📚 Year 7 AQA Music: Quick-Reference Formulas & Theorems | AQA 7年级音乐：公式定理速查手册
This handbook collects the essential musical formulas, rules, and theorems you will encounter in Year 7 AQA Music. Think of it as your cheat sheet for rhythm maths, scale construction, interval calculation, and dynamic markings. Use it to check your work or to memorise patterns before tests. Each section pairs an English explanation immediately with its Chinese translation so you can learn the terminology in both languages.
本手册汇集了七年级 AQA 音乐课程中所有核心的音乐公式、规则与定理。它如同你的节奏数学速查表、音阶构建指南、音程计算手册和力度标记辞典。你可以用它检查作业、考前记忆规律。每一节都采用英文讲解紧接中文翻译的配对方式，帮助你掌握双语术语。
1. Note Durations & Time Signatures | 音符时值与拍号
Each note has a fixed mathematical relationship to the whole note (semibreve). The whole note equals 4 beats in 4/4 time; a half note (minim) is half that, a quarter note (crotchet) one quarter, and so on.
每一个音符都与全音符（semibreve）保持固定的数学比例。在4/4拍中，全音符为4拍；二分音符（minim）是其一半，四分音符（crotchet）是四分之一，依此类推。
In simple time signatures, the top number tells you how many beats per bar, and the bottom number tells you which note value gets one beat (4 = crotchet, 8 = quaver).
在单拍子中，上方数字表示每小节的拍数，下方数字表示以哪种音符为一拍（4代表四分音符，8代表八分音符）。
The total duration of notes and rests in a bar must equal the time signature’s beat count. Rests follow the same hierarchical values as notes: semibreve rest, minim rest, crotchet rest, etc.
小节内所有音符和休止符的总时值必须与拍号标注的拍数相等。休止符的等级与音符完全对应：全休止符、二分休止符、四分休止符等。
2. Dotted Notes, Ties & Tuplets | 附点、连线与连音符
A dot after a note adds half the value of that note. Formula: Dotted value = note value × 1.5. A double dot adds a further quarter of the original value.
音符后的附点增加该音符时值的一半。公式：附点音符时值 = 原音符时值 × 1.5。双附点则再增加原时值的四分之一。
A tie joins two notes of the same pitch, adding their durations together without re-striking the note. The tied value is simply the sum of the tied notes.
连线连接两个相同音高的音符，将其时值相加而不需再次击弦或发音。连线后的总时值就是被连音符时值之和。
Triplets divide a beat into three equal parts instead of two. The formula is: Triplet duration = 2 notes of the same kind ÷ 3. For example, a quaver triplet fits into one crotchet beat.
三连音将一拍平均分成三等份，而不是通常的两等份。公式：三连音组的总时值 = 两个同等音符的时值 ÷ 3。例如，八分音符三连音恰好占一个四分音符的拍子。
3. Major Scale Construction | 大调音阶公式
All major scales follow the pattern of tones (T) and semitones (S): T – T – S – T – T – T – S. In terms of whole steps (W) and half steps (H): W W H W W W H.
所有大调音阶都遵循全音与半音的固定模式：全–全–半–全–全–全–半。以全音（T）和半音（S）表示为 T T S T T T S，或以 W W H W W W H 表示。
To build a major scale, start on the tonic and move up according to the pattern. For C major, no sharps or flats are needed; C D E F G A B C.
构建大调音阶时，从主音开始，按照上述模式向上排列。C大调不需任何升降号：C D E F G A B C。
The key signature is determined by the number of sharps or flats required to maintain the pattern. Order of sharps: F C G D A E B. Order of flats: B E A D G C F.
调号由满足该模式所需升降号的数量决定。升号调的出现顺序为 F, C, G, D, A, E, B。降号调的顺序为 B, E, A, D, G, C, F。
4. Minor Scales & Relative Keys | 小调音阶与关系大小调
Every major key has a relative minor key located a minor third (3 semitones) below. For example, A minor is the relative minor of C major. They share the same key signature.
每个大调都有一个关系小调，位于其主音下方小三度（3个半音）处。例如，A小调是C大调的关系小调，它们共享相同的调号。
The natural minor scale formula: T – S – T – T – S – T – T (W H W W H W W). Starting on A, A B C D E F G A follows this pattern automatically with no sharps or flats.
自然小调公式：全–半–全–全–半–全–全（W H W W H W W）。从A音开始，A B C D E F G A 无需升降号就完全符合此模式。
The harmonic minor scale raises the 7th degree by a semitone, creating a step of a tone and a half between the 6th and 7th. Melodic minor raises the 6th and 7th ascending, and reverts to natural minor descending.
和声小调将第七级音升高半音，使第Ⅵ-Ⅶ音之间形成一个增二度。旋律小调在上行时升高第六和第七级音，下行时还原为自然小调。
5. Intervals: Naming & Counting | 音程：名称与计算
An interval measures the distance in pitch between two notes. Count the letter names from the lower note to the higher, inclusive, to get the number. For C up to G, C(1) D(2) E(3) F(4) G(5) = a 5th.
音程衡量两个音符之间的音高距离。从低音到高音包含首尾音名在内的数目得出度数。从C到G，C(1) D(2) E(3) F(4) G(5) 为五度。
The quality (perfect, major, minor, augmented, diminished) is determined by counting semitones. In a major scale, unisons, 4ths, 5ths and octaves are perfect; 2nds, 3rds, 6ths, and 7ths are major.
音程的性质（纯、大、小、增、减）由半音数确定。在大调音阶中，一度、四度、五度、八度为纯音程；二度、三度、六度、七度为大音程。
Semitone shortcuts: Minor 2nd = 1 semitone; Major 2nd = 2 semitones; Minor 3rd = 3; Major 3rd = 4; Perfect 4th = 5; Augmented 4th/Diminished 5th = 6; Perfect 5th = 7; Minor 6th = 8; Major 6th = 9; Minor 7th = 10; Major 7th = 11; Octave = 12.
半音速查表：小二度=1个半音；大二度=2；小三度=3；大三度=4；纯四度=5；增四度/减五度=6；纯五度=7；小六度=8；大六度=9；小七度=10；大七度=11；纯八度=12。
6. Triad Construction & Chord Types | 三和弦构建与和弦类型
A triad is a three-note chord built by stacking two thirds on a root. The formula for a major triad: root + major 3rd (4 semitones) + perfect 5th (7 semitones from root).
三和弦是由三个音按三度叠置而成的和弦。大三和弦公式：根音 + 大三度（4个半音）+ 纯五度（距根音7个半音）。
Minor triad formula: root + minor 3rd (3 semitones) + perfect 5th. Diminished triad: root + minor 3rd + diminished 5th (6 semitones). Augmented triad: root + major 3rd + augmented 5th (8 semitones).
小三和弦：根音 + 小三度（3个半音）+ 纯五度。减三和弦：根音 + 小三度 + 减五度（6个半音）。增三和弦：根音 + 大三度 + 增五度（8个半音）。
In Roman numeral analysis, triads built on each scale degree are: I (tonic, major), ii (supertonic, minor), iii (mediant, minor), IV (subdominant, major), V (dominant, major), vi (submediant, minor), vii° (leading tone, diminished).
用罗马数字表示各音级上的和弦：I (主和弦，大三)，ii (上主和弦，小三)，iii (中音和弦，小三)，IV (下属和弦，大三)，V (属和弦，大三)，vi (下中音和弦，小三)，vii° (导音和弦，减三)。
7. The Circle of 5ths & Key Relationships | 五度圈与调性关系
Moving clockwise around the circle of 5ths adds one sharp each step (C – G – D – A – E – B – F♯ – C♯). Moving anticlockwise adds one flat (C – F – B♭ – E♭ – A♭ – D♭ – G♭ – C♭).
顺时针沿五度圈每进一步增加一个升号 (C – G – D – A – E – B – F♯ – C♯)。逆时针每步增加一个降号 (C – F – B♭ – E♭ – A♭ – D♭ – G♭ – C♭)。
Closely related keys are those adjacent on the circle: the dominant, the subdominant, and their relative minors. They share all but one note of the scale.
近关系调是指在五度圈上相邻的调：属调、下属调及其关系小调。它们与原调只有一个音不同。
The circle also helps memorise the order of sharps (Father Charles Goes Down And Ends Battle) and flats (Battle Ends And Down Goes Charles’ Father). Reverse the mnemonic for flats.
五度圈还能帮助记忆升号出现的顺序：F, C, G, D, A, E, B（Father Charles Goes Down And Ends Battle），降号顺序恰好相反：B, E, A, D, G, C, F。
8. Rhythm Patterns & Syncopation | 节奏型与切分音
Syncopation occurs when a note is accented on a normally weak beat or between beats. Formula to spot it: the note starts off the strong beat and is tied or articulated to create an off-beat emphasis.
当音符被强调在通常为弱拍的位置，或在拍点之间时，就形成切分。识别公式：音符从强拍之外开始，并通过连线或重音造成弱位强调。
Common syncopated patterns: eighth – quarter – eighth tied over the barline, or a rest on the downbeat followed by notes on the upbeat. These patterns shift the listener’s expected pulse.
常见切分节奏型：八分音符——跨小节线的四分连线，或强拍休止、弱拍起奏。这些型态改变了听众心中预期的重音位置。
Tempo markings give formulas for beat speed: Largo (slow, 40–60 bpm), Adagio (slow, 66–76 bpm), Andante (walking pace, 76–108 bpm), Moderato (moderate, 108–120 bpm), Allegro (fast, 120–168 bpm), Presto (very fast, 168–200 bpm).
速度术语提供了节拍速率的公式：Largo (广板，40-60 bpm)，Adagio (柔板，66-76)，Andante (行板，76-108)，Moderato (中板，108-120)，Allegro (快板，120-168)，Presto (急板，168-200)。
9. Dynamics, Articulation & Expression | 力度、奏法与表情
Dynamics describe volume and use standard Italian abbreviations: pp (pianissimo, very soft), p (piano, soft), mp (mezzo-piano, moderately soft), mf (mezzo-forte, moderately loud), f (forte, loud), ff (fortissimo, very loud). Crescendo (cresc.) means gradually getting louder; diminuendo (dim.) getting softer.
力度描述音量，使用标准意大利语缩写：pp (很弱), p (弱), mp (中弱), mf (中强), f (强), ff (很强)。Crescendo (渐强) 表示音量逐渐增大；diminuendo (渐弱) 音量逐渐减小。
Articulation affects how notes are played. Staccato: detached, short (dot above/below note). Legato: smoothly, connected (slur). Accent: strong attack (>). Tenuto: held for full value, slightly stressed (line).
奏法影响音符的演奏方式。Staccato (断奏)：短而分离，音符上/下方有圆点。Legato (连奏)：平滑连接，用连线表示。Accent (重音)：强音头 (>)。Tenuto (保持音)：奏满时值并稍加压力 (短横线)。
Repeat signs and navigation: D.C. al Fine means go back to the beginning and play until Fine (the end). D.S. al Coda means go back to the sign (𝄋) and then take the Coda.
反复记号与导航：D.C. al Fine 表示从头反复，演奏至 Fine (终止) 为止。D.S. al Coda 表示从记号 (𝄋) 处反复，然后跳至 Coda (尾声)。
10. Transposition & Clefs | 移调与谱号
Transposition is moving a melody to a new pitch level while keeping the same interval pattern. Formula: determine the interval of transposition, then add or subtract the same number of semitones/staff steps to every note. Adjust accidentals to preserve major/minor qualities.
移调是在保持音程关系不变的条件下，将旋律移到新的音高位置。公式：确定移调音程，然后将每个音符升高或降低相同的半音/谱表级数，并调整临时升降记号以保持大小调性质。
The treble clef (G clef) curls around the second line, naming it G. The bass clef (F clef) has two dots around the fourth line, naming that F. The alto clef fixes Middle C on the third line.
高音谱号 (G谱号) 环绕第二线，确定其为G音。低音谱号 (F谱号) 的两个点跨越第四线，确定其为F音。中音谱号将中央C定于第三线。
Instrument transpositions: Some instruments sound at a different pitch than written. B♭ instruments (clarinet, trumpet) sound a major 2nd lower than written; F instruments (horn) sound a perfect 5th lower. This is a ‘transposing formula’ to remember for ensemble work.
乐器移调：部分乐器的实际音高与记谱不同。B♭调乐器 (单簧管、小号) 实际发音比记谱低大二度；F调乐器 (圆号) 实际低纯五度。这是合奏中需要牢记的’移调公式’。
11. Musical Texture & Form | 音乐织体与曲式
Texture describes how layers of sound interact. Monophonic: a single unaccompanied melody (one voice). Homophonic: melody with chordal accompaniment (melody + block chords). Polyphonic: two or more independent melodies interweaving (counterpoint).
织体描述音响层次的相互作用。单声织体 (Monophonic)：无伴奏的单旋律。主调织体 (Homophonic)：旋律加柱式和弦伴奏。复调织体 (Polyphonic)：两条或以上独立旋律相互交错 (对位)。
Common forms use letter names: Binary AB, Ternary ABA, Rondo ABACA. Verse-chorus form alternates verses with a repeated chorus. 12-bar blues follows a fixed chord pattern: I – I – I – I – IV – IV – I – I – V – IV – I – I.
常见曲式用字母命名：二段体 AB，三段体 ABA，回旋曲 ABACA。主歌–副歌形式交替出现。12小节蓝调遵循固定的和弦套路：I – I – I – I – IV – IV – I – I – V – IV – I – I。
Phrases are musical ‘sentences’. A typical 8-bar phrase can be divided into two 4-bar phrases, often following a question (antecedent) and answer (consequent) structure ending on dominant then tonic.
乐句是音乐的“句子”。典型的8小节乐句可分为两个4小节分句，通常呈现前句 (提问) 和后句 (回答) 的结构，分别结束于属音和主音。
12. World Music & Instrument Families | 世界音乐与乐器家族
The orchestra is divided into four families: strings (violin, viola, cello, double bass), woodwind (flute, clarinet, oboe, bassoon), brass (trumpet, French horn, trombone, tuba), percussion (timpani, snare drum, cymbals). Each has a characteristic playing technique and formula for range.
管弦乐队分为四个家族：弦乐 (小提琴、中提琴、大提琴、低音提琴)、木管 (长笛、单簧管、双簧管、大管)、铜管 (小号、圆号、长号、大号)、打击乐 (定音鼓、小鼓、钹)。每个家族都有典型的演奏技法和音域规律。
Pentatonic scale formula: omit the 4th and 7th degrees of a major scale to get the major pentatonic (C D E G A). For minor pentatonic, take the 1st, 3rd, 4th, 5th, 7th of the natural minor scale.
五声音阶公式：去掉大调音阶的IV级和VII级音即得大调五声音阶 (C D E G A)。小调五声音阶则取自然小调的第I, III, IV, V, VII级音。
African drumming often uses polyrhythms – the simultaneous sounding of two or more independent rhythms. The clave pattern in Latin music is a rhythmic formula of 3+2 or 2+3 hits in a bar.
非洲鼓乐常运用复节奏 – 同时演奏两个或以上的独立节奏。拉丁音乐中的克拉维节奏型是一个节拍公式，在一小节中敲击3+2或2+3下。
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