📚 KS3 Cambridge Music: Quick Reference Guide to Formulae and Theorems | KS3 Cambridge 音乐：公式定理速查手册
Music theory often feels more like a language than a science, but hidden within it are clear, formula-like patterns and rules. This quick-reference handbook gathers the essential ‘formulae and theorems’ of KS3 Cambridge Music – from note-value ratios to scale patterns, from chord-building recipes to cadence rules – so you can check, revise and memorise them efficiently. Think of it as your musical equation sheet.
音乐理论往往更像一门语言而非科学，但其中隐藏着清晰的、公式般的规律和法则。这本速查手册汇集了 KS3 Cambridge 音乐课程中最核心的“公式和定理”——从音符时值比例到音阶构型，从和弦构建诀窍到终止式规则——让你能高效查阅、复习和记忆。请把它当作你的音乐公式表。
1. Note Values and Rhythm Formulae | 音符时值与节奏公式
The backbone of rhythm reading lies in proportional relationships between note durations. In standard notation, each note value splits equally into two of the next smaller value; this binary division forms the foundation for all rhythmic calculations.
节奏阅读的支柱在于音符时值之间的比例关系。在标准记谱中，每个音符都可以等分成两个相邻的较短音符；这种二分法是所有节奏计算的基础。
1 Semibreve = 2 Minims | 1 Minim = 2 Crotchets | 1 Crotchet = 2 Quavers | 1 Quaver = 2 Semiquavers
These equivalences hold regardless of tempo or time signature – they are pure mathematical relationships. For example, one semibreve always lasts as long as two minims tied together.
无论速度或拍号如何，这些等式始终成立——它们是纯粹的数学关系。例如，一个全音符的时值永远等于两个二分音符加在一起。
A dot placed after any note increases its length by exactly half of the original value. This rule works universally for all note types.
附点放在任何音符之后，都会将原来的时值精确地延长一半。该规则适用于所有音符类型。
Dotted Note = Note + (Note ÷ 2)
Thus a dotted minim equals a minim plus a crotchet (2 + 1 beats in simple time), and a dotted crotchet equals a crotchet plus a quaver.
因此，附点二分音符等于一个二分音符加一个四分音符（在单拍子中为 2 + 1 拍），附点四分音符等于一个四分音符加一个八分音符。
Triplets override the standard duple division: a triplet group packs three notes into the space normally occupied by two of the same kind.
三连音打破了标准的二等分规则：一个三连音组会把三个音符挤进通常由两个同类音符占据的时值里。
Triplet = 3 notes in the time of 2
For instance, a quaver triplet fills the time of two ordinary quavers – effectively one crotchet beat when the pulse is a crotchet. You will often see a small ‘3’ above or below the group to signal the triplet ratio.
例如，一组八分三连音占据两个普通八分音符的时间——在以四分音符为一拍时，实际上就是一拍。你常会看到音符上方或下方有一个小小的“3”，用来提示三连音的比例。
2. Time Signature Rules | 拍号规则
A time signature is a compact formula that tells you how each bar is organised. The top number states how many beats are in a bar; the bottom number tells you which note value counts as one beat.
拍号是一个简明的公式，告诉你每个小节是如何组织的。上面的数字表示每小节有多少拍；下面的数字指明以哪种音符为一拍。
| Time Signature | Beats per bar | Beat unit | 中文解读 |
|---|---|---|---|
| 4/4 | 4 | crotchet (♩) | 每小节4个四分音符 |
| 3/4 | 3 | crotchet | 每小节3个四分音符 |
| 2/4 | 2 | crotchet | 每小节2个四分音符 |
| 2/2 | 2 | minim (𝅗𝅥) | 每小节2个二分音符 |
| 6/8 | 2 dotted-crotchet beats | compound duple | 每小节2个附点四分音符（复二拍） |
The bottom number follows a simple code: 4 stands for a crotchet, 8 for a quaver, 2 for a minim, and so on. You can think of it as a denominator in a fraction: 1/4 note, 1/8 note, etc.
下面的数字遵循一个简单代码：4 代表四分音符，8 代表八分音符，2 代表二分音符，以此类推。你可以把它想象成分数的分母：1/4 音符、1/8 音符等。
A vital ‘theorem’ distinguishes simple and compound time: in simple time the beat naturally divides into two equal parts, while in compound time the beat divides into three.
一个区分单拍子和复拍子的关键“定理”：在单拍子中，每拍自然分成两个均等部分；而在复拍子中，每拍分成三个。
Simple: Beat = 2 divisions | Compound: Beat = 3 divisions
This is why 6/8, even though it has six quavers, is actually felt as two big beats, each made of three quavers.
这就是为什么 6/8 拍虽然有六个八分音符，实际感受却是两大拍，每拍由三个八分音符组成。
3. Major Scale Formula | 大调音阶公式
Every major scale, regardless of starting note, follows exactly the same sequence of tones (T) and semitones (S). This pattern is the universal ‘formula’ for constructing any major scale.
无论从哪个音开始，所有大调音阶都遵循完全相同的全音（T）和半音（S）序列。这个模式是构建任何大调音阶的通用“公式”。
T – T – S – T – T – T – S
In terms of steps, a tone equals two semitones (two adjacent keys on a keyboard), and a semitone is the smallest step in Western music – one key to the very next, with no key in between.
以步长来说，一个全音等于两个半音（键盘上相邻的两个键），而半音是西方音乐中最小的步长——从一个键到紧邻的下一个键，中间没有其他键。
To build C major using the formula: start on C, move up a tone to D, another tone to E, a semitone to F, tone to G, tone to A, tone to B, and finally a semitone back to C. The result contains no sharps or flats.
用该公式构建 C 大调：从 C 开始，上行一个全音到 D，再一个全音到 E，一个半音到 F，全音到 G，全音到 A，全音到 B，最后一个半音回到 C。结果既不升高也不降低任何音。
C D E F G A B C
The formula guarantees that every major scale sounds the same in terms of internal relationships, even though the actual pitches vary.
这个公式保证了每个大调音阶在内部关系上听感相同，尽管实际音高不同。
4. Minor Scale Formulae | 小调音阶公式
Minor scales come in three main forms, each with a distinct interval formula. The natural minor uses the same notes as its relative major but starts on a different tonic.
小调音阶有三种主要形式，每种都有不同的音程公式。自然小调使用的音符与其关系大调完全相同，但起始音不同。
Natural Minor: T – S – T – T – S – T – T
For A natural minor (relative of C major), the notes are A B C D E F G A – all white keys. The pattern places semitones between steps 2–3 and 5–6.
以 A 自然小调（C 大调的关系小调）为例，音符为 A B C D E F G A——全部是白键。该模式将半音放在第 2–3 级和第 5–6 级之间。
The harmonic minor raises the 7th degree by a semitone to create a stronger pull back to the tonic, producing a distinctive interval of an augmented 2nd (three semitones) between the 6th and 7th notes.
和声小调将第 7 级音升高半音，以制造向主音回归的更强倾向，从而在第 6 和第 7 音之间产生一个特有的增二度（三个半音）。
Harmonic Minor: T – S – T – T – S – 3S – S
Where ‘3S’ indicates the three-semitone step (augmented 2nd). In A harmonic minor, this gives A B C D E F G♯ A.
其中的“3S”表示三半音的步长（增二度）。在 A 和声小调中，这形成 A B C D E F G♯ A。
The melodic minor adjusts both the 6th and 7th degrees when ascending to smooth out the augmented step, but typically reverts to the natural minor when descending.
旋律小调在上行时同时调整第 6 和第 7 级音，以平滑增二度，但在下行时通常还原为自然小调。
Ascending Melodic Minor: T – S – T – T – T – T – S
Ascending A melodic minor: A B C D E F♯ G♯ A; descending usually returns to natural minor.
上行 A 旋律小调：A B C D E F♯ G♯ A；下行通常回到自然小调。
5. Interval Calculation | 音程计算方法
An interval is the distance between two pitches, measured in semitones and described by a number (the degree) and a quality (major, minor, perfect, etc.). You can calculate any interval by counting half steps in relation to the major scale built on the lower note.
音程是两个音高之间的距离，以半音为单位测量，并用级数和性质（大、小、纯等）来描述。你可以通过相对于下方音所构成的大调音阶来数半音，从而计算出任何音程。
| Semitones | Interval name | 中文名称 |
|---|---|---|
| 0 | Perfect unison | 纯一度 |
| 1 | Minor 2nd | 小二度 |
| 2 | Major 2nd | 大二度 |
| 3 | Minor 3rd | 小三度 |
| 4 | Major 3rd |
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