📚 Year 10 AQA Music: Formula and Theorem Quick Reference Guide | GCSE 音乐公式定理速查手册
Music is a language built on patterns, rules, and recurring structures. Just like mathematics, it has its own set of formulas and theorems that govern rhythm, harmony, melody, and form. This quick reference guide collects essential 'formulas' for the Year 10 AQA GCSE Music specification, helping you to recognise, recall, and apply these musical building blocks in listening, performing, and composing tasks.
音乐是一门建立在模式、规则和反复出现的结构之上的语言。就像数学一样，它也有自己的一套公式和定理，支配着节奏、和声、旋律和形式。这本速查手册收集了 Year 10 AQA GCSE 音乐课程中的核心“公式”，帮助你在听觉训练、演奏和作曲活动中识别、回忆并应用这些音乐构成要素。
1. Rhythm Duration 'Formulas' | 节奏时值公式
Note values follow a simple doubling or halving formula. Each note can be divided into two of the next smaller value, or combined to form longer durations.
音符时值遵循简单的加倍或减半公式。每个音符可以分成两个下一个较小时值的音符，也可以合并形成更长的时值。
| Note Name | Relative Value (in simple time) | Formula |
| Semibreve (whole note) | 4 crotchet beats | 1 semibreve = 2 minims = 4 crotchets |
| Minim (half note) | 2 crotchet beats | 1 minim = 2 crotchets = 4 quavers |
| Crotchet (quarter note) | 1 beat | 1 crotchet = 2 quavers = 4 semiquavers |
| Quaver (eighth note) | ½ beat | 1 quaver = 2 semiquavers |
| Semiquaver (sixteenth note) | ¼ beat | 1 semiquaver = 2 demisemiquavers |
Dotted rhythm formula: Dotted crotchet = crotchet + quaver (1½ beats). Dotted minim = minim + crotchet (3 beats).
附点节奏公式：附点增加原音符时值的一半。附点四分音符 = 四分音符 + 八分音符（1½ 拍）。附点二分音符 = 二分音符 + 四分音符（3 拍）。
Tuplet formula: s of the same value. Quaver triplet bracket = 3 quavers in the time of 2 quavers (1 beat).
连音公式：三连音通常在两个相同音符的时间内演奏三个音符。八分三连音 = 在一个四分音符的拍内演奏三个八分音符。
2. Time Signature 'Theorem' | 拍号定理
, the lower number = type of note representing one beat (4 = crotchet, 8 = quaver, 2 = minim).
拍号给出每小节拍数和拍子单位。它像是一个应用于全音符的分数：上方数字 = 每小节拍数，下方数字 = 代表一拍的音符类型（4 = 四分音符，8 = 八分音符，2 = 二分音符）。
| Time Signature | Beats per bar / Beat unit | Common usage |
| 4/4 (C) | 4 crotchet beats | Simple quadruple, most common |
| 3/4 | 3 crotchet beats | Simple triple, waltz |
| 2/4 | 2 crotchet beats | Simple duple, marches |
| 6/8 | 6 quaver beats, grouped in 2 dotted-crotchet pulses | Compound duple |
| 9/8 | 9 quaver beats, 3 dotted-crotchet pulses | Compound triple |
| 12/8 | 12 quaver beats, 4 dotted-crotchet pulses | Compound quadruple |
Compound time formula: d : The dotted note (beat = dotted crotchet in 6/8) divides into three quavers instead of two, giving a 'lilting' feel.
复拍子公式：附点音符（在 6/8 中拍子 = 附点四分音符）分成三个八分音符而不是两个，产生“摇曳”的感觉。
3. Scale Construction Formulas | 音阶构成公式
Scales are built from a sequence of tones (T) and semitones (S). The pattern determines the scale quality. A semitone is the smallest interval on a keyboard; a tone equals two semitones.
音阶由一系列全音 (T) 和半音 (S) 构成。排列模式决定了音阶的性质。半音是键盘上最小的音程；一个全音等于两个半音。
Major scale formula: T T S T T T S (e.g., C-D-E-F-G-A-B-C).
大调音阶公式：全 全 半 全 全 全 半（例如 C-D-E-F-G-A-B-C）。
Natural minor scale formula: T S T T S T T (e.g., A-B-C-D-E-F-G-A).
自然小调音阶公式：全 半 全 全 半 全 全（例如 A-B-C-D-E-F-G-A）。
Harmonic minor scale formula: T S A2 S (where A2 = augmented 2nd, equivalent to three semitones). Example: A-B-C-D-E-F-G#-A.
和声小调音阶公式：全 半 全 全 半 增二度 半（增二度 = 三个半音）。例如：A-B-C-D-E-F-G#-A。
Melodic minor scale formula (ascending): T S T T T T S (raise 6th and 7th). Descending is same as natural minor. Example: A-B-C-D-E-F#-G#-A up, A-G-F-E-D-C-B-A down.
旋律小调音阶公式（上行）：全 半 全 全 全 全 半（升高第 6、7 级）。下行与自然小调相同。例如：上行 A-B-C-D-E-F#-G#-A，下行 A-G-F-E-D-C-B-A。
4. Key Signatures and the Circle of Fifths | 调号与五度圈
Key signatures follow a strict order of sharps and flats, derived from the circle of fifths. Sharps are added in 5ths ascending; flats in 5ths descending.
调号遵循严格的升、降号顺序，源自五度圈。升号按上行五度添加；降号按下行五度添加。
Order of sharps: F# C# G# D# A# E# B# (Father Charles Goes Down And Ends Battle).
升号顺序：F# C# G# D# A# E# B#（可直接记忆：Fa Do Sol Re La Mi Si）。
Order of flats: Bb Eb Ab Db Gb Cb Fb (reverse of sharps).
降号顺序：Bb Eb Ab Db Gb Cb Fb（升号顺序的反向）。
Major key formula from sharps: ding note (7th degree). Go up a semitone to find the tonic. E.g., 2 sharps: last sharp = C# → tonic D major.
由升号找大调公式：最后一个升号是导音（第 7 级）。向上半音找到主音。例如 2 个升号：最后升号是 C# → 主音 D 大调。
Major key formula from flats: the tonic. E.g., 3 flats Bb-Eb-Ab → penultimate flat = Eb → Eb major. One flat = F major.
由降号找大调公式：对于两个及以上降号，倒数第二个降号就是主音。例如 3 个降号 Bb-Eb-Ab → 倒数第二降号 = Eb → Eb 大调。一个降号 = F 大调。
Relative minor formula: f the major scale, or a minor 3rd below the major tonic. Same key signature. E.g., C major's relative minor = A minor.
关系小调公式：关系小调的主音是大调音阶的第 6 级，或大调主音下方小三度。调号相同。例如 C 大调的关系小调 = A 小调。
5. Interval Calculation Formula | 音程计算公式
An interval is the distance between two pitches, counted in letter names (number) and qualified by semitone count (quality). Combine the staff position count with the semitone count to label it.
音程是两个音高之间的距离，按字母名（度数）和半音数量（性质）计算。结合五线谱位置计数与半音数量进行标记。
| Interval name | Number of semitones | Example from C |
| Perfect unison | 0 | C - C |
| Minor 2nd | 1 | C - Db |
| Major 2nd | 2 | C - D |
| Minor 3rd | 3 | C - Eb |
| Major 3rd | 4 | C - E |
| Perfect 4th | 5 | C - F |
| Augmented 4th / Diminished 5th (tritone) | 6 | C - F# / C - Gb |
| Perfect 5th | 7 | C - G |
| Minor 6th | 8 | C - Ab |
| Major 6th | 9 | C - A |
| Minor 7th | 10 | C - Bb |
| Major 7th | 11 | C - B |
| Perfect octave | 12 | C - C (higher) |
Quick formula for intervals in a major scale: All intervals from the tonic up to the same degree are either major or perfect (2nd, 3rd, 6th, 7th are major; 4th, 5th, octave are perfect). Lowering a major interval by a semitone makes it minor; lowering a perfect interval makes it diminished; raising makes it augmented.
大调音阶中音程的快速公式：主音到上方音阶内所有音程都是大音程或纯音程（二度、三度、六度、七度为大音程；四度、五度、八度为纯音程）。将大音程降低半音变成小音程；纯音程降低半音变成减音程；升高半音则变成增音程。
6. Chord Construction Formulas | 和弦构成公式
Triads and seventh chords are stacked thirds. The quality of the chord depends on the combination of major (4 semitones) and minor (3 semitones) thirds. The formula uses semitone counts from the root.
三和弦与七和弦由三度音程叠置而成。和弦性质取决于大三度（4 个半音）和小三度（3 个半音）的组合。公式使用从根音算起的半音数量。
Major triad: Root + 4 semitones + 3 semitones (M3 + m3)
大三和弦：根音 + 4 半音 + 3 半音（大三度 + 小三度）
Minor triad: Root + 3 semitones + 4 semitones (m3 + M3)
小三和弦：根音 + 3 半音 + 4 半音（小三度 + 大三度）
Diminished triad: Root + 3 semitones + 3 semitones (m3 + m3)
减三和弦：根音 + 3 半音 + 3 半音（小三度 + 小三度）
Augmented triad: Root + 4 semitones + 4 semitones (M3 + M3)
增三和弦：根音 + 4 半音 + 4 半音（大三度 + 大三度）
Seventh chord formulas (add a 7th from the root):
- Major 7th: Major triad + major 7th (11 semitones above root) → C-E-G-B
- Dominant 7th: Major triad + minor 7th (10 semitones) → C-E-G-Bb
- Minor 7th: Minor triad + minor 7th (10 semitones) → C-Eb-G-Bb
- Half-diminished 7th: Diminished triad + minor 7th (10 semitones) → C-Eb-Gb-Bb
- Diminished 7th: Diminished triad + diminished 7th (9 semitones) → C-Eb-Gb-Bbb (A)
七和弦公式（加上从根音开始的七音）：
- 大七和弦：大三和弦 + 大七度（根音上方 11 半音）→ C-E-G-B
- 属七和弦：大三和弦 + 小七度（10 半音）→ C-E-G-Bb
- 小七和弦：小三和弦 + 小七度（10 半音）→ C-Eb-G-Bb
- 半减七和弦：减三和弦 + 小七度（10 半音）→ C-Eb-Gb-Bb
- 减七和弦：减三和弦 + 减七度（9 半音）→ C-Eb-Gb-Bbb（等音 A）
7. Cadence Formulas | 终止式公式
Cadences are two-chord progressions at the end of a phrase, creating a sense of pause or conclusion. The formula is defined by the chords used, usually in root position.
终止式是乐句结尾处的两个和弦进行，产生停顿或终止感。公式由所用的和弦定义，通常使用原位和弦。
| Cadence name | Chord progression (in major key) | Effect / Formula |
| Perfect (authentic) | V → I (e.g., G → C) | Strong, final, like a full stop. Often both chords in root position with tonic in soprano for finality. |
| Plagal | IV → I (e.g., F → C) | ‘Amen’ cadence, gentle finish. |
| Imperfect | I → V, ii → V, IV → V (etc. → V) | Ends on V; sounds unfinished, like a comma. |
| Interrupted (deceptive) | V → vi (e.g., G → Am) | Surprise; the expected I chord is replaced by vi, the submediant. Sounds like a question or twist. |
完美终止：V → I，强烈终止感，如句号；常以原位和弦及主旋律落在主音上实现完全终止。
变格终止：IV → I，“阿门”终止，柔和收束。
不完全终止：以 V 结束，有未完成感，如逗号。
中断终止：V → vi，意外终止，预期 I 被 vi 替代，像是问题或转折。
8. Tempo Marking 'Index' | 速度标记索引公式
Tempo markings indicate the speed of the music. While not strict formulas, they commonly fall into BPM ranges. Metronome markings give an exact beat-per-minute formula.
速度标记表示音乐的速度。虽无严格公式，但它们通常落在一定的 BPM 范围内。节拍器标记给出精确的每分钟拍数。
| Marking | Meaning | Typical BPM range |
| Largo | Broad, very slow | 40 - 60 |
| Adagio | Slow, stately | 66 - 76 |
| Andante | Walking pace | 76 - 108 |
| Moderato | Moderate | 108 - 120 |
| Allegro | Fast, lively | 120 - 156 |
| Presto | Very fast | 168 - 208 |
Modifier formulas: Adding '-issimo' intensifies (e.g., Prestissimo ≈ 200+ BPM). Adding '-etto' or '-ino' es it a little less (e.g., Allegretto ≈ slightly slower than Allegro, around 112-120 BPM). 'Molto' means very (Molto allegro = very fast).
修饰词公式：添加“-issimo”加强程度（如 Prestissimo 约 200+ BPM）。添加“-etto”或“-ino”略微减弱（如 Allegretto 比 Allegro 稍慢，约 112-120 BPM）。“Molto”意为非常（Molto allegro = 非常快）。
9. Dynamics and Articulation Shorthand | 力法与奏法速记公式
Dynamics follow a graduated scale from very soft to very loud, often expressed with abbreviations. Articulation markings act as performance 'formulas' for how notes are attacked or connected.
力度遵循从极弱到极强的渐变等级，常以缩写表示。演奏法标记则像是音符如何发声或连接的演奏
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