📚 Year 9 AQA Music: Formula & Theorem Quick-Reference Handbook | Year 9 AQA 音乐：公式定理速查手册
This compact guide distils the essential “formulae” and “theorems” you will encounter in Year 9 AQA Music. Much like mathematical rules, these musical patterns, scale constructions, chord recipes, and structural conventions provide a reliable toolkit for listening, composing, and performing. Use this handbook to revise key concepts and to decode the inner logic of the music you study.
这本紧凑的速查手册提炼了 Year 9 AQA 音乐课程中必学的核心“公式”与“定理”。正如数学法则一样，这些音阶构造、和弦配方、结构惯例和听觉规则为你提供了聆听、作曲和表演的可靠工具箱。使用这本手册来复习关键概念，并解读所学音乐的内在逻辑。
1. The Formula of Major Scales | 大调音阶公式
The major scale follows the interval pattern: Tone, Tone, Semitone, Tone, Tone, Tone, Semitone — abbreviated T-T-S-T-T-T-S, where T = whole tone and S = semitone.
大调音阶遵循固定的音程模式：全音、全音、半音、全音、全音、全音、半音——简记为全-全-半-全-全-全-半，其中全代表全音，半代表半音。
Applying the formula from C yields the natural notes C D E F G A B C with no sharps or flats.
从C音开始套用公式，得到自然音 C D E F G A B C，不含任何升降号。
For sharp keys: starting on G gives G A B C D E F♯ G. The mnemonic for the order of sharps is Father Charles Goes Down And Ends Battle (F♯, C♯, G♯, D♯, A♯, E♯, B♯).
升号调：从G开始得到 G A B C D E F♯ G。记忆升号顺序的口诀是 Father Charles Goes Down And Ends Battle，即 F♯, C♯, G♯, D♯, A♯, E♯, B♯。
For flat keys: starting on F gives F G A B♭ C D E F. The order of flats is Battle Ends And Down Goes Charles’ Father (B♭, E♭, A♭, D♭, G♭, C♭, F♭).
降号调：从F开始得到 F G A B♭ C D E F。降号顺序口诀是 Battle Ends And Down Goes Charles’ Father，即 B♭, E♭, A♭, D♭, G♭, C♭, F♭。
2. The Formula of Minor Scales | 小调音阶公式
The natural minor scale is formed from the pattern T-S-T-T-S-T-T. Starting on A, this gives A B C D E F G A.
自然小调音阶由音程模式 全-半-全-全-半-全-全 构成。从A开始，得到 A B C D E F G A。
The harmonic minor scale raises the 7th degree by a semitone (e.g., A harmonic minor: A B C D E F G♯ A), creating an augmented second between the 6th and 7th degrees.
和声小调将第VII级音升高半音（如 A 和声小调：A B C D E F G♯ A），在第VI与第VII级之间产生一个增二度。
The melodic minor ascends with a raised 6th and 7th degree and descends as the natural minor. Ascending: A B C D E F♯ G♯ A; descending: A G F E D C B A.
旋律小调上行时升高第VI和第VII级音，下行时还原为自然小调。上行为 A B C D E F♯ G♯ A；下行为 A G F E D C B A。
3. Interval Theorems | 音程定理
An interval is the gap between two pitches, measured in semitones. Knowing these “theorems” allows you to identify and construct intervals instantly.
音程是两个乐音之间的差距，以半音为单位。掌握这些“定理”能让你瞬间辨认和构建音程。
Perfect Unison: 0 semitones. Minor 2nd: 1 semitone. Major 2nd: 2 semitones. Minor 3rd: 3 semitones. Major 3rd: 4 semitones. Perfect 4th: 5 semitones. Tritone (Augmented 4th / Diminished 5th): 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.
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。三全音（增四度 / 减五度）：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。
To invert an interval: subtract its number from 9. A 3rd inverts to a 6th, a 2nd to a 7th. Major becomes minor, perfect remains perfect.
音程转位：用9减去原音程度数。三度转位成六度，二度转位成七度。大音程转成小音程，纯音程保持纯音程。
4. Chord Construction Theorems | 和弦构成定理
A triad is built by stacking two thirds on a root. The formula for a major triad: root + 4 semitones (major 3rd) + 3 semitones (minor 3rd) from the root, giving root – 3rd – 5th.
三和弦由根音上方叠加两个三度构成。大三和弦公式：根音 + 4个半音（大三度）+ 3个半音（小三度），得到根音、三音、五音。
A 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）。
An augmented triad: root + 4 semitones + 4 semitones (major 3rd + major 3rd).
增三和弦：根音 + 4个半音 + 4个半音（大三度+大三度）。
A diminished triad: root + 3 semitones + 3 semitones (minor 3rd + minor 3rd).
减三和弦：根音 + 3个半音 + 3个半音（小三度+小三度）。
The dominant 7th formula: major triad + minor 7th above the root (10 semitones). E.g., C⁷ = C E G B♭.
属七和弦公式：大三和弦 + 根音上方小七度（10个半音）。例如 C⁷ = C E G B♭。
In any major key, the chords built on the scale degrees follow the pattern: I – major, ii – minor, iii – minor, IV – major, V – major, vi – minor, vii° – diminished.
在任何大调中，各级音上构建的三和弦遵循模式：I级 大三和弦，ii级 小三和弦，iii级 小三和弦，IV级 大三和弦，V级 大三和弦，vi级 小三和弦，vii°级 减三和弦。
5. Key Signatures & the Circle of Fifths | 调号与五度圈公式
The circle of fifths is a visual formula showing the relationship among keys. Moving clockwise by perfect 5ths adds one sharp; moving anticlockwise by perfect 5ths adds one flat.
五度圈是展示调性关系的视觉公式。顺时针按纯五度移动，每步增加一个升号；逆时针按纯五度移动，每步增加一个降号。
C major (0 sharps/flats) → G major (1 sharp) → D major (2 sharps) → A major (3 sharps) → E major (4 sharps) → B major (5 sharps) → F♯ major (6 sharps) → C♯ major (7 sharps).
C大调（0升0降）→ G大调（1升）→ D大调（2升）→ A大调（3升）→ E大调（4升）→ B大调（5升）→ F♯大调（6升）→ C♯大调（7升）。
Anticlockwise: C major → F major (1 flat) → B♭ major (2 flats) → E♭ major (3 flats) → A♭ major (4 flats) → D♭ major (5 flats) → G♭ major (6 flats) → C♭ major (7 flats).
逆时针：C大调 → F大调（1降）→ B♭大调（2降）→ E♭大调（3降）→ A♭大调（4降）→ D♭大调（5降）→ G♭大调（6降）→ C♭大调（7降）。
The relative minor of any major key is found a minor 3rd below the tonic. E.g., C major’s relative minor is A minor.
任何大调的关系小调位于主音下方小三度。例如，C大调的关系小调是a小调。
6. Time Signatures & Rhythm Divisions | 拍号与节奏划分公式
A time signature’s top number indicates beats per bar, the bottom number indicates the beat unit. In simple time, each beat divides into two equal parts.
拍号的上方数字表示每小节拍数，下方数字表示以几分音符为一拍。在单拍子中，每一拍可以均分为两个部分。
Simple duple: 2/4 (2 crotchet beats). Simple triple: 3/4 (3 crotchet beats). Simple quadruple: 4/4 (4 crotchet beats).
单二拍子：2/4（以四分音符为一拍，每小节2拍）。单三拍子：3/4。单四拍子：4/4。
Compound time signatures have a dotted note as the beat unit, each beat dividing into three. Compound duple: 6/8 (2 dotted crotchet beats). Compound triple: 9/8. Compound quadruple: 12/8.
复拍子以附点音符为一拍，每拍均分为三份。复二拍子：6/8（以附点四分音符为一拍，每小节2拍）。复三拍子：9/8。复四拍子：12/8。
The rhythmic duration tree: semibreve (4 beats) → minim (2) → crotchet (1) → quaver (½) → semiquaver (¼).
时值关系：全音符（4拍）→ 二分音符（2拍）→ 四分音符（1拍）→ 八分音符（½拍）→ 十六分音符（¼拍）。
7. Dynamics, Tempo & Articulation Rules | 力度、速度与演奏法规则
Dynamics denote volume and follow a graduated scale: pp (pianissimo, very soft), p (piano, soft), mp (mezzo-piano, moderately soft), mf (mezzo-forte, moderately loud), f (forte, loud), ff (fortissimo, very loud).
力度标记表示音量，按等级排列：pp（pianissimo，极弱）、p（piano，弱）、mp（mezzo-piano，中弱）、mf（mezzo-forte，中强）、f（forte，强）、ff（fortissimo，极强）。
Crescendo (cresc.) means gradually getting louder; diminuendo (dim.) or decrescendo means gradually getting softer.
渐强（cresc.）表示音量逐步增大；渐弱（dim. 或 decresc.）表示音量逐步减小。
Common tempo instructions: largo (broadly, slow), adagio (slow and stately), andante (walking pace), moderato (moderately), allegro (fast, lively), presto (very fast).
常见速度标记：largo（广板，缓慢）、adagio（慢板，从容）、andante（行板，步行速度）、moderato（中板）、allegro（快板，活泼）、presto（急板，极快）。
Articulation marks include staccato (detached, marked with a dot) and legato (smooth, indicated by a slur). Accents (> or ^) emphasise a single note.
演奏法记号包括：staccato（断奏，用圆点标记）、legato（连奏，用连线标记）。重音记号（> 或 ^）强调单个音符。
8. Musical Forms & Structure Patterns | 曲式与结构模式
Binary form (AB) features two contrasting sections, often each repeated. It is common in Baroque dance suites.
二段体（AB）包含两个对比段落，通常各自反复。常见于巴洛克舞蹈组曲。
Ternary form (ABA) presents a main section, a contrasting middle section, and a return to the main section. Menuet and trio is a classic ternary structure.
三段体（ABA）呈现主要段落、对比中部和主要段落的再现。小步舞曲与三声中部是典型的三段体结构。
Rondo form alternates a recurring theme with contrasting episodes: ABACA or ABACABA.
回旋曲式以固定主题与不同插部交替出现：ABACA 或 ABACABA。
Theme and variations (A, A1, A2, A3…) takes a melody and alters it through techniques such as changes in rhythm, tempo, harmony, register, or timbre.
主题与变奏（A, A1, A2, A3…）选取一条旋律并通过节奏、速度、和声、音区或音色变化等手法进行加工。
Strophic form repeats the same music for each verse, typical in folk songs. Through-composed music has no large-scale repetition.
分节歌形式为每段歌词配以相同旋律，常见于民歌。通谱体音乐则避免大规模重复。
9. Melodic Devices & Ornaments | 旋律手法与装饰音公式
A sequence repeats a melodic pattern at a higher or lower pitch. It can be tonal (diatonic) or real (exact intervals).
模进是将一个旋律型在不同音高上重复。可以是调内模进（自然音程）或严格模进（精确音程）。
Imitation occurs when a melodic idea is restated in another part, often staggered. It is a key feature of canon and fugue.
模仿指一个旋律乐思在另一声部再次陈述，通常错开进入。这是卡农和赋格的核心特征。
Inversion turns a melody upside down: ascending intervals become descending ones and vice versa.
倒影是将旋律垂直翻转：上行音程变为下行，反之亦然。
Ornaments are decorative formulas applied to a note. Trill: rapid alternation with the note above, indicated by ‘tr’. Turn: a four-note figure moving around the main note. Mordent: a quick single alternation with the adjacent note (upper or lower). Appoggiatura: a leaning note that takes half the value of the main note. Acciaccatura: a crushed, very short grace note.
装饰音是附加在音符上的装饰公式。颤音（trill）：与上方音快速交替，标记为tr。回音（turn）：围绕主要音的四音音型。波音（mordent）：与邻音的一次快速交替（上波音或下波音）。倚音（appoggiatura）：占主音符时值一半的倚音。碎音（acciaccatura）：极短的装饰音，几乎不占时值。
10. Texture & Harmony Conventions | 织体与和声惯例
Monophonic texture consists of a single unaccompanied melodic line. It can be performed by one or multiple voices/instruments in unison or octaves.
单声织体由一条无伴奏的旋律线条构成。它可以由一人或多人以齐奏或八度形式演奏。
Homophonic texture features a prominent melody supported by chordal accompaniment. Most pop songs and hymn tunes are homophonic.
主调织体以一个突出的旋律为主，配以和弦伴奏。大部分流行歌曲和赞美诗都属于主调织体。
Polyphonic (contrapuntal) texture weaves two or more independent melodic lines together simultaneously, as in a fugue.
复调织体将两条或多条独立的旋律线条同时交织在一起，如赋格中所示。
Heterophonic texture occurs when two or more performers play the same melody but with slight individual embellishments, found in folk traditions.
支声织体指两个或多个表演者演奏同一旋律，但各自加入细微的即兴装饰，常见于民间音乐传统。
Harmonic rhythm is the rate at which chords change. A pedal note (often the tonic or dominant) held continuously while harmonies change above it adds tension.
和声节奏指和弦变换的速度。持续音（通常是主音或属音）在上方和声变化时始终不变，可以增加张力。
11. World Music Scale Formulae | 世界音乐音阶公式
The major pentatonic scale is derived from the major scale by omitting the 4th and 7th degrees. For C major: C D E G A (degrees 1, 2, 3, 5, 6).
大调五声音阶由大调音阶省去第四、第七级音而成。C大调五声音阶：C
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