📚 Year 8 WJEC Music: Formula & Theorem Quick Reference Handbook | Year 8 WJEC 音乐：公式定理速查手册
Music is built on a set of precise, repeatable patterns and relationships. Just as mathematics has formulas and science has laws, music theory relies on recognised structures of rhythm, pitch, harmony and expression. This quick reference handbook gathers the essential ‘formulas’ and ‘theorems’ that Year 8 students following the WJEC curriculum need to know. Think of it as your musical toolkit: learn these patterns, and you will be able to read, write, analyse and perform music with confidence.
音乐建立在一系列精确且可重复的模式与关系之上。正如数学有公式、科学有定律，音乐理论也依赖于节奏、音高、和声与表现力方面的公认结构。这份速查手册汇集了遵循 WJEC 课程的 Year 8 学生必须掌握的基本“公式”和“定理”。把它当作你的音乐工具箱：学会这些模式，你就能自信地读谱、写谱、分析和演奏音乐。
1. Note Value Pyramid | 音符时值金字塔
The relationships between note durations follow a simple doubling system. One semibreve is equal to two minims; one minim equals two crotchets; one crotchet equals two quavers; one quaver equals two semiquavers. These proportions remain constant regardless of tempo or style of music, much like a mathematical theorem.
音符时值之间的关系遵循一个简单的倍增系统。一个全音符等于两个二分音符；一个二分音符等于两个四分音符；一个四分音符等于两个八分音符；一个八分音符等于两个十六分音符。无论音乐的速度或风格如何变化，这些比例保持不变，就像数学定理一样。
| English Name | 中文名称 | Symbol | Relative Duration (crotchet = 1) |
|---|---|---|---|
| Semibreve | 全音符 | 𝅝 | 4 beats |
| Minim | 二分音符 | 𝅗𝅥 | 2 beats |
| Crotchet | 四分音符 | 𝅘𝅥 | 1 beat |
| Quaver | 八分音符 | 𝅘𝅥𝅮 | ½ beat |
| Semiquaver | 十六分音符 | 𝅘𝅥𝅯 | ¼ beat |
2. Dotted Notes and Ties: The Extension Formulas | 附点音符与延音线：时值延长公式
A dot after any note increases its duration by half of its original value. The formula is: Dotted value = original value × 1.5. For example, a dotted minim lasts for 3 crotchet beats (2 + 1), and a dotted crotchet lasts for 1.5 beats. A tie joins two notes of the same pitch, adding their values together, allowing durations that cannot be expressed by a single note alone.
任何音符后面的附点会将其时值延长原有时值的一半。公式为：附点音符时值 = 原有长度 × 1.5。例如，附点二分音符持续 3 个四分音符拍（2+1），附点四分音符持续 1.5 拍。延音线连接两个相同音高的音符，将它们的时值相加，使笔记能够表达单个音符无法表达的时长。
A double dot is occasionally used in advanced works: the second dot adds half of the first dot’s value. For example, a double-dotted crotchet equals 1 + 0.5 + 0.25 = 1.75 beats. At Year 8 level, single dots are the main focus.
复附点偶尔在进阶作品里使用：第二个附点再增加第一个附点的一半时值。例如，复附点四分音符等于 1 + 0.5 + 0.25 = 1.75 拍。在 Year 8 阶段，单附点是主要学习内容。
3. Time Signature Rules | 拍号规则
A time signature tells you how many beats are in each bar (top number) and what kind of note gets one beat (bottom number). For example, 4/4 means four crotchet beats per bar. 3/4 means three crotchets per bar. The bottom number uses a code: 4 stands for crotchet, 8 for quaver, 2 for minim.
拍号告诉你每小节有多少拍（上方数字），以及哪一种音符为一拍（下方数字）。例如，4/4 拍表示每小节有四个四分音符时值的拍子。3/4 拍表示每小节三个四分音符。下方数字采用编码：4 代表四分音符，8 代表八分音符，2 代表二分音符。
Simple time signatures have beats that divide naturally into two equal parts (e.g., 2/4, 3/4, 4/4). Compound time signatures have beats that divide into three equal parts (e.g., 6/8, 9/8, 12/8). The ‘formula’ for compound time is: number of main beats × 3. So 6/8 has two dotted-crotchet beats per bar (2 × 3 quavers).
单拍号的每一拍能自然分成两个均等的部分（如 2/4、3/4、4/4）。复拍号的每一拍分成三个均等的部分（如 6/8、9/8、12/8）。复拍号的“公式”为：主要拍数 × 3。因此 6/8 拍每小节有两个附点四分音符拍（2 × 3 个八分音符）。
4. Major Scale Formula | 大调音阶公式
The major scale is built using a fixed pattern of whole tones (T) and semitones (S). The ascending formula, regardless of starting pitch, is: T – T – S – T – T – T – S. This pattern generates all major scales. For example, starting on C: C (T) D (T) E (S) F (T) G (T) A (T) B (S) C. No sharps or flats are needed in C major because the pattern aligns precisely with the white notes on a keyboard.
大调音阶由固定的全音（T）和半音（S）模式构成。不论从哪个音开始，上行公式都是：T – T – S – T – T – T – S。该模式生成了所有大调。例如，从 C 开始：C (T) D (T) E (S) F (T) G (T) A (T) B (S) C。C 大调不需要任何升号或降号，因为这一模式刚好与键盘上的白键完全吻合。
When you start on a different note, you must apply sharps or flats to maintain the T–T–S–T–T–T–S sequence. For G major, you need F♯: G (T) A (T) B (S) C (T) D (T) E (T) F♯ (S) G. This is why key signatures exist.
当你从另一个音开始构建大调时，必须运用升号或降号来维持 T–T–S–T–T–T–S 序列。以 G 大调为例，你需要 F♯：G (T) A (T) B (S) C (T) D (T) E (T) F♯ (S) G。这就是调号存在的原因。
5. Natural Minor Scale Formula | 自然小调音阶公式
The natural minor scale uses the pattern: T – S – T – T – S – T – T. Starting from A, this produces the A natural minor scale on white notes: A (T) B (S) C (T) D (T) E (S) F (T) G (T) A. The minor scale has a lowered third, sixth and seventh degree compared to the parallel major scale.
自然小调音阶使用的模式是：T – S – T – T – S – T – T。从 A 开始，就得到白键上的 A 自然小调音阶：A (T) B (S) C (T) D (T) E (S) F (T) G (T) A。与同主音大调相比，小调的第三级、第六级和第七级音被降低了。
Harmonic and melodic minors introduce alterations. The harmonic minor raises the 7th degree by a semitone (creating the T–S–T–T–S– augmented 2nd –S pattern). The melodic minor raises the 6th and 7th degrees when ascending (T–S–T–T–T–T–S) and reverts to natural minor when descending. Year 8 typically focuses on the natural and harmonic forms.
和声小调与旋律小调引入了变化。和声小调将第七级音升高半音（产生 T–S–T–T–S–增二度–S 的模式）。旋律小调在上行时升高第六和第七级音（T–S–T–T–T–T–S），下行时还原为自然小调。Year 8 通常着重于自然与和声两种形式。
6. Interval Calculation | 音程度数计算
An interval measures the distance in pitch between two notes. The number (size) is counted by the letter names involved, including both endpoints. For example, C to E is a 3rd (C–D–E). C to G is a 5th (C–D–E–F–G). The quality (major, minor, perfect, augmented, diminished) is then determined by the exact number of semitones.
音程衡量两个音符之间的音高距离。度数根据涉及到的音名字母数目来计算，包括两端点。例如，C 到 E 是三度（C–D–E）；C 到 G 是五度（C–D–E–F–G）。再通过准确的半音数量来确定其性质（大、小、纯、增、减）。
Key interval formulas in semitones: Perfect unison = 0, minor 2nd = 1, major 2nd = 2, 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, perfect octave = 12. Remember: perfect intervals (1, 4, 5, 8) never become major or minor; they can be diminished or augmented instead.
以半音计的关键音程公式为：纯一度 = 0，小二度 = 1，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。请记住：纯音程（1、4、5、8 度）永远不会有大小之分；它们可以变为增或减音程。
7. Triad Construction (Chords) | 三和弦构造公式
A triad is a three-note chord consisting of a root, a third and a fifth. The quality depends on the intervals above the root. A major triad formula is: root + major 3rd (4 semitones) + perfect 5th (7 semitones). Example: C major = C – E – G. A minor triad formula is: root + minor 3rd (3 semitones) + perfect 5th (7 semitones). Example: A minor = A – C – E.
三和弦是由根音、三音和五音组成的三个音的和弦。其性质取决于根音上方的音程。大三和弦的公式为：根音 + 大三度（4 个半音）+ 纯五度（7 个半音）。例如：C 大三和弦 = C – E – G。小三和弦的公式为：根音 + 小三度（3 个半音）+ 纯五度（7 个半音）。例如：A 小三和弦 = A – C – E。
A diminished triad is formed by stacking two minor thirds: root + minor 3rd + diminished 5th (6 semitones). An augmented triad stacks two major thirds: root + major 3rd + augmented 5th (8 semitones). Diatonic chords in a major key follow the pattern: I major, ii minor, iii minor, IV major, V major, vi minor, vii° diminished. This is a fundamental harmonic theorem.
减三和弦由叠加两个小三度构成：根音 + 小三度 + 减五度（6 个半音）。增三和弦则叠加两个大三度：根音 + 大三度 + 增五度（8 个半音）。大调音阶上的自然和弦遵循以下模式：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。这是一条基础的和声定理。
8. Key Signatures and the Circle of Fifths | 调号与五度循环
The order of sharps in key signatures follows the pattern: F♯ – C♯ – G♯ – D♯ – A♯ – E♯ – B♯. Each sharp appears a perfect 5th above the previous one. The order of flats is the reverse: B♭ – E♭ – A♭ – D♭ – G♭ – C♭ – F♭. To find the major key from a sharp key signature, take the last sharp and raise it by a semitone. For example, if the last sharp is D♯, the key is E major.
调号中升号的顺序为：F♯ – C♯ – G♯ – D♯ – A♯ – E♯ – B♯。每一个升号都比前一个高纯五度。降号的顺序与之相反：B♭ – E♭ – A♭ – D♭ – G♭ – C♭ – F♭。要从升号调号中找出大调的主音，只需取最后一个升号再升高半音。例如，如果最后一个升号是 D♯，调就是 E 大调。
For flat key signatures, the major key is the second-to-last flat (except F major, which has one flat). So B♭ – E♭ gives B♭ major. The circle of fifths arranges keys clockwise by ascending perfect 5ths (C – G – D – A – E – B – F♯ – C♯) and anticlockwise by descending perfect 5ths (C – F – B♭ – E♭ – A♭ – D♭ – G♭ – C♭). This circular model helps you memorise all 15 major keys and their relative minors.
对于降号调号，大调的主音是倒数第二个降号（除了只有一个降号的 F 大调）。因此 B♭ – E♭ 得出的是 B♭ 大调。五度循环将调性按上行纯五度顺时针排列（C – G – D – A – E – B – F♯ – C♯），按下行纯五度逆时针排列（C – F – B♭ – E♭ – A♭ – D♭ – G♭ – C♭）。这个环形模型有助于你记忆全部 15 个大调及其关系小调。
9. Dynamics and Tempo Terms: Constant Rules | 力度与速度术语：恒定规则
Dynamics indicate the volume of music. The standard Italian terms follow a graduated scale. The most common soft-to-loud sequence is: pp (pianissimo, very soft), p (piano, soft), mp (mezzo-piano, moderately soft), mf (mezzo-forte, moderately loud), f (forte, loud), ff (fortissimo, very loud). Gradual changes use crescendo (cresc., getting louder) and diminuendo (dim., getting softer) or decrescendo.
力度标记指示乐曲的音量。标准意大利术语遵循一个渐进的等级。最常见的从弱到强的次序为：pp（极弱）、p（弱）、mp（中弱）、mf（中强）、f（强）、ff（极强）。渐变变化则使用 crescendo（渐强）和 diminuendo 或 decrescendo（渐弱）。
Tempo markings set the speed of the beat. The basic range, from slow to fast, includes: Largo (very slow, stately), Adagio (slow), Andante (walking pace), Moderato (moderate), Allegro (fast, cheerful), Vivace (lively and fast), Presto (very fast). A metronome mark gives precise beats per minute, such as ♩ = 120, meaning 120 crotchet beats per minute. Ritenuto (rit.) and accelerando (accel.) indicate sudden or gradual changes of pace.
速度标记设定音乐节拍的速度。从慢到快的基本范围包括：Largo（广板，非常慢）、Adagio（柔板，慢速）、Andante（行板，步行速度）、Moderato（中板，中等速度）、Allegro（快板，快速而欢快）、Vivace（活泼的快板）、Presto（急板，很快）。节拍器标记则给出每分钟精确的拍数，如 ♩ = 120 表示每分钟 120 个四分音符拍。ritenuto（突慢）和 accelerando（渐快）表示速度的突然或逐渐变化。
10. Articulation and Expression Marks | 奏法与表情记号
Articulation tells the performer how to attack and connect notes. Staccato (dot above or below the note) means short and detached. Legato (slur) means smoothly connected. Accent ( > ) means a strong attack. Tenuto ( — ) means hold the note for its full value, often slightly stressed. These marks act like punctuation in musical sentences.
奏法告诉演奏者如何处理音符的吐放与连接。Staccato（音符上方或下方的圆点）表示短促而分离。Legato（连音线）表示圆滑地连接。重音记号（ > ）表示强力度起音。Tenuto（横线）表示充分保持音符的时值，并常带轻微强调。这些记号就像音乐句子里的标点符号。
Phrasing marks, such as slurs over a group of notes, indicate a musical ‘sentence’ to be played with continuous breath or bowing. Dynamics and articulation together shape musical expression. The combination of staccato dots under a slur indicates portato, a soft pulsed articulation. All these markings follow consistent interpretative rules across styles.
分句标记，比如跨越多个音符的连音线，表示一个音乐“句子”，需要用连贯的气息或运弓来演奏。力度与奏法共同塑造了音乐的表现力。连音线下加断奏点表示 portato，一种轻柔且有脉动的奏法。所有这些符号在不同风格中都遵循着统一的演绎规则。
11. Simple Harmonic Cadence Formulas | 简单终止式公式
A cadence is a progression of two chords that ends a phrase. The four main types each create a distinct sense of closure or continuation. The perfect cadence (V–I) sounds finished and conclusive, like a full stop. The plagal cadence (IV–I) is often called the ‘Amen’ cadence, also sounding finished but softer. The imperfect cadence (I–V, ii–V, IV–V) ends on V, sounding incomplete; it is like a musical comma. The interrupted cadence (V–vi) surprises the listener by moving to the minor vi chord instead of the expected I.
终止式是结束乐句的两和弦进行。四种主要类型各自营造出不同的收束或延续感。正格终止（V–I）听起来完满而确定，像句号。变格终止（IV–I）常被称为“阿们终止”，同样有结束感但更为柔和。半终止（I–V、ii–V、IV–V）结束在 V 级，听起来未完成，如同音乐中的逗号。阻碍终止（V–vi）以进行到小调 vi 级和弦代替预期的 I 级，给听者带来意外感。
These cadence formulas are reliable in both major and minor keys. In a minor key, the V chord is usually major (requiring a raised leading note) to create the strong semitone pull back to the tonic. Year 8 students are expected to recognise these four patterns by ear and in notation. Memorising the chord relationships as a ‘theorem’ helps when composing satisfying phrase endings.
这些终止式公式在大调和小调中都可靠有效。在小调中，V 和弦通常是大三和弦（需要升高导音），以产生回到主音的半音倾向性。Year 8 学生应能通过听觉和识谱辨认这四种模式。将和弦关系作为“定理”来记忆，有助于在创作中写出令人满意的乐句结尾。
12. Quick Reference Cheat Sheet | 快速查阅备忘表
Below is a consolidated table of the most important formulas and theorems for Year 8 WJEC Music. Use this section for rapid revision before assessments.
以下是 Year 8 WJEC 音乐中最重要的公式与定理汇总表，可用于评估前的快速复习。
| Concept | Formula / Rule | Example |
|---|---|---|
| Major scale | T–T–S–T–T–T–S | D major: D–E–F♯–G–A–B–C♯–D |
| Natural minor scale | T–S–T–T–S–T–T | E minor: E–F♯–G–A–B–C–D–E |
| Major triad | M3 + m3 (4 + 3 semitones) | G major: G–B–D |
| Minor triad | m3 + M3 (3 + 4 semitones) | D minor: D–F–A |
| Dotted note value | Original value × 1.5 | Dotted minim = 3 crotchets |
| Simple time signature | Top number: beats per bar; bottom: note value | 3/4 = three crotchet beats |
| Compound time | Beats grouped in 3s: top number = 6,9,12 | 6/8 = two dotted-crotchet beats |
| Perfect cadence | V–I | G major to C major |
| Plagal cadence | IV–I | F major to C major |
| Interrupted cadence | V–vi | G major to A minor |
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