📚 Year 8 WJEC Music: Quick-Reference Handbook of Formulae & Theorems | 威雅八年级音乐公式定理速查手册
This quick-reference handbook gathers the essential ‘formulae’ and ‘theorems’ of music that every Year 8 WJEC student should know. Just as mathematics uses equations to build patterns, music uses interval patterns, rhythmic ratios and chord recipes to create harmony, melody and structure. Bookmark this page for rapid revision and let the patterns unlock your composing, performing and listening skills.
这本速查手册汇集了每位威雅八年级学生都应掌握的音乐“公式”与“定理”。正如数学运用方程式构建模式，音乐使用音程模式、节奏比率与和弦配方来创造和声、旋律与结构。收藏本页，随时快速复习，让这些模式释放你的作曲、演奏与听力能力。
1. Note-Duration Formula | 音符时值公式
A standard whole note (semibreve) equals 4 beats. Every shorter note divides the previous value by 2. The dot formula adds half the original value: dotted note = note + (note ÷ 2). Ties add values together without a new attack.
一个标准全音符等于4拍。每个更短的音符将上一级时值除以2。附点公式增加原时值的一半：附点音符 = 原音符 + (原音符 ÷ 2)。延音线将两个时值相加，不重新发音。
- Semibreve = 4 beats | 全音符 = 4拍
- Minim = 2 beats | 二分音符 = 2拍
- Crotchet = 1 beat | 四分音符 = 1拍
- Quaver = ½ beat | 八分音符 = ½拍
- Semiquaver = ¼ beat | 十六分音符 = ¼拍
- Dotted minim = 2 + 1 = 3 beats | 附点二分音符 = 3拍
- Dotted crotchet = 1 + ½ = 1½ beats | 附点四分音符 = 1½拍
2. Time-Signature Theorem | 拍号定理
A time signature is a fraction without a line: the top number tells how many beats per bar; the bottom number tells what type of beat counts as one unit (4 = crotchet, 8 = quaver, 2 = minim).
拍号是没有分数线的分数：上方数字表示每小节几拍；下方数字表示以何种音符为一拍（4 = 四分音符，8 = 八分音符，2 = 二分音符）。
- 4/4 = 4 crotchet beats per bar | 每小节4个四分音符拍
- 3/4 = 3 crotchet beats | 每小节3个四分音符拍
- 2/4 = 2 crotchet beats | 每小节2个四分音符拍
- 6/8 = 6 quaver beats, often felt in 2 dotted-crotchet pulses | 6个八分音符，常以2个附点四分音符为律动
3. Tempo-to-BPM Formula | 速度与节拍换算
Tempo marking gives beats per minute (BPM). To find the duration of one beat in seconds: duration = 60 ÷ BPM. A 120 BPM crotchet lasts 0.5 seconds.
速度标记给出每分钟拍数(BPM)。求单拍秒数：时长 = 60 ÷ BPM。120 BPM的四分音符持续0.5秒。
Crotchet duration (s) = 60 ÷ BPM
4. Major-Scale Formula | 大调音阶公式
A major scale follows a fixed pattern of tones (T) and semitones (S): T T S T T T S. Apply this to any starting note to build its major scale, using accidentals where needed.
大调音阶遵循固定的全音(T)与半音(S)模式：全 全 半 全 全 全 半。将此模式应用于任一起始音，即可构建该大调音阶，必要时使用变音记号。
Example: C major – C T D T E S F T G T A T B S C | 示例：C大调 – C 全 D 全 E 半 F 全 G 全 A 全 B 半 C
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. It shares the same key signature as its relative major (starting a minor third lower).
自然小调音阶使用模式：全 半 全 全 半 全 全。其调号与关系大调相同（起始音低小三度）。
Example: A natural minor – A T B S C T D T E S F T G T A | 示例：a自然小调 – A 全 B 半 C 全 D 全 E 半 F 全 G 全 A
6. Interval-Reckoning Theorem | 音程度量定理
Count the letter names from the lower note to the higher (including both) to get the interval number. Count semitones to determine quality (major/minor/perfect). In a major scale, intervals from the tonic are all major or perfect; lowering a major interval by a semitone makes it minor.
从低音数到高音的字母数（含首尾）得到音程度数。数半音数决定性质（大/小/纯）。在大调音阶中，从主音开始的音程均为大或纯；将大音程降低半音即成为小音程。
- Unison (1) | 同度
- Major 2nd (2) = 2 semitones | 大二度 = 2个半音
- Major 3rd (3) = 4 semitones | 大三度 = 4个半音
- Perfect 4th (4) = 5 semitones | 纯四度 = 5个半音
- Perfect 5th (5) = 7 semitones | 纯五度 = 7个半音
- Major 6th (6) = 9 semitones | 大六度 = 9个半音
- Major 7th (7) = 11 semitones | 大七度 = 11个半音
- Octave (8) = 12 semitones | 八度 = 12个半音
7. Triad-Chord Recipe | 三和弦配方
A triad is built by stacking two thirds + major 3rd (3 + 4 semitones). Diminished triad = minor 3rd + minor 3rd (3 + 3 semitones).
三和弦由根音上方叠置两个三度构成。根音 + 三音 + 五音。大三和弦 = 大三度 + 小三度（4+3半音）。小三和弦 = 小三度 + 大三度（3+4半音）。减三和弦 = 小三度 + 小三度（3+3半音）。
| Triad | 和弦 | Semitone formula | 半音公式 | Example (C root) | 示例 (C根音) |
|---|---|---|
| Major | 大 | 4 + 3 | C–E–G |
| Minor | 小 | 3 + 4 | C–E♭–G |
| Diminished | 减 | 3 + 3 | C–E♭–G♭ |
8. Key-Signature Circle Theorem | 调号循环定理
Sharps appear in the order: F C G D A E B (Father Charles Goes Down And Ends Battle). Flats appear in reverse: B E A D G C F. For major keys, the last sharp is the 7th degree (leading note); the second-to-last flat is the tonic.
升号出现顺序：F C G D A E B。降号顺序与之相反：B E A D G C F。对于大调，最后一个升号是第七级音（导音）；倒数第二个降号是主音。
- 1 sharp (F♯) → G major | 一个升号 (F♯) → G大调
- 2 sharps (F♯, C♯) → D major | 两个升号 → D大调
- 1 flat (B♭) → F major | 一个降号 → F大调
- 2 flats (B♭, E♭) → B♭ major | 两个降号 → B♭大调
9. Primary-Chord Theorem | 正三和弦定理
In any major key, the three primary chords built on the 1st (tonic), 4th (subdominant) and 5th (dominant) degrees are all major. They contain every note of the scale and form the harmonic backbone of countless songs and cadences.
在任何大调中，建立在第I级（主音）、第IV级（下属音）和第V级（属音）上的三个正三和弦全为大三和弦。它们包含了音阶的每个音，构成无数歌曲与终止式的和声支柱。
In C major: I = C, IV = F, V = G. | 以C大调为例：I = C, IV = F, V = G.
10. Perfect-Cadence Formula | 完全终止公式
A perfect cadence moves from chord V to I. This creates a strong, final-sounding close. Both chords are usually in root position, and the tonic note appears in the melody of the I chord.
完全终止从V级和弦进行到I级。这产生强烈的结束感。两个和弦通常均为原位，且I和弦旋律音为主音。
Example: G major → C major in the key of C | 示例：C大调中 G → C
11. Plagal-Cadence Formula | 变格终止公式
A plagal cadence moves from chord IV to I. Often called the ‘Amen’ cadence, it sounds gentle and complete. Both chords are major.
变格终止从IV级和弦进行到I级。常被称为“阿们”终止，听感柔和而完整。两个和弦均为大三和弦。
Example: F major → C major in the key of C | 示例：C大调中 F → C
12. Chord-Inversion Formula | 和弦转位公式
A chord is in root position when the root is the lowest note. 1st inversion has the 3rd in the bass; 2nd inversion has the 5th in the bass. The pattern of intervals above the bass shifts, changing the colour while keeping the chord identity.
根音为最低音时，和弦处于原位。第一转位以三音为低音；第二转位以五音为低音。低音上方的音程模式改变，带来不同色彩，但和弦身份保持不变。
Root position: root–3rd–5th | 原位：根–3–5
1st inversion: 3rd–5th–root | 第一转位：3–5–根
2nd inversion: 5th–root–3rd | 第二转位：5–根–3
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