 0.5 = 1.5 beats. A dotted minim (𝅗𝅥.) = 2 + 1 = 3 beats. The tie combines two notes of the same pitch into a single sustained duration. Syncopation occurs when the emphasis falls on a weak beat or between beats, creating an off-beat formula.
例如，附点四分音符（♩.）= 1 + 0.5 = 1.5 拍。附点二分音符（𝅗𝅥.）= 2 + 1 = 3 拍。延音线将两个相同音高的音符连接成一个持续音值。切分节奏发生在重音落在弱拍或拍子之间时，这产生了一种弱拍强调的公式。
Grouping rule formula: In 4/4, four quavers can be beamed together, but they must not obscure the middle of the bar. The first and third beats should be visually distinguishable. Rests follow the same logic: do not use a minim rest to cover beat 2 and 3 if it crosses the middle of a 4/4 bar; instead use two crotchet rests.
组合规则公式：在 4/4 拍中，四个八分音符可以用一条符杠连接，但不能模糊小节中间的分界。第一拍和第三拍在视觉上应当能区分开来。休止符同理：如果一个二分休止符跨过了 4/4 小节的正中央（第2拍和第3拍之间），就不应使用它，而应使用两个四分休止符。
10. The Stave, Clefs, and Accidentals | 五线谱、谱号与临时变音记号
The stave is the grid on which music is written. The treble clef (G clef) and bass clef (F clef) are the two most common clefs for Year 7. Their names provide the formula to locate notes: the treble clef curls around the second line, fixing it as G; the bass clef has two dots straddling the fourth line, fixing it as F.
五线谱是记录音乐的坐标格。高音谱号（G 谱号）和低音谱号（F 谱号）是 Year 7 最常见的两种谱号。它们的名字提供了定位音符的公式：高音谱号的曲线围绕第二线，确定它为 G；低音谱号的两个点跨骑在第四线上，确定它为 F。
Note naming on lines (treble): E – G – B – D – F (Every Good Boy Deserves Fruit)
Spaces (treble): F – A – C – E (spells FACE)
Bass clef lines: G – B – D – F – A (Good Boys Deserve Fruit Always)
Bass clef spaces: A – C – E – G (All Cows Eat Grass)
Accidentals (sharps ♯, flats ♭, naturals ♮) alter a note by one semitone. A sharp raises the pitch; a flat lowers it; a natural cancels any previous accidental. In a bar, an accidental applies to all subsequent notes of the same pitch within that bar, unless cancelled. The rule is a theorem of scope: the accidental’s effect lasts only for the current bar.
临时变音记号（升号 ♯、降号 ♭、还原记号 ♮）可以把音符改变一个半音。升号升高音高，降号降低音高，还原记号取消之前的任何变音记号。在一个小节内，临时变音记号作用于该小节中所有之后同音高的音符，除非被取消。这一规则是一条作用域定理：临时变音记号的效果只持续到该小节结束。
11. Ornaments and Expressive Techniques | 装饰音与表现技巧
Ornaments are small decorative notes or symbols that add expression and embellishment to a melody. The common ornaments introduced in Year 7 include the trill, mordent, turn, and acciaccatura. Each has a precise formula regarding how many notes are played and their relationship to the main note.
装饰音是加在旋律上的小型装饰性音符或符号，用于增添表情和华彩。Year 7 常见的装饰音包括颤音、波音、回音和短倚音。每种装饰音都有其精确的公式，规定演奏几个音以及它们与主要音的关系。
- Trill (tr): Rapid alternation between the written note and the note above. Formula: main note – upper neighbor – main note … ending on main note. | 颤音 (tr)： 记谱音与上方音快速交替。公式：主要音–上方邻音–主要音……结束在主要音上。
- Upper Mordent (short zigzag):
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