📚 KS3 CCEA Music Quick Reference: Formulas and Theorems | KS3 CCEA 音乐：公式定理速查手册
Music is built on patterns and structures – think of them as the ‘formulas’ that composers use to create melody, harmony, and rhythm. This quick-reference handbook brings together the essential musical ‘rules of thumb’ you need for Key Stage 3 CCEA Music. From note values to cadences, each concept is presented as a clear, memorable formula to support your listening, performing, and composing work.
音乐建立在模式与结构之上——你可以把它们看作作曲家用来创作旋律、和声与节奏的“公式”。这本速查手册汇集了KS3 CCEA音乐课程所需的基本音乐“经验法则”。从音符时值到终止式，每个概念都以清晰、易记的公式呈现，帮助你在聆听、表演和作曲中更自信。
1. Note Values (Duration) | 音符时值公式
Every note has a numerical relationship. The semibreve (whole note) is the baseline unit, and all other notes divide it equally.
每个音符都有数值化的关系。全音符是基础单位，所有其他音符都是它的等分。
| English Note Name | 中文名称 | Symbol | Relative Value (Semibreve = 1) | American Name |
|---|---|---|---|---|
| Semibreve | 全音符 | 𝅝 | 1 | Whole note |
| Minim | 二分音符 | 𝅗𝅥 | ½ | Half note |
| Crotchet | 四分音符 | 𝅘𝅥 | ¼ | Quarter note |
| Quaver | 八分音符 | 𝅘𝅥𝅮 | ⅛ | Eighth note |
| Semiquaver | 十六分音符 | 𝅘𝅥𝅯 | 1/16 | Sixteenth note |
Dotted note formula: a dot adds half the value of the original note. For example, a dotted minim = minim (2 beats) + crotchet (1 beat) = 3 beats in 4/4 time.
附点音符公式：附点增加原音符时值的一半。例如，附点二分音符 = 二分音符（2拍）+ 四分音符（1拍）= 在4/4拍中为3拍。
2. Rests and Their Values | 休止符时值公式
Rests mirror the durations of notes exactly, using the same fractional logic. Each note value has a corresponding rest symbol.
休止符的时值与音符完全对应，使用相同的分数逻辑。每个音符时值都有对应的休止符符号。
| Rest Name | 中文 | Symbol | Equivalent Note |
|---|---|---|---|
| Semibreve rest | 全休止符 | 𝄻 | Semibreve |
| Minim rest | 二分休止符 | 𝄼 | Minim |
| Crotchet rest | 四分休止符 | 𝄽 | Crotchet |
| Quaver rest | 八分休止符 | 𝄾 | Quaver |
| Semiquaver rest | 十六分休止符 | 𝄿 | Semiquaver |
The whole-bar rest formula: a semibreve rest hanging from the second line of the stave indicates a full bar of silence, regardless of the actual time signature (except in 4/2, where a breve rest is used).
整小节休止公式：全休止符悬挂在五线谱第二线下，表示整小节休止，无论拍号如何（除了4/2拍使用二全休止符）。
3. Time Signature Formulas | 拍号公式
A time signature is a fraction without a line. The top number tells you how many beats in a bar; the bottom number tells you what note value gets one beat.
拍号是一个没有分数线的分数。上方数字表示每小节有几拍；下方数字表示以哪种音符为一拍。
Basic formula: Top number = beats per bar. Bottom number: 4 = crotchet beat, 8 = quaver beat, 2 = minim beat.
基本公式：上方数字 = 每小节拍数。下方数字：4 = 四分音符为一拍，8 = 八分音符为一拍，2 = 二分音符为一拍。
- Duple time: 2 beats per bar (e.g., 2/4, 2/2) – strong-weak pattern.
- 二拍子：每小节2拍（如2/4、2/2）——强-弱模式。
- Triple time: 3 beats per bar (e.g., 3/4, 3/8) – strong-weak-weak.
- 三拍子：每小节3拍（如3/4、3/8）——强-弱-弱。
- Quadruple time: 4 beats per bar (e.g., 4/4, 4/2) – strong-weak-medium-weak.
- 四拍子：每小节4拍（如4/4、4/2）——强-弱-次强-弱。
Compound time: when the beat divides into three equal parts. The top number is a multiple of 3 (6, 9, 12). To find the number of beats, divide the top number by 3.
复拍子：当一拍自然地分成三等份时。上方数字是3的倍数（6、9、12）。要得到实际拍数，将上方数字除以3。
4. Major Scale Formula | 大调音阶公式
Every major scale follows the same pattern of tones (T) and semitones (S): T, T, S, T, T, T, S. This works from any starting note.
每个大调音阶都遵循相同的全音（T）和半音（S）模式：全-全-半-全-全-全-半。无论从哪个音开始，这个模式都成立。
Formula in semitone steps from the tonic: 0, 2, 4, 5, 7, 9, 11, 12.
从主音开始的半音步数公式：0, 2, 4, 5, 7, 9, 11, 12。
Example: C major uses only white keys: C-D (T), D-E (T), E-F (S), F-G (T), G-A (T), A-B (T), B-C (S).
示例：C大调只使用白键：C-D（全音），D-E（全音），E-F（半音），F-G（全音），G-A（全音），A-B（全音），B-C（半音）。
The order of sharps in key signatures: Father Charles Goes Down And Ends Battle (F♯, C♯, G♯, D♯, A♯, E♯, B♯). For flats, reverse: Battle Ends And Down Goes Charles’ Father (B♭, E♭, A♭, D♭, G♭, C♭, F♭).
调号中升号顺序：Father Charles Goes Down And Ends Battle（F♯, C♯, G♯, D♯, A♯, E♯, B♯）。降号顺序反过来：Battle Ends And Down Goes Charles’ Father（B♭, E♭, A♭, D♭, G♭, C♭, F♭）。
5. Natural Minor Scale Formula | 自然小调音阶公式
The natural minor scale shares the same key signature as its relative major but starts on the sixth degree. Its tone-semitone pattern is: T, S, T, T, S, T, T.
自然小调与其关系大调共用同一个调号，但起始于大调的第六级音。它的全-半音模式是：全-半-全-全-半-全-全。
Semitone formula from tonic: 0, 2, 3, 5, 7, 8, 10, 12.
从主音开始的半音公式：0, 2, 3, 5, 7, 8, 10, 12。
A minor is the relative minor of C major: A-B (T), B-C (S), C-D (T), D-E (T), E-F (S), F-G (T), G-A (T).
A小调是C大调的关系小调：A-B（全音），B-C（半音），C-D（全音），D-E（全音），E-F（半音），F-G（全音），G-A（全音）。
Harmonic minor adjustment: raise the 7th degree by a semitone (G to G♯ in A minor). Melodic minor (ascending) raises both 6th and 7th by a semitone; descending uses natural minor.
和声小调调整：升高第七级音半音（A小调中G变为G♯）。旋律小调（上行）升高第六和第七级音半音；下行使用自然小调。
6. Interval Formulas (Semitone Counting) | 音程公式（半音计数）
An interval measures the distance between two notes, counted in semitones and described by number (1st, 2nd, etc.) and quality (perfect, major, minor, etc.).
音程衡量两个音之间的距离，以半音计数，并用数字（一度、二度等）和质量（纯、大、小等）描述。
| Interval | 中文 | Semitones | Example (from C) |
|---|---|---|---|
| Minor 2nd | 小二度 | 1 | C-D♭ |
| Major 2nd | 大二度 | 2 | C-D |
| Minor 3rd | 小三度 | 3 | C-E♭ |
| Major 3rd | 大三度 | 4 | C-E |
| Perfect 4th | 纯四度 | 5 | C-F |
| Perfect 5th | 纯五度 | 7 | C-G |
| Minor 6th | 小六度 | 8 | C-A♭ |
| Major 6th | 大六度 | 9 | C-A |
| Minor 7th | 小七度 | 10 | C-B♭ |
| Major 7th | 大七度 | 11 | C-B |
| Octave | 纯八度 | 12 | C-C |
Interval inversion rule: the sum of a simple interval and its inversion is always 9 (e.g., a 3rd inverts to a 6th, a 4th to a 5th). Major becomes minor, perfect stays perfect.
音程转位规则：一个单音程与其转位的数字之和恒为9（如三度转位为六度，四度转位为五度）。大音程转为小音程，纯音程仍然保持纯。
7. Triad Construction Formulas | 三和弦构建公式
A triad is a three-note chord stacked in thirds. The quality of the triad is determined by the pattern of intervals (in semitones) between the root, third, and fifth.
三和弦是由三个音按三度关系叠置而成的和弦。和弦的性质由根音、三音和五音之间的音程（半音数）决定。
- Major triad formula: root + 4 semitones + 3 semitones (e.g., C-E-G = C + 4 + 3).
- 大三和弦公式：根音 + 4个半音 + 3个半音（例如 C-E-G = C + 4 + 3）。
- Minor triad formula: root + 3 semitones + 4 semitones (e.g., A-C-E = A + 3 + 4).
- 小三和弦公式：根音 + 3个半音 + 4个半音（例如 A-C-E = A + 3 + 4）。
- Diminished triad formula: root + 3 semitones + 3 semitones (e.g., B-D-F = B + 3 + 3).
- 减三和弦公式：根音 + 3个半音 + 3个半音（例如 B-D-F = B + 3 + 3）。
- Augmented triad formula: root + 4 semitones + 4 semitones (e.g., C-E-G♯ = C + 4 + 4).
- 增三和弦公式：根音 + 4个半音 + 4个半音（例如 C-E-G♯ = C + 4 + 4）。
Triads in a major key (roman numerals): I (major), ii (minor), iii (minor), IV (major), V (major), vi (minor), vii° (diminished).
大调中的三和弦（罗马数字标记）：I（大），ii（小），iii（小），IV（大），V（大），vi（小），vii°（减）。
8. Cadence Formulas | 终止式公式
A cadence is a pair of chords that ends a phrase. The formula describes the chord progression and its effect.
终止式是结束乐句的一对和弦。公式描述了和弦进行及其效果。
- Perfect cadence (V-I): sounds finished and strong. In C major: G major to C major.
- 完全终止（V-I）：听起来结束感强。在C大调中：G大三和弦到C大三和弦。
- Plagal cadence (IV-I): the ‘Amen’ cadence, sounds gentle and complete. In C major: F major to C major.
- 变格终止（IV-I）：“阿门”终止，听起来柔和且完整。在C大调中：F大三和弦到C大三和弦。
- Imperfect cadence (I-V, ii-V, IV-V): ends on V, sounding unfinished. In C major: any chord to G major.
- 不完全终止（I-V、ii-V、IV-V）：结束在V级，听起来未完成。在C大调中：任何和弦到G大三和弦。
- Interrupted cadence (V-vi): a surprise ending; V moves to the submediant. In C major: G major to A minor.
- 阻碍终止（V-vi）：意外结尾；V级进行到下中音和弦。在C大调中：G大三和弦到A小三和弦。
9. Key Signature Memory Aids | 调号速记公式
To quickly identify the major key from a sharp key signature: go to the last sharp and raise it by a semitone. For flat key signatures: the second-to-last flat is the key (except F major, which has one flat).
从升号调号快速识别大调：找到最后一个升号，将其升高半音。降号调：倒数第二个降号就是调名（除了F大调只有一个降号）。
Number of sharps and corresponding major keys: 0 = C, 1 = G, 2 = D, 3 = A, 4 = E, 5 = B, 6 = F♯, 7 = C♯. With flats: 0 = C, 1 = F, 2 = B♭, 3 = E♭, 4 = A♭, 5 = D♭, 6 = G♭, 7 = C♭.
升号数量与对应大调：0 = C，1 = G，2 = D，3 = A，4 = E，5 = B，6 = F♯，7 = C♯。降号：0 = C，1 = F，2 = B♭，3 = E♭，4 = A♭，5 = D♭，6 = G♭，7 = C♭。
Relative minor shortcut: the relative minor is a minor 3rd (3 semitones) below the major tonic. For C major, count down 3 semitones → A minor.
关系小调捷径：关系小调位于大调主音下方小三度（3个半音）。从C大调主音向下数3个半音 → A小调。
10. Dynamics and Tempo Markings | 力度与速度标记公式
Italian terms follow a scale-like logic. Dynamics range from very quiet to very loud; tempo markings from very slow to very fast.
意大利术语遵循类似量表的逻辑。力度从很弱到很强；速度标记从很慢到很快。
| Dynamic | 中文 | Symbol | Tempo | 中文 | Approx. BPM |
|---|---|---|---|---|---|
| pp (pianissimo) | 很弱 | pp | Largo | 广板 | 40-60 |
| p (piano) | 弱 | p | Adagio | 柔板 | 66-76 |
| mp (mezzo-piano) | 中弱 | mp | Andante | 行板 | 76-108 |
| mf (mezzo-forte) | 中强 | mf | Moderato | 中板 | 108-120 |
| f (forte) | 强 | f | Allegro | 快板 | 120-156 |
| ff (fortissimo) | 很强 | ff | Presto | 急板 | 168-200 |
Gradual change formulas: crescendo (cresc.) = gradually louder; decrescendo/diminuendo (dim.) = gradually softer. Accel. (accelerando) = gradually faster; rit. (ritardando) = gradually slower.
渐变公式：crescendo（cresc.）= 渐强；decrescendo/diminuendo（dim.）= 渐弱。accel.（accelerando）= 渐快；rit.（ritardando）= 渐慢。
11. Articulation and Expression Quick Codes | 演奏法与表情速查公式
Articulation marks act like punctuation for music. Each symbol has a specific effect on how a note is attacked or connected.
演奏法记号就像音乐的标点符号。每个符号都定义了音符如何发音或连接。
- Staccato (dot above/below note): short and detached. The note is held for roughly half its written value.
- 断奏（音符上下方的小圆点）：短促且分离。音符的实际时值约为记谱的一半。
- Legato (slur): smooth and connected. No silence between notes.
- 连奏（连线）：平滑连贯，音符之间没有间隙。
- Accent (> or ∧ above note): a stressed attack; play louder at the start.
- 重音（音符上方的 > 或 ∧）：强调式发音；开始时奏得更响。
- Tenuto (- above note): hold the note for its full value, sometimes slightly weighted.
- 保持音（音符上方的横线 -）：充分保持该音的时值，有时稍带重量感。
- Pause / Fermata (𝄐): hold the note or rest longer than its written duration, at the performer’s/discretion.
- 延长记号（𝄐）：将音符或休止符保持比记谱更长的时值，由演奏者自行处理。
12. Structure and Form Patterns | 曲式结构公式
Musical forms follow repeatable frameworks. Recognising these patterns helps in analysis and composition.
音乐曲式遵循可重复的框架。识别这些模式有助于分析与创作。
- Binary form (AB): two contrasting sections, each usually repeated. Common in Baroque dances.
- 二部曲式（AB）：两个对比乐段，各段通常反复。常见于巴洛克舞曲。
- Ternary form (ABA): a main theme (A), contrasting middle section (B), and a return of A. The da capo aria uses this pattern.
- 三部曲式（ABA）：一个主要主题（A），对比中段（B），再回到A。返始咏叹调使用这种模式。
- Rondo form (ABACA or ABACABA): a recurring A theme alternates with contrasting episodes.
- 回旋曲式（ABACA或ABACABA）：反复出现的A主题与对比插部交替
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