📚 KS3 WJEC Music: Quick-Reference Formulae & Theorems | KS3 WJEC 音乐：公式定理速查手册
This handbook gathers the essential music theory ‘equations’ – note values, scale patterns, interval semitone counts, chord recipes, cadence rules and structural blueprints – all in one place, directly aligned with the WJEC KS3 Music specification.
本手册汇集了 WJEC KS3 音乐课程的核心音乐理论“公式”——音符时值、音阶模式、音程半音计数、和弦配方、终止式规则与结构蓝图，一册在手，速查无忧。
1. Note Values and Rhythm Formulae | 音符时值与节奏公式
Each note symbol has a fixed proportional duration. Knowing these relationships lets you work out any rhythm. The semibreve equals two minims, a minim equals two crotchets, a crotchet equals two quavers, and a quaver equals two semiquavers.
每个音符符号都有固定的比例时值。全音符等于两个二分音符，二分音符等于两个四分音符，四分音符等于两个八分音符，八分音符等于两个十六分音符。
A dot placed after a note increases its length by half. The formula is: dotted value = original value × 1.5. Thus a dotted minim lasts for three crotchet beats.
附点将音符时值延长一半。公式：附点音符时值 = 原时值 × 1.5。因此，附点二分音符持续三个四分音符的拍数。
A tie joins two notes of the same pitch into one sustained sound; the total duration is the sum of the tied notes’ values.
延音线把两个相同音高的音符连成一个持续音，总时值为两者之和。
A triplet squeezes three equal notes into the time normally taken by two. Its rhythmic ratio is 3:2, shown by a bracket with the number ‘3’.
三连音将三个均等音符挤进通常两个音符的时值中，节奏比例为 3:2，用带数字“3”的连音线标记。
2. Time Signatures and Metre | 拍号与节拍
The top number tells you how many beats are in each bar; the bottom number tells you the type of beat (e.g. 4 = crotchet, 8 = quaver). Simple time signatures have beats that divide into two equal parts; compound time signatures have beats that divide into three.
上方数字表示每小节有几拍；下方数字表示以何种音符为一拍（如 4 代表四分音符，8 代表八分音符）。单拍子的每拍可均分为两份；复拍子的每拍可均分为三份。
Common simple times: 2/4 (two crotchet beats), 3/4 (three crotchet beats), 4/4 (four crotchet beats). Common compound times: 6/8 (two dotted-crotchet beats, each splitting into three quavers), 9/8 (three beats), 12/8 (four beats).
常见的单拍子：2/4（两拍）、3/4（三拍）、4/4（四拍）。常见的复拍子：6/8（两个附点四分音符拍，每拍再分为三个八分音符）、9/8（三个拍）、12/8（四个拍）。
Beam your notes so that each beat-group is visually clear. In 4/4 never beam across the middle of the bar (between beats 2 and 3).
用符杠连接音符以清晰地显示拍子组合。在 4/4 拍中，切勿跨越小节中线（即不要把第 2、3 拍的音符连在一起）。
3. Major Scale Formula | 大调音阶公式
Every major scale follows the same pattern of tones (T) and semitones (S): T – T – S – T – T – T – S. For C major, this gives C–D–E–F–G–A–B–C, with semitones occurring naturally between E–F and B–C.
所有大调音阶都遵循相同的全音（T）与半音（S）序列：全 – 全 – 半 – 全 – 全 – 全 – 半。以 C 大调为例，形成 C–D–E–F–G–A–B–C，其中 E–F 和 B–C 自然构成半音。
Using this formula on any starting note produces the major scale with the correct sharps or flats. For instance, starting on G: G–A–B–C–D–E–F#–G applies the same T–T–S–T–T–T–S.
在任何起始音上套用此公式，就能得出带有正确升降号的大调音阶。例如从 G 开始：G–A–B–C–D–E–F#–G，同样遵循全全半全全全半。
4. Minor Scale Formulae | 小调音阶公式
The natural minor scale uses the pattern: T – S – T – T – S – T – T. A natural minor (relative to C major) is A–B–C–D–E–F–G–A.
自然小调音阶的模式为：全 – 半 – 全 – 全 – 半 – 全 – 全。A 自然小调（C 大调的关系小调）即 A–B–C–D–E–F–G–A。
The harmonic minor raises the 7th degree by a semitone, creating an augmented 2nd (3 semitones) between the 6th and 7th degrees: T – S – T – T – S – 3S – S. A harmonic minor becomes A–B–C–D–E–F–G#–A.
和声小调将第 VII 级升高半音，在第 VI 与 VII 级之间制造一个增二度（3 个半音）：全 – 半 – 全 – 全 – 半 – 3 半音 – 半音。A 和声小调变为 A–B–C–D–E–F–G#–A。
The melodic minor raises both the 6th and 7th degrees when ascending (T – S – T – T – T – T – S) and reverts to the natural minor when descending. Ascending A melodic minor: A–B–C–D–E–F#–G#–A.
旋律小调在上行时升高第 VI 和第 VII 级（全 – 半 – 全 – 全 – 全 – 全 – 半），下行时还原为自然小调。上行 A 旋律小调：A–B–C–D–E–F#–G#–A。
5. Pentatonic and Blues Scale Formulae | 五声音阶与布鲁斯音阶公式
The major pentatonic scale omits the 4th and 7th degrees of the major scale, leaving scale degrees 1, 2, 3, 5, 6. C major pentatonic: C–D–E–G–A. Intervals in semitones from the tonic: 2, 2, 3, 2, 3.
大调五声音阶去除了大调的第 IV 和第 VII 级，保留 1、2、3、5、6 音级。C 大调五声：C–D–E–G–A。从主音算起的半音间隔：2, 2, 3, 2, 3。
The minor pentatonic scale uses degrees 1, ♭3, 4, 5, ♭7 from the natural minor. A minor pentatonic: A–C–D–E–G. Semitone intervals: 3, 2, 2, 3, 2.
小调五声音阶取用自然小调的 1、♭3、4、5、♭7 音级。A 小调五声：A–C–D–E–G，半音间隔为 3, 2, 2, 3, 2。
The blues scale adds a flattened 5th (the ‘blue note’) to the minor pentatonic: 1, ♭3, 4, ♭5, 5, ♭7. A blues: A–C–D–E♭–E–G.
布鲁斯音阶在小调五声音阶基础上加入降五级（“蓝调音”）：1、♭3、4、♭5、5、♭7。A 布鲁斯音阶为 A–C–D–E♭–E–G。
6. Intervals: Semitone Counting and Quality | 音程：半音计数与性质
An interval is the distance between two notes, measured in semitones. Below are the common intervals up to an octave with their semitone counts.
音程是两音之间的距离，以半音数量衡量。以下为常见八度内音程及其半音数。
| 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 | 大三度 |
| 5 | Perfect 4th | 纯四度 |
| 6 | Augmented 4th / Diminished 5th (tritone) | 增四度 / 减五度（三全音） |
| 7 | Perfect 5th | 纯五度 |
| 8 | Minor 6th | 小六度 |
| 9 | Major 6th | 大六度 |
| 10 | Minor 7th | 小七度 |
| 11 | Major 7th | 大七度 |
| 12 | Perfect octave | 纯八度 |
Augmented intervals are one semitone wider than perfect or major intervals; diminished intervals are one semitone narrower than perfect or minor intervals.
增音程比纯音程或大音程宽一个半音；减音程比纯音程或小音程窄一个半音。
7. Triad and Chord Construction | 三和弦与和弦构建
Triads are three-note chords built by stacking intervals of a 3rd. The quality depends on the combination of major 3rds (4 semitones) and minor 3rds (3 semitones).
三和弦是由两个三度音程叠置而成的三音和弦，其性质取决于大三度（4 半音）和小三度（3 半音）的组合。
Major triad: root + 4 semitones + 3 semitones (major 3rd + minor 3rd). Example: C–E–G.
大三和弦：根音上加大三度（4 半音）再加小三度（3 半音），如 C–E–G。
Minor triad: root + 3 semitones + 4 semitones (minor 3rd + major 3rd). Example: D–F–A.
小三和弦：根音上加小三度（3 半音）再加大三度（4 半音），如 D–F–A。
Diminished triad: root + 3 + 3 (two minor 3rds). Example: B–D–F.
减三和弦：根音上加两个小三度（3+3 半音），如 B–D–F。
Augmented triad: root + 4 + 4 (two major 3rds). Example: C–E–G#.
增三和弦：根音上加两个大三度（4+4 半音），如 C–E–G#。
In a major key the diatonic triads built on each scale degree follow this pattern: I (major), ii (minor), iii (minor), IV (major), V (major), vi (minor), vii° (diminished). Use Roman numerals with upper case for major and lower case for minor.
大调中各级自然三和弦的规律为：I（大）、ii（小）、iii（小）、IV（大）、V（大）、vi（小）、vii°（减）。用大写罗马数字表大和弦，小写表小和弦。
8. Circle of Fifths and Key Signatures | 五度圈与调号
The circle of fifths arranges keys so that each step clockwise adds one sharp, each step anticlockwise adds one flat. The order of sharps is F♯ – C♯ – G♯ – D♯ – A♯ – E♯ – B♯ (mnemonic: Father Charles Goes Down And Ends Battle). The order of flats is B♭ – E♭ – A♭ – D♭ – G♭ – C♭ – F♭ (Battle Ends And Down Goes Charles’ Father).
五度圈顺时针每走一步增加一个升号，逆时针增加一个降号。升号顺序为 F♯ – C♯ – G♯ – D♯ – A♯ – E♯ – B♯；降号顺序为 B♭ – E♭ – A♭ – D♭ – G♭ – C♭ – F♭。
To identify a sharp major key, find the last sharp and go up one semitone – that note is the tonic. For flat major keys, the second-to-last flat is the tonic (the key of F major with one flat is the exception; just memorize B♭ = F major).
辨认升号大调：找到最后一个升号再升高半音即为调性主音。降号大调：倒数第二个降号即为主音（一个降号的 F 大调例外，直接记忆 B♭ 表示 F 大调）。
Relative minor keys share the same key signature and are found a minor 3rd (3 semitones) below the major tonic. For example, A minor is the relative of C major.
关系小调与对应大调共享同一调号，主音位于大调主音下方小三度（3 半音）处。如 A 小调是 C 大调的关系小调。
9. Cadence Formulae | 终止式公式
A cadence is a pair of chords that closes a phrase. The four essential cadences are defined by their chord progressions.
终止式是结束一个乐句的两和弦进行。四种基本终止式由其和弦进行定义。
| Cadence | Chord Formula | 中文 | Effect |
|---|---|---|---|
| Perfect | V – I (or V⁷ – I) | 正格终止 | Strong, final |
| Plagal | IV – I | 变格终止 | ‘Amen’, gentle ending |
| Imperfect | I – V (or ii – V, IV – V) | 半终止 | Unfinished, sounds like a question |
| Interrupted | V – vi (or V – VI) | 阻碍终止 |
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