📚 KS3 CIE Music: Formula & Theorem Quick Reference Handbook | KS3 CIE 音乐：公式定理速查手册
This quick reference guide brings together the essential 'formulas' and 'theorems' that underpin KS3 CIE Music. Just as you would memorise key equations in mathematics or science, learning the building blocks of music — from scale patterns and chord recipes to interval rules and dynamic markings — will give you a solid foundation for listening, performing and composing.
这份速查手册汇集了支撑 KS3 CIE 音乐的核心“公式”与“定理”。如同在数学或科学中牢记关键方程一样，掌握音乐的构成要素——从音阶模式与和弦配方到音程规则与力度标记——将为你的聆听、演奏和创作奠定坚实基础。
1. The Major Scale Formula: T-T-s-T-T-T-s | 大调音阶公式：全-全-半-全-全-全-半
The major scale is the most important pattern in Western music. Its interval formula uses tones (T) and semitones (s): T – T – s – T – T – T – s. A semitone is the smallest step on a keyboard (e.g. E to F), and a tone equals two semitones (e.g. C to D).
大调音阶是西方音乐中最重要的模式。其音程公式使用了全音 (T) 与半音 (s)：全 – 全 – 半 – 全 – 全 – 全 – 半。半音是键盘上最小的距离（如 E 到 F），一个全音等于两个半音（如 C 到 D）。
T – T – s – T – T – T – s
Applying this formula starting on C gives the scale of C major: C – D – E – F – G – A – B – C. Notice the natural semitones occur between E–F and B–C.
从 C 音开始应用此公式便得到 C 大调音阶：C – D – E – F – G – A – B – C。注意自然半音出现在 E–F 和 B–C 之间。
| Degree | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| Note | C | D | E | F | G | A | B | C |
| Interval | T | T | s | T | T | T | s | – |
任何大调音阶都可通过此公式从任意起始音构建。记忆这个模式比死记每个调的音符要高效得多。
2. The Natural Minor Scale Formula: T-s-T-T-s-T-T | 自然小调音阶公式：全-半-全-全-半-全-全
The natural minor scale has a darker, sadder character. Its formula is T – s – T – T – s – T – T. Comparing it to the major scale, the 3rd, 6th and 7th degrees are flattened by a semitone.
自然小调音阶带有更暗淡、忧伤的色彩。其公式为全 – 半 – 全 – 全 – 半 – 全 – 全。与大调相比，它的第 3、6、7 级都降低了半音。
T – s – T – T – s – T – T
Starting on A, the A natural minor scale uses only white keys: A – B – C – D – E – F – G – A. The semitones fall between B–C and E–F.
从 A 音开始，A 自然小调音阶只用白键：A – B – C – D – E – F – G – A。半音出现在 B–C 和 E–F 之间。
Every major key has a relative minor three semitones below it (e.g. C major's relative minor is A minor). This relationship is a powerful 'theorem' for finding key signatures quickly.
每个大调都有一个关系小调，位于它下方三个半音处（例如 C 大调的关系小调是 A 小调）。这一关系是快速找到调号的强大“定理”。
3. Interval Rules: Counting Semitones | 音程规则：半音计数法
An interval is the distance between two notes, measured in semitones. The table below shows the semitone count for simple intervals up to an octave. Knowing these numbers helps you identify intervals by ear and on the staff.
音程是两个音之间的距离，以半音为单位计量。下表列出了八度以内基本音程的半音数。掌握这些数字有助于听辨和读谱。
| Interval Name | Semitones | Example (C to ...) |
|---|---|---|
| Perfect Unison | 0 | C |
| Minor 2nd | 1 | D♭ |
| Major 2nd | 2 | D |
| Minor 3rd | 3 | E♭ |
| Major 3rd | 4 | E |
| Perfect 4th | 5 | F |
| Tritone (Aug 4th / Dim 5th) | 6 | F♯ / G♭ |
| Perfect 5th | 7 | G |
| Minor 6th | 8 | A♭ |
| Major 6th | 9 | A |
| Minor 7th | 10 | B♭ |
| Major 7th | 11 | B |
| Perfect Octave | 12 | C |
To invert an interval, subtract its semitone count from 12. For example, a Major 3rd (4 semitones) becomes a Minor 6th (8 semitones) when inverted. This is a handy 'theorem' for composing and aural tests.
要将音程转位，用 12 减去它的半音数。例如，大三度（4 个半音）转位后变成小六度（8 个半音）。这对创作和听力测试而言是一条便捷的“定理”。
4. Triad Chord Formulas: Major, Minor, Diminished, Augmented | 三和弦公式：大、小、减、增
Triads are three-note chords built by stacking intervals from a root. The quality of a triad depends on the exact arrangement of semitones between the notes. These four formulas are your chord-building 'equations'.
三和弦是由根音向上叠加音程构成的三个音组成的和弦。三和弦的性质取决于音与音之间半音的精确排列。以下四个公式就是构建和弦的“方程”。
Major triad: root + 4 semitones (Major 3rd) + 3 semitones (Minor 3rd) to the 5th
大三和弦：根音 + 4 个半音（大三度）+ 3 个半音（小三度）到五音
Minor triad: root + 3 semitones (Minor 3rd) + 4 semitones (Major 3rd)
小三和弦：根音 + 3 个半音（小三度）+ 4 个半音（大三度）
Diminished triad: root + 3 semitones + 3 semitones
减三和弦：根音 + 3 个半音 + 3 个半音
Augmented triad: root + 4 semitones + 4 semitones
增三和弦：根音 + 4 个半音 + 4 个半音
Major: 4 + 3 | Minor: 3 + 4 | Diminished: 3 + 3 | Augmented: 4 + 4
Example in C: C major = C–E–G; C minor = C–E♭–G; C diminished = C–E♭–G♭; C augmented = C–E–G♯. These triads form the harmonic foundation of KS3 music.
C 调示例：C 大三和弦 = C–E–G；C 小三和弦 = C–E♭–G；C 减三和弦 = C–E♭–G♭；C 增三和弦 = C–E–G♯。这些三和弦构成了 KS3 音乐的和谐基础。
5. Primary Triads and Roman Numerals (I–IV–V) | 正三和弦与罗马数字（I–IV–V）
ry triads. They are labelled with uppercase Roman numerals: I, IV and V. In C major, I = C–E–G, IV = F–A–C, V = G–B–D.
在任何大调中，建立在第 I 级（主音）、第 IV 级（下属音）和第 V 级（属音）上的三和弦称为正三和弦，用大写罗马数字 I、IV 和 V 表示。在 C 大调中，I = C–E–G，IV = F–A–C，V = G–B–D。
These three chords can harmonise countless simple tunes. The cadence of V moving to I (perfect cadence) and IV moving to I (plagal cadence) are two of the most important 'theorems' of tonal harmony.
仅凭这三个和弦便能为无数简单旋律配和声。V 级到 I 级的进行（正格终止）和 IV 级到 I 级的进行（变格终止）是调性和声最重要的两条“定理”。
6. Time Signatures and Note Lengths | 拍号与音符时值
s, the bottom number tells you what type of note gets one beat (4 = crotchet, 8 = quaver).
拍号决定了每小节的拍数以及以何种音符为一拍。上方数字表示每小节有多少拍，下方数字表示以哪种音符为一拍（4 = 四分音符，8 = 八分音符）。
Common time (4/4): 4 crotchet beats per bar
常见拍号 4/4 拍：每小节 4 个四分音符
3/4: 3 crotchet beats per bar (waltz feel)
3/4 拍：每小节 3 个四分音符（圆舞曲感觉）
2/4: 2 crotchet beats per bar (march feel)
2/4 拍：每小节 2 个四分音符（进行曲感觉）
6/8: 6 quaver beats per bar, usually felt as 2 dotted-crotchet beats
6/8 拍：每小节 6 个八分音符，通常感觉为 2 个附点四分音符拍
s = 8 quavers = 16 semiquavers. Treat note lengths as fractions to master rhythm notation.
音符时值遵循简单的数学关系：一个全音符 = 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。把音符长度当作分数来对待，你就能掌握节奏记谱法。
7. Circle of Fifths: Key Signatures Quick Reference | 五度圈：调号速查表
The Circle of Fifths organises the 12 major and minor keys by their key signatures. Moving clockwise adds sharps; moving counterclockwise adds flats. The order of sharps is F♯ – C♯ – G♯ – D♯ – A♯ – E♯ – B♯, and the order of flats is B♭ – E♭ – A♭ – D♭ – G♭ – C♭ – F♭.
五度圈根据调号将 12 个大调和小调组织起来。顺时针移动增加升号，逆时针移动增加降号。升号的顺序为 F♯ – C♯ – G♯ – D♯ – A♯ – E♯ – B♯，降号的顺序为 B♭ – E♭ – A♭ – D♭ – G♭ – C♭ – F♭。
A useful 'theorem': to find the major key from a sharp key signature, look at the last sharp and go up a semitone. For flat key signatures, the penultimate flat is the name of the major key.
一条有用的“定理”：通过升号调号找大调，看最后一个升号再往上一个半音即可。对于降号调号，倒数第二个降号就是大调的名称。
For example, three sharps (F♯, C♯, G♯): last sharp is G♯, go up a semitone to A major. Three flats (B♭, E♭, A♭): penultimate flat is E♭ major.
例如，三个升号（F♯、C♯、G♯）：最后一个升号是 G♯，向上一个半音得到 A 大调。三个降号（B♭、E♭、A♭）：倒数第二个降号为 E♭ 大调。
8. Dynamics and Tempo Markings: Common Terms | 力度与速度标记：常用术语
These Italian terms are used universally in scores. Treat them as part of the 'vocabulary formula' for interpreting musical expression.
这些意大利术语在乐谱中通用。将它们视为解读音乐表情的“词汇公式”的一部分。
| Dynamic | Meaning | Tempo | Meaning |
|---|---|---|---|
| pp | very soft (pianissimo) | Largo | very slow and broad |
| p | soft (piano) | Adagio | slow and stately |
| mp | moderately soft | Andante | walking pace |
| mf | moderately loud | Moderato | moderate speed |
| f | loud (forte) | Allegro | fast and lively |
| ff | very loud (fortissimo) | Presto | very fast |
Gradual changes include crescendo (gradually louder) and diminuendo/dim. (gradually softer). Accent marks (> ) and staccato dots also belong to this expressive toolkit.
渐变术语包括 crescendo（渐强）和 diminuendo/dim.（渐弱）。重音记号 (> ) 与断奏点也属于这一表现手法工具箱。
9. Accidentals and Enharmonic Equivalents | 临时变音记号与等音
Accidentals alter the pitch of a note: a sharp (♯) raises it by a semitone, a flat (♭) lowers it by a semitone, and a natural (♮) cancels any previous accidental. A double sharp (✕) raises a note by two semitones, a double flat (♭♭) lowers it by two semitones.
临时变音记号改变音高：升号 (♯) 将音升高半音，降号 (♭) 将音降低半音，还原号 (♮) 取消先前的变音记号。重升号 (✕) 升高两个半音，重降号 (♭♭) 降低两个半音。
Enharmonic equivalents are notes that sound the same but are written differently, e.g. C♯ and D♭. This concept is crucial for understanding key signatures and chromatic harmony. Think of it as 'different spelling, same sound'.
等音指听起来相同但记谱不同的音，例如 C♯ 与 D♭。这一概念对理解调号与变化音和声至关重要，可以看作“拼写不同，声音相同”。
10. Melody Writing Tips: Steps, Leaps and Sequences | 旋律写作技巧：级进、跳进与模进
Effective melodies balance conjunct motion (steps, moving by a tone or semitone) with disjunct motion (leaps, intervals larger than a 2nd). A sequence occurs when a melodic idea is repeated at a higher or lower pitch – a powerful 'formula' for extending a melody.
好的旋律会平衡级进（按全音或半音移动）与跳进（大于二度的音程）。模进指将一个旋律动机在更高或更低的音高上重复——这是扩展旋律的有力“公式”。
A leap of more than a 4th should ideally be followed by stepwise motion in the opposite direction to create a smooth contour.
超过四度的跳进最好接反向的级进，以形成平滑的线条轮廓。
Sequences can be real (exact intervals) or tonal (intervals adjusted to fit the key).
模进可以是严格模进（音程完全一致）或调性模进（音程按调调整）。
Start and end a melody on a note of the tonic triad for a strong sense of key.
旋律起止于主三和弦的音上，能带来稳固的调性感。
By treating these patterns as 'formulas', you can generate coherent melodies for KS3 composition tasks with confidence.
把这些模式当作“公式”运用，你就能自信地在 KS3 作曲任务中构思出连贯的旋律。
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