📚 Year 12 WJEC Music: Formula & Theorem Quick Reference Handbook | WJEC 十二年级音乐：公式定理速查手册
This quick reference handbook brings together the essential formulae, rules and theorems you need to master for the Year 12 WJEC Music course. From reading rhythms and building intervals to voice-leading and cadences, every core concept is presented with clear English explanations followed by their Chinese translations, so you can revise efficiently and with confidence.
本速查手册汇集了十二年级 WJEC 音乐课程必须掌握的核心公式、规则和定理。从读节奏、构建音程到声部进行与终止式，每一个关键概念都先以英文清晰解释，再附上对应的中文翻译，让你高效复习、充满信心。
1. Note Values & Rests | 音符时值与休止符
Semibreve (whole note): 4 beats in simple time.
全音符：简单拍子中时值4拍。
Minim (half note): 2 beats.
二分音符：2拍。
Crotchet (quarter note): 1 beat.
四分音符：1拍。
Quaver (eighth note): ½ beat.
八分音符：½拍。
Semiquaver (sixteenth note): ¼ beat.
十六分音符：¼拍。
Demisemiquaver (thirty-second note): ⅛ beat.
三十二分音符：⅛拍。
Dotted minim: 3 beats (2 + 1).
附点二分音符：3拍（2+1）。
Dotted crotchet: 1½ beats.
附点四分音符：1½拍。
Dotted quaver: ¾ beat.
附点八分音符：¾拍。
Double dotted quaver: ⅞ beat (½ + ¼ + ⅛).
双附点八分音符：⅞拍（½ + ¼ + ⅛）。
Semibreve rest: hangs below the fourth line, 4 beats.
全休止符：悬挂在第四线下方，4拍。
Minim rest: sits on the third line, 2 beats.
二分休止符：放置在第三线上，2拍。
Crotchet rest: 1 beat.
四分休止符：1拍。
Quaver rest: ½ beat, single hook.
八分休止符：½拍，一个符钩。
Semiquaver rest: ¼ beat, two hooks.
十六分休止符：¼拍，两个符钩。
2. Time Signatures & Metre | 拍号与节拍
Simple duple: 2/4, 2/2 – two beats per bar, each beat divides into two equal parts.
单二拍子：2/4、2/2——每小节两拍，每拍均分为二等份。
Simple triple: 3/4, 3/2 – three beats per bar.
单三拍子：3/4、3/2——每小节三拍。
Simple quadruple: 4/4 (common time C), 4/2 – four beats per bar.
单四拍子：4/4（普通拍子记号C）、4/2——每小节四拍。
Compound duple: 6/8 – two dotted-crotchet beats, each beat splits into three quavers.
复二拍子：6/8——两个附点四分音符拍，每拍分为三个八分音符。
Compound triple: 9/8 – three dotted-crotchet beats.
复三拍子：9/8——三个附点四分音符拍。
Compound quadruple: 12/8 – four dotted-crotchet beats.
复四拍子：12/8——四个附点四分音符拍。
Irregular/Asymmetrical metre: 5/4, 7/8 – beats grouped in unequal divisions, often 3+2 or 2+3.
不规则/不对称节拍：5/4、7/8——拍子以不等分形式分组，常见3+2或2+3。
Anacrusis: an upbeat before the first full bar.
弱起小节：第一个完整小节前的上拍。
Syncopation: accent placed on normally weak beats or between beats.
切分音：重音落在通常为弱拍或拍点之间的位置。
3. Interval Formulae | 音程公式
Unison: 0 semitones.
同度：0个半音。
Minor 2nd: 1 semitone (e.g. C–Db).
小二度：1个半音（如C–降D）。
Major 2nd: 2 semitones (C–D).
大二度：2个半音（C–D）。
Minor 3rd: 3 semitones (C–Eb).
小三度：3个半音（C–降E）。
Major 3rd: 4 semitones (C–E).
大三度：4个半音（C–E）。
Perfect 4th: 5 semitones (C–F).
纯四度：5个半音（C–F）。
Augmented 4th / Diminished 5th (tritone): 6 semitones (C–F#).
增四度/减五度（三全音）：6个半音（C–升F）。
Perfect 5th: 7 semitones (C–G).
纯五度：7个半音（C–G）。
Minor 6th: 8 semitones (C–Ab).
小六度：8个半音（C–降A）。
Major 6th: 9 semitones (C–A).
大六度：9个半音（C–A）。
Minor 7th: 10 semitones (C–Bb).
小七度：10个半音（C–降B）。
Major 7th: 11 semitones (C–B).
大七度：11个半音（C–B）。
Perfect 8ve (octave): 12 semitones.
纯八度：12个半音。
Inversion rule: the sum of an interval and its inversion always equals 9. Perfect remains perfect; major becomes minor; augmented becomes diminished, and vice versa.
转位规则：音程与其转位的度数之和恒为9。纯音程转位仍为纯；大音程变为小音程；增音程变为减音程，反之亦然。
4. Scale Construction | 音阶构成
Major scale: Tone–Tone–Semitone–Tone–Tone–Tone–Semitone (T T S T T T S).
大调音阶：全音–全音–半音–全音–全音–全音–半音。
Natural minor: T S T T S T T (derived from the major scale on the 6th degree).
自然小调：全–半–全–全–半–全–全（从大调音阶第六级音开始）。
Harmonic minor: raise the 7th degree by a semitone (T S T T S A2 S).
和声小调：升高第七级音半音（全–半–全–全–半–增二度–半）。
Melodic minor (ascending): raise 6th and 7th degrees (T S T T T T S); descending it reverts to natural minor.
旋律小调（上行）：升高第六、第七级音（全–半–全–全–全–全–半）；下行时还原为自然小调。
Chromatic scale: built entirely by semitones (12 pitches per octave).
半音阶：完全由半音构成（每个八度12个音）。
Whole-tone scale: six tones, each separated by a whole step (T T T T T T).
全音音阶：六个音，每个音之间为全音。
Pentatonic scale: five notes per octave, e.g. C D E G A (major pentatonic) or A C D E G (minor pentatonic).
五声音阶：每八度五个音，如C D E G A（大调五声）或A C D E G（小调五声）。
Blues scale: minor pentatonic plus a flattened 5th (blue note), e.g. A C D Eb E G.
布鲁斯音阶：小调五声音阶加降五度（蓝调音），如A C D 降E E G。
5. Triad & Seventh Chord Building | 三和弦与七和弦构造
Major triad: root + major 3rd (4 semitones) + perfect 5th (7 semitones). E.g. C–E–G.
大三和弦：根音+大三度（4个半音）+纯五度（7个半音）。如C–E–G。
Minor triad: root + minor 3rd (3 semitones) + perfect 5th. E.g. A–C–E.
小三和弦：根音+小三度（3个半音）+纯五度。如A–C–E。
Diminished triad: root + minor 3rd + diminished 5th (6 semitones). E.g. B–D–F.
减三和弦：根音+小三度+减五度（6个半音）。如B–D–F。
Augmented triad: root + major 3rd + augmented 5th (8 semitones). E.g. C–E–G#.
增三和弦：根音+大三度+增五度（8个半音）。如C–E–升G。
Dominant 7th: major triad + minor 7th (10 semitones above root). E.g. G–B–D–F.
属七和弦：大三和弦+小七度（根音上方10个半音）。如G–B–D–F。
Major 7th: major triad + major 7th (11 semitones). E.g. C–E–G–B.
大七和弦：大三和弦+大七度（11个半音）。如C–E–G–B。
Minor 7th: minor triad + minor 7th. E.g. A–C–E–G.
小七和弦：小三和弦+小七度。如A–C–E–G。
Half-diminished 7th (m7♭5): diminished triad + minor 7th. E.g. B–D–F–A.
半减七和弦（小七降五）：减三和弦+小七度。如B–D–F–A。
Diminished 7th: diminished triad + diminished 7th (9 semitones). E.g. B–D–F–Ab.
减七和弦：减三和弦+减七度（9个半音）。如B–D–F–降A。
6. Figured Bass & Chord Inversions | 数字低音与和弦转位
Root position triad: no figures needed (5/3 implied).
根音位置三和弦：无需数字标记（隐含5/3）。
First inversion triad: figure 6 (or 6/3). E.g. C/E.
第一转位三和弦：数字标记6（或6/3）。如C/E。
Second inversion triad: figure 6/4. E.g. C/G.
第二转位三和弦：数字标记6/4。如C/G。
Root position 7th chord: figure 7 (7/5/3).
根音位置七和弦：数字标记7（7/5/3）。
First inversion 7th chord: figure 6/5.
第一转位七和弦：数字标记6/5。
Second inversion 7th chord: figure 4/3.
第二转位七和弦：数字标记4/3。
Third inversion 7th chord: figure 4/2 (or simply 2). E.g. G7/F.
第三转位七和弦：数字标记4/2（或简写为2）。如G7/F。
Figured bass accidentals: a sharp (♯), flat (♭) or natural (♮) next to a figure alters the interval above the bass.
数字低音中的临时记号：数字旁的升号(♯)、降号(♭)或还原号(♮)用于改变低音上方该音程的音高。
7. Cadences & Harmonic Progressions | 终止式与和声进行
Perfect cadence: V–I (or V7–I). Sounds final and conclusive.
正格终止：V–I（或V7–I）。听感完满、确定。
Plagal cadence: IV–I. Often called the 'Amen' cadence.
变格终止：IV–I。常被称为"阿们"终止。
Imperfect cadence: any chord moving to V (e.g. I–V, ii–V, IV–V). Sounds unfinished.
不完全终止：任何和弦进行到V（如I–V、ii–V、IV–V）。听感未结束。
Interrupted cadence: V–vi (or V–VI in minor). A deceptive resolution.
阻碍终止：V–vi（小调中为V–VI）。一种意外进行。
Primary triads in major: I, IV, V. In natural minor: i, iv, V (with raised leading note).
大调中的正三和弦：I、IV、V。自然小调中：i、iv、V（升高导音）。
Common chord progression: I–vi–IV–V–I. This underpins thousands of songs.
常见和弦进行：I–vi–IV–V–I。无数歌曲的基础进行。
Circle of 5ths progression: moving by descending 5ths (or ascending 4ths), e.g. vi–ii–V–I in major; IV–vii°–iii–vi in minor, etc.
五度循环进行：以向下五度（或向上四度）移动，如大调中vi–ii–V–I；小调中iv–vii°–III–VI等。
8. Voice Leading Rules | 声部进行规则
Keep common notes in the same voice when possible; move other voices by the smallest step.
尽可能保留共同音于同一声部；其他声部以最小音程移动。
Avoid parallel perfect 5ths and parallel octaves between any two voices.
避免任何两个声部间出现平行纯五度和平行八度。
Avoid exposed (hidden) 5ths and octaves in outer voices when the soprano leaps to a perfect consonance approached by similar motion.
外声部中，当女高音以同向进行跳进到纯协和音程时，避免出现隐伏五度与隐伏八度。
Leading note (7th degree) in major/minor keys should rise to the tonic when it appears over a dominant-function chord.
大调与小调中的导音（第七级音）在属功能和弦时应上行解决到主音。
Chromatic alterations must resolve correctly: raised notes tend to rise, lowered notes tend to fall.
变音必须正确解决：升高音倾向继续上行，降低音倾向下行。
In root-position four-part writing, double the root preferably; in first inversion, double the soprano or bass note (often the third can be doubled, but avoid doubling the leading note).
四部和声根音位置中，优先重复根音；第一转位中，可重复女高音旋律音或低音部（常可重复三音，但避免重复导音）。
For diminished triads, avoid doubling the root if it is the leading note; instead double the third (or the fifth if necessary).
减三和弦中，若根音为导音，避免重复根音；可重复三音（必要时重复五音）。
9. Non-Chord Tones | 和弦外音
Passing note (PT): approached by step, left by step in the same direction, linking two chord tones.
经过音：级进引入、级进离开且方向一致，连接两个和弦音。
Neighbour note (auxiliary, NT): step away from a chord tone and step back to the same tone. Upper neighbour and lower neighbour are possible.
辅助音：从和弦音级进离开再级进返回同一音。有上辅助音与下辅助音之分。
Suspension (SUS): a note held over from the previous chord, creating a dissonance, then resolved down by step. Preparation–Suspension–Resolution pattern.
延留音：从前一和弦延留过来的音，造成不协和，然后下行级进解决。准备–延留–解决模式。
Appoggiatura (APP): approached by leap and resolved by step, often accented, creating strong expressive dissonance.
倚音：以跳进引入、级进解决，常出现在强拍，制造强烈的表情性不协和。
Escape tone (échappée): approached by step and left by leap in opposite direction.
规避音（逸音）：级进引入，反向跳进离开。
Anticipation (ANT): a chord tone played early, before the harmony changes; resolves by common tone, usually unaccented.
先现音：在和声改变之前提早出现的和弦音；通常不加重音，以同音解决。
Changing note group (cambiata): a four-note figure that combines lower neighbour and escape tone patterns, usually step–down–leap up–step down.
换音组：一个四音组合，结合下辅助音与规避音模式，通常为：级进–下跳–上大跳–级进。
10. Ornaments | 装饰音
Trill (tr): rapid alternation between the written note and the upper diatonic note, often starting on the upper note in Baroque repertoire.
颤音：在本音与上方自然音级音之间快速交替；巴洛克作品中常由上音开始。
Mordent (upper mordent): the written note, the note above, and back to the written note; indicated by a short squiggle.
波音（上波音）：本音–上方音–本音；用短波浪线标记。
Lower mordent (inverted mordent): written note, lower note, written note; marked with the same squiggle crossed by a vertical line.
下波音：本音–下方音–本音；用带竖线的波浪线标记。
Turn: a four-note figure around the main note: upper auxiliary – main note – lower auxiliary – main note. If the turn is placed between two notes, the rhythm must be adjusted accordingly.
回音：围绕主要音的四个音：上方辅助音–主要音–下方辅助音–主要音。若回音记号写在两个音之间，节奏须作相应调整。
Appoggiatura: a small note (usually unstressed) that takes half or more of the main note's value, resolving by step. Not to be confused with the non-chord tone appoggiatura, but historically related.
长倚音：一个小音符，通常占用主要音一半或更多时值，然后级进解决。与和弦外音中的倚音有历史渊源但不完全相同。
Acciaccatura: a crushed note, a small grace note with a stroke through its stem, played very quickly before the main note.
短倚音（碎音）：带斜线的小音符，在主要音之前极快速奏出。
11. Dynamics, Tempo & Expression | 力度、速度与表情术语
pp (pianissimo): very soft; p (piano): soft; mp (mezzo-piano): moderately soft.
pp（甚弱）；p（弱）；mp（中弱）。
mf (mezzo-forte): moderately loud; f (forte): loud; ff (fortissimo): very loud.
mf（中强）；f（强）；ff（甚强）。
cresc. (crescendo): gradually getting louder; dim. (diminuendo): gradually getting softer.
cresc.（渐强）；dim.（渐弱）或 decresc.。
sfz (sforzando): a sudden strong accent on a single note or chord.
sfz（突强）：对一个音或和弦突然施加的重音。
Grave: very slow and solemn; Lento: slow; Largo: broadly.
Grave：极慢而庄重；Lento：慢；Largo：宽广地。
Adagio: slow and stately; Andante: at a walking pace; Moderato: moderate tempo.
Adagio：缓慢而宁静；Andante：行板；Moderato：中速。
Allegretto: moderately fast; Allegro: fast, lively; Vivace: lively and brisk; Presto: very fast.
Allegretto：小快板；Allegro：快板；Vivace：活泼地；Presto：急板。
Rit. (ritardando): gradually slowing down; Rall. (rallentando): also a gradual slowing, often more of a relaxation; Accel. (accelerando): gradually speeding up.
rit.（渐慢）；rall.（渐慢，常更松弛地）；accel.（渐快）。
A tempo: return to the original tempo after a deviation.
A tempo：在速度变化后回到原速。
Rubato: expressive flexibility in tempo; not strictly in time.
Rubato（自由速度）：演奏时在速度上富有表现力的拉伸，不完全严守节拍。
12. Key Relationships & Modulation | 调性关系与转调
Relative minor: the minor key built on the 6th degree of a major scale; shares the same key signature. E.g. C major and A minor.
关系小调：在大调第六级音上构成的小调；共用同一调号。如C大调与a小调。
Relative major: the major key built on the 3rd degree of a natural minor scale. E.g. A minor's relative major is C major.
关系大调：在自然小调第三级音上构成的大调。如a小调的关系大调是C大调。
Closely related keys: keys whose tonic triads belong to the original key. In major: ii, iii, IV, V, vi + the relative minor of each. In minor: III, iv
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