📚 Year 11 WJEC Music: Formula & Theorem Quick Reference Handbook | WJEC Year 11 音乐：公式定理速查手册
This handbook brings together the essential theoretical formulas, rules of thumb and quick-reference theorems that every Year 11 WJEC GCSE Music student needs at their fingertips. From key signatures and scale patterns to chord recipes and cadence structures, these building blocks will sharpen your listening, composition and performance analysis. Use it as a daily drill or a final revision checklist.
这本手册汇集了每位 WJEC GCSE 音乐 Year 11 学生必须掌握的乐理公式、经验法则和速查定理。从调号、音阶模式到和弦配方和终止式结构，这些基石将提升你的听力、作曲和作品分析能力。可将其作为日常练习或终极复习清单。
1. Key Signatures & Circle of Fifths | 调号与五度循环
Sharp key signatures follow the order Father Charles Goes Down And Ends Battle (F♯, C♯, G♯, D♯, A♯, E♯, B♯). For any sharp key, the tonic is a semitone above the last sharp. For example, if the key signature has two sharps (F♯ and C♯), the last sharp is C♯; raising it by a semitone gives D, so the key is D major.
升号调的顺序是 F♯, C♯, G♯, D♯, A♯, E♯, B♯（记作 Father Charles Goes Down And Ends Battle）。对于任何升号调，主音比最后一个升号高半音。例如调号有两个升号（F♯ 与 C♯），最后一个升号为 C♯，升高半音得到 D，因此该调为 D 大调。
Flat key signatures follow the reverse: Battle Ends And Down Goes Charles’ Father (B♭, E♭, A♭, D♭, G♭, C♭, F♭). The tonic is the second-to-last flat in the key signature. For example, if the key signature has three flats (B♭, E♭, A♭), the second-to-last flat is E♭, so the key is E♭ major. The exception is F major, which has one flat (B♭); you must simply memorise it.
降号调顺序为相反的 B♭, E♭, A♭, D♭, G♭, C♭, F♭。主音是调号中倒数第二个降号。例如三个降号（B♭, E♭, A♭），倒数第二个降号为 E♭，因此该调为 E♭ 大调。唯一的例外是 F 大调，只有一个降号（B♭），需要单独记忆。
The Circle of Fifths arranges keys so that moving clockwise adds a sharp (or removes a flat) and raises the tonic by a perfect fifth. Moving anticlockwise adds a flat (or removes a sharp) and lowers the tonic by a perfect fifth. Relative minors share the same key signature and lie a minor third below their relative major.
五度循环圈将各调排列，顺时针进行则增加一个升号（或减少一个降号）且主音升高纯五度。逆时针进行则增加一个降号（或减少一个升号）且主音降低纯五度。关系小调共享相同的调号，位于其关系大调下方小三度。
2. Scale Construction Formulas | 音阶构建公式
The major scale pattern is always Tone, Tone, Semitone, Tone, Tone, Tone, Semitone. On a piano, this is equivalent to the whole-step/half-step sequence W W H W W W H.
大调音阶的模式永远是全音、全音、半音、全音、全音、全音、半音。在钢琴上的全音/半音序列为 全 全 半 全 全 全 半。
Major: T T S T T T S
The natural minor scale is formed by starting on the sixth degree of its relative major, giving the pattern Tone, Semitone, Tone, Tone, Semitone, Tone, Tone.
自然小调从关系大调的第六级开始，形成全音、半音、全音、全音、半音、全音、全音的模式。
Natural Minor: T S T T S T T
The harmonic minor raises the seventh degree by a semitone, creating an augmented second (A2) between the sixth and seventh degrees: T S T T S A2 S.
和声小调将第七级升高半音，在第六级与第七级之间制造一个增二度（A2）：全 半 全 全 半 增二度 半。
The melodic minor ascends with a raised sixth and seventh (T S T T T T S), but descends like the natural minor (T T S T T S T). This avoids the awkward augmented second in vocal melodies.
旋律小调上行时将第六和第七级升高（全 半 全 全 全 全 半），但下行时恢复为自然小调（全 全 半 全 全 半 全）。这避免了声乐旋律中别扭的增二度。
The major pentatonic scale uses degrees 1, 2, 3, 5, 6 of the major scale (e.g. C D E G A). The minor pentatonic uses 1, ♭3, 4, 5, ♭7 (e.g. C E♭ F G B♭). The blues scale adds a ♭5 to the minor pentatonic.
大调五声音阶使用大调音阶的第 1, 2, 3, 5, 6 级（如 C D E G A）。小调五声音阶使用 1, ♭3, 4, 5, ♭7（如 C E♭ F G B♭）。布鲁斯音阶在小调五声音阶基础上加入 ♭5 级。
3. Interval Recognition Rules | 音程识别规则
First count the letter names (including both notes) to get the interval number. Then count the semitones between the lower and upper note to determine the quality. Perfect intervals (unison, 4th, 5th, octave) become augmented when expanded by a semitone and diminished when contracted. Major intervals (2nd, 3rd, 6th, 7th) become minor when reduced by a semitone; minor intervals become diminished when reduced further, and major intervals become augmented when expanded.
先数字母名（包括两个音）得出音程度数。然后数下方音到上方音之间的半音数，决定音程性质。纯音程（同度、四度、五度、八度）扩大一个半音成为增音程，缩小一个半音成为减音程。大音程（二度、三度、六度、七度）减少一个半音成为小音程；小音程再减少成为减音程，大音程扩大成为增音程。
Common intervals and their semitone counts:
Perfect unison: 0 semitones
Minor 2nd: 1 semitone
Major 2nd: 2 semitones
Minor 3rd: 3 semitones
Major 3rd: 4 semitones
Perfect 4th: 5 semitones
Augmented 4th/Diminished 5th (tritone): 6 semitones
Perfect 5th: 7 semitones
Minor 6th: 8 semitones
Major 6th: 9 semitones
Minor 7th: 10 semitones
Major 7th: 11 semitones
Perfect octave: 12 semitones
常见音程及其半音数：
纯一度：0 个半音
小二度：1 个半音
大二度：2 个半音
小三度：3 个半音
大三度：4 个半音
纯四度：5 个半音
增四度/减五度（三全音）：6 个半音
纯五度：7 个半音
小六度：8 个半音
大六度：9 个半音
小七度：10 个半音
大七度：11 个半音
纯八度：12 个半音
4. Chord Building Formulas (Triads & Sevenths) | 和弦构建公式（三和弦与七和弦）
A triad is built by stacking two thirds on a root. Use semitone counts between successive notes to construct any quality. A major triad = root + 4 semitones + 3 semitones (major 3rd + minor 3rd). A minor triad = root + 3 + 4. A diminished triad = root + 3 + 3. An augmented triad = root + 4 + 4.
三和弦由根音上叠加两个三度构成。用相邻音之间的半音数可构建任何性质的和弦。大三和弦 = 根音 + 4 个半音 + 3 个半音（大三度 + 小三度）。小三和弦 = 根音 + 3 + 4。减三和弦 = 根音 + 3 + 3。增三和弦 = 根音 + 4 + 4。
Triad Formulas: Maj = R+4+3; min = R+3+4; dim = R+3+3; aug = R+4+4
Seventh chords add another third on top. The dominant 7th (most common) stacks a major triad with a minor 7th: root + 4 + 3 + 3. Major 7th = root + 4 + 3 + 4. Minor 7th = root + 3 + 4 + 3. Half-diminished 7th = root + 3 + 3 + 4. Diminished 7th = root + 3 + 3 + 3.
七和弦再叠加一个三度。属七和弦（最常见）在大三和弦上加一个小七度：根音 + 4 + 3 + 3。大七和弦 = 根音 + 4 + 3 + 4。小七和弦 = 根音 + 3 + 4 + 3。半减七和弦 = 根音 + 3 + 3 + 4。减七和弦 = 根音 + 3 + 3 + 3。
Inversion symbols for triads: root position (nothing or 5/3), first inversion (6, with the 3rd in the bass), second inversion (6/4, with the 5th in the bass). For seventh chords: root position (7), first inversion (6/5), second inversion (4/3), third inversion (4/2).
三和弦的转位标记：原位（无标记或 ⁵₃），第一转位（⁶，三音在低音），第二转位（⁶₄，五音在低音）。七和弦转位：原位（⁷），第一转位（⁶₅），第二转位（⁴₃），第三转位（⁴₂）。
5. Cadences & Harmonic Progressions | 终止式与和声进行
A perfect cadence (V–I) sounds final and conclusive, like a full stop. An imperfect cadence (I–V, ii–V or IV–V) sounds unfinished, as if pausing on a comma. A plagal cadence (IV–I) is often called the ‘Amen’ cadence and sounds gentle and resolved. An interrupted (or deceptive) cadence (V–vi) sets up an expectation of I but moves to vi instead, creating a surprise.
完全终止（V–I）听感结束、决断，如同句号。不完全终止（I–V、ii–V 或 IV–V）听感未完结，像逗号停顿。变格终止（IV–I）常被称为”阿门终止”，听感柔和而解决。阻碍终止（V–vi）制造对 I 的期待却走向 vi，产生意外感。
Functional harmony assigns roles: tonic (I, vi), subdominant (IV, ii) and dominant (V, vii°). Typical progressions move from tonic to subdominant to dominant and back to tonic, but countless variations exist. Recognizing these patterns by ear helps you identify cadences in listening exams and strengthen your own compositions.
功能和声赋予和弦角色：主功能（I, vi）、下属功能（IV, ii）、属功能（V, vii°）。典型的进行从主到下属再到属，最后回到主，但仍有无数变体。通过听觉识别这些模式有助于在听力考试中辨认终止式，也能强化你自己的作曲。
6. Time Signatures & Rhythmic Values | 拍号与节奏时值
The top number of a time signature tells how many beats are in each bar; the bottom number tells what note value represents one beat. Simple time signatures (e.g. 2/4, 3/4, 4/4) have beats that divide into two equal parts. Compound time signatures (e.g. 6/8, 9/8, 12/8) have beats that divide into three equal parts (dotted beat).
拍号的上方数字表示每小节有几拍；下方数字表示以几分音符为一拍。简单拍子（如 2/4, 3/4, 4/4）每拍可一分为二。复合拍子（如 6/8, 9/8, 12/8）每拍可一分为三（附点拍）。
Note value relationships: 1 semibreve = 2 minims = 4 crotchets = 8 quavers = 16 semiquavers. A dotted note lasts 1.5 times the undotted value; a double-dotted note lasts 1.75 times the undotted value. A triplet groups three notes in the time normally taken by two of the same kind.
音符时值关系：1 全音符 = 2 二分音符 = 4 四分音符 = 8 八分音符 = 16 十六分音符。附点音符的时值是原时值的 1.5 倍；双附点音符为原时值的 1.75 倍。三连音将三个音压缩到通常两个同样音符的时长内。
Dotted note = original value x 1.5; Triplet = 3 ÷ 2 (three in the time of two)
When notating rhythms, beam quavers and semiquavers to show the beat structure clearly. In compound time, each beat is a dotted note, so 6/8 has two dotted-crotchet beats per bar.
记谱时用符杠将八分音符和十六分音符连结，清晰显示节拍结构。在复合拍子中，每拍是一个附点音符，例如 6/8 拍每小节有两拍，每拍为附点四分音符。
7. Transposition Formula | 移调公式
Transposing instruments sound at a different pitch from the written note. The most common in
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