📚 Year 9 Edexcel Music: Formula & Theorem Quick Reference Handbook | Year 9 Edexcel 音乐：公式定理速查手册
This handbook compiles the essential formulas, rules and theorems you need to master for the Year 9 Edexcel Music curriculum. From intervals and scale patterns to chord building and rhythmic relationships, these principles form the backbone of music theory and analysis. Keep this guide with you when practising aural skills, composing, or preparing for your listening exam.
这本手册汇编了 Year 9 Edexcel 音乐课程必须掌握的基本公式、规则和定理。从音程和音阶模式到和弦构建以及节奏关系，这些原理构成了音乐理论和分析的支柱。在练习听力、作曲或准备听力考试时，请将此指南放在手边。
1. Semitone and Tone Rule | 半音与全音法则
A semitone is the smallest interval used in Western music, the distance between two adjacent keys on a piano. A tone equals two semitones. The pattern of tones and semitones determines the quality of scales and intervals.
半音是西方音乐中使用的最小音程，即钢琴上两个相邻琴键之间的距离。一个全音等于两个半音。全音和半音的模式决定了音阶和音程的性质。
The chromatic scale moves entirely by semitones. On a keyboard, E to F and B to C are natural semitones because no black key lies between them. Every other natural note pair is a tone apart.
半音阶完全由半音移动构成。在键盘上，E 到 F 以及 B 到 C 是自然的半音，因为它们之间没有黑键。其他每对自然音之间的距离都是全音。
2. Major Scale Formula | 大调音阶公式
The major scale follows a fixed pattern of tones (T) and semitones (S): T - T - S - T - T - T - S. Starting on any note and applying this sequence will produce a major scale.
大调音阶遵循固定的全音 (T) 和半音 (S) 模式：T - T - S - T - T - T - S。从任何音开始应用此序列，即可生成一个大调音阶。
For example, C major: C - T - D - T - E - S - F - T - G - T - A - T - B - S - C. The sharps or flats required are placed in the key signature. G major uses F♯ to preserve the pattern; F major uses B♭.
例如 C 大调：C - T - D - T - E - S - F - T - G - T - A - T - B - S - C。所需的升号或降号放在调号中。G 大调使用 F♯ 来保持模式；F 大调使用 B♭。
3. Natural Minor Scale Formula | 自然小调音阶公式
The natural minor scale pattern is: T - S - T - T - S - T - T. A minor is the relative minor of C major and uses the same key signature (no sharps or flats).
自然小调音阶的模式是：T - S - T - T - S - T - T。A 小调是 C 大调的关系小调，使用相同的调号（无升号或降号）。
To find the relative minor of any major key, count down three semitones from the major key tonic. For instance, G major's relative minor is E minor; D major's is B minor.
要找到任何大调的关系小调，从大调主音向下数三个半音。例如 G 大调的关系小调是 E 小调；D 大调的关系小调是 B 小调。
4. Interval Formula Based on Semitones | 基于半音的音程公式
An interval is the distance between two pitches, named by a number (size) and a quality (major, minor, perfect, augmented, diminished). Within an octave, common intervals can be memorised by semitone count:
音程是两个音高之间的距离，由数字（度数）和性质（大、小、纯、增、减）命名。在一个八度内，常见的音程可以通过半音数量来记忆：
| Semitones | Interval | 半音数 | 音程 |
|---|---|---|---|
| 0 | Perfect unison | 0 | 纯一度 |
| 1 | Minor 2nd | 1 | 小二度 |
| 2 | Major 2nd | 2 | 大二度 |
| 3 | Minor 3rd | 3 | 小三度 |
| 4 | Major 3rd | 4 | 大三度 |
| 5 | Perfect 4th | 5 | 纯四度 |
| 6 | Tritone (Aug 4th / Dim 5th) | 6 | 三全音（增四度/减五度） |
| 7 | Perfect 5th | 7 | 纯五度 |
| 8 | Minor 6th | 8 | 小六度 |
| 9 | Major 6th | 9 | 大六度 |
| 10 | Minor 7th | 10 | 小七度 |
| 11 | Major 7th | 11 | 大七度 |
| 12 | Perfect octave | 12 | 纯八度 |
When an interval is inverted, the new interval number plus the original number always equals 9. Also, major becomes minor, perfect stays perfect, and augmented becomes diminished.
当一个音程转位后，新音程的度数加上原音程度数总是等于 9。同时，大音程变为小音程，纯音程保持为纯，增音程变为减音程。
5. Triad Construction Rules | 三和弦构建规则
A triad is a three-note chord built from two superimposed thirds. There are four main types:
三和弦是由两个叠加的三度构成的三音和弦。主要有四种类型：
Major triad: root + major 3rd + perfect 5th (e.g., C - E - G). Semitone count from root: 4 + 3.
Minor triad: root + minor 3rd + perfect 5th (e.g., C - E♭ - G). Semitone count: 3 + 4.
Diminished triad: root + minor 3rd + diminished 5th (e.g., C - E♭ - G♭). Semitone count: 3 + 3.
Augmented triad: root + major 3rd + augmented 5th (e.g., C - E - G♯). Semitone count: 4 + 4.
大三和弦： 根音 + 大三度 + 纯五度（例如 C - E - G）。半音数从根音算起：4 + 3。
小三和弦： 根音 + 小三度 + 纯五度（例如 C - E♭ - G）。半音数：3 + 4。
减三和弦： 根音 + 小三度 + 减五度（例如 C - E♭ - G♭）。半音数：3 + 3。
增三和弦： 根音 + 大三度 + 增五度（例如 C - E - G♯）。半音数：4 + 4。
Triads on each scale degree have predictable qualities. In a major key, chords I, IV, V are major; ii, iii, vi are minor; vii° is diminished. In a natural minor key, i, iv, v are minor; III, VI, VII are major; ii° is diminished.
每个调式音级上的三和弦有可预测的性质。在大调中，和弦 I, IV, V 是大三和弦；ii, iii, vi 是小三和弦；vii° 是减三和弦。在自然小调中，i, iv, v 是小三和弦；III, VI, VII 是大三和弦；ii° 是減三和弦。
6. Seventh Chord Building Blocks | 七和弦构建模块
A seventh chord adds a fourth note to a triad, a seventh above the root. The most common ones follow these semitone structures (counting from the root):
七和弦在三和弦基础上增加第四个音，即根音上方的七度音。最常见的七和弦遵循以下半音结构（从根音算起）：
- Major 7th: 4 + 3 + 4 (root - major 3rd - perfect 5th - major 7th). Example: C - E - G - B.
- Dominant 7th: 4 + 3 + 3 (root - major 3rd - perfect 5th - minor 7th). Example: C - E - G - B♭.
- Minor 7th: 3 + 4 + 3 (root - minor 3rd - perfect 5th - minor 7th). Example: C - E♭ - G - B♭.
- Half-diminished 7th: 3 + 3 + 4 (root - minor 3rd - diminished 5th - minor 7th). Example: C - E♭ - G♭ - B♭.
- Diminished 7th: 3 + 3 + 3 (root - minor 3rd - diminished 5th - diminished 7th). Example: C - E♭ - G♭ - B♭♭.
- 大七和弦： 4 + 3 + 4（根音 - 大三度 - 纯五度 - 大七度）。例如：C - E - G - B。
- 属七和弦： 4 + 3 + 3（根音 - 大三度 - 纯五度 - 小七度）。例如：C - E - G - B♭。
- 小七和弦： 3 + 4 + 3（根音 - 小三度 - 纯五度 - 小七度）。例如：C - E♭ - G - B♭。
- 半减七和弦： 3 + 3 + 4（根音 - 小三度 - 减五度 - 小七度）。例如：C - E♭ - G♭ - B♭。
- 减七和弦： 3 + 3 + 3（根音 - 小三度 - 减五度 - 减七度）。例如：C - E♭ - G♭ - B♭♭。
The dominant seventh built on the 5th scale degree (V⁷) has a strong pull back to the tonic and is crucial in functional harmony.
建立在第 5 音级上的属七和弦 (V⁷) 对主音有强烈的倾向性，在功能性和声中至关重要。
7. Key Signature Identification Theorem | 调号识别定理
For sharp key signatures: take the last sharp and raise it by a semitone to find the major key name. For example, if the last sharp is D♯, the key is E major.
对于升号调号：取最后一个升号，升高半音，即为大调名称。例如，若最后一个升号是 D♯，则大调是 E 大调。
For flat key signatures: the second-to-last flat gives the major key name. The exception is F major, which has one flat (B♭). E♭ major has B♭, E♭, A♭ - the second-to-last flat is E♭, so the key is E♭ major.
对于降号调号：倒数第二个降号即为大调名称。例外是 F 大调，它只有一个降号 (B♭)。E♭ 大调有 B♭, E♭, A♭，倒数第二个降号是 E♭，因此大调是 E♭ 大调。
Relative minors share the same key signature. So if the key signature has three sharps (F♯, C♯, G♯), the major key is A major, and the relative minor is F♯ minor.
关系小调共用相同的调号。因此若调号有三个升号 (F♯, C♯, G♯)，大调是 A 大调，关系小调是 F♯ 小调。
8. Circle of Fifths Order | 五度圈顺序
The circle of fifths arranges keys according to the perfect fifth interval. Moving clockwise from C major (0 sharps/flats), each step adds one sharp: G, D, A, E, B, F♯, C♯. Moving anticlockwise adds one flat: F, B♭, E♭, A♭, D♭, G♭, C♭.
五度圈根据纯五度音程排列调性。从 C 大调（无升降号）开始顺时针移动，每一步增加一个升号：G, D, A, E, B, F♯, C♯。逆时针移动增加一个降号：F, B♭, E♭, A♭, D♭, G♭, C♭。
The sharp order (Father Charles Goes Down And Ends Battle): F♯, C♯, G♯, D♯, A♯, E♯, B♯. The flat order is the reverse: B♭, E♭, A♭, D♭, G♭, C♭, F♭.
升号顺序（Father Charles Goes Down And Ends Battle）：F♯, C♯, G♯, D♯, A♯, E♯, B♯。降号顺序是反向的：B♭, E♭, A♭, D♭, G♭, C♭, F♭。
9. Time Signature and Beat Hierarchy | 拍号与节拍层级
umber indicates the note value that equals one beat (2 = minim, 4 = crotchet, 8 = quaver).
拍号告诉你音乐如何组织进小节。上方数字表示每小节有多少拍；下方数字表示以哪种音符为一拍（2 = 二分音符，4 = 四分音符，8 = 八分音符）。
Simple time signatures have beats that divide naturally into two equal parts. Compound time signatures have beats that divide into three equal parts. Formula quick check:
- Simple duple: 2/4, 2/2
- Simple triple: 3/4, 3/2
- Simple quadruple: 4/4 (C), 4/2
- Compound duple: 6/8 (two dotted-crotchet beats)
- Compound triple: 9/8
- Compound quadruple: 12/8
简单拍号的每拍自然分成两个均等部分。复合拍号的每拍自然分成三个均等部分。公式速查：
- 简单二拍子：2/4, 2/2
- 简单三拍子：3/4, 3/2
- 简单四拍子：4/4 (C), 4/2
- 复合二拍子：6/8（两个附点四分音符拍）
- 复合三拍子：9/8
- 复合四拍子：12/8
10. Rhythm Tree and Dotted Note Formula | 节奏树与附点音符公式
The rhythm tree shows how note values relate to each other:
节奏树展示了音符时值之间的关系：
- 1 semibreve = 2 minims = 4 crotchets = 8 quavers = 16 semiquavers.
- 1 minim = 2 crotchets = 4 quavers = 8 semiquavers.
- 1 crotchet = 2 quavers = 4 semiquavers.
- 1 quaver = 2 semiquavers.
- 1 个全音符 = 2 个二分音符 = 4 个四分音符 = 8 个八分音符 = 16 个十六分音符。
- 1 个二分音符 = 2 个四分音符 = 4 个八分音符 = 8 个十六分音符。
- 1 个四分音符 = 2 个八分音符 = 4 个十六分音符。
- 1 个八分音符 = 2 个十六分音符。
f again. A double-dotted crotchet = 1 + ½ + ¼ = 1¾ crotchets, equivalent to 7 semiquavers.
音符后面的附点增加原时值的一半。例如，一个附点四分音符 = 1 个四分音符 + 1 个八分音符 = 3 个八分音符。第二个附点再增加所加值的一半。双附点四分音符 = 1 + ½ + ¼ = 1¾ 个四分音符，相当于 7 个十六分音符。
11. Primary and Secondary Chord Functions | 正和弦与副和弦功能
In tonal harmony, the primary chords (I, IV, V) define the key. The tonic (I) is home; the subdominant (IV) provides motion away; the dominant (V) creates tension that pulls back to the tonic.
在调性和声中，正和弦 (I, IV, V) 确定调性。主和弦 (I) 是归宿；下属和弦 (IV) 提供向外移动的动力；属和弦 (V) 制造紧张感，倾向回到主和弦。
Common cadence formulas:
- Perfect cadence: V - I (strong, final).
- Plagal cadence: IV - I (Amen).
- Imperfect cadence: I - V, ii - V, IV - V (expectant).
- Interrupted cadence: V - vi (surprising).
常见终止式公式：
- 正格终止：V - I（强烈，结束感）。
- 变格终止：IV - I（阿们终止）。
- 半终止：I - V, ii - V, IV - V（期待感）。
- 阻碍终止：V - vi（令人意外）。
Secondary chords (ii, iii, vi, vii°) enrich the harmony. For example, ii often precedes V in a ii - V - I progression.
副和弦 (ii, iii, vi, vii°) 丰富和声色彩。例如 ii 常在 V 之前，形成 ii - V - I 进行。
12. Transposition Rule | 移调规则
To transpose a melody into a new key, first identify the interval of transposition between the original key note and the target key note. Then move every pitch by that same interval, keeping the quality of steps intact. Adjust accidentals according to the new key signature.
要将旋律移调到新调，首先确定原调主音与目标调主音之间的移调音程。然后将每个音高按相同音程移动，保持音程性质不变。根据新调号调整临时变音记号。
For example, transposing from C major to G major means moving every note up a perfect fifth (7 semitones). A note C becomes G, D becomes A, E becomes B, F becomes C (with F♯ in the new key, so F becomes F♯).
例如从 C 大调移调到 G 大调，意味着每个音向上移动一个纯五度（7 个半音）。音 C 变成 G，D 变成 A，E 变成 B，F 变成 C（在新调中 F 应为 F♯，所以 F 变为 F♯）。
When transposing instruments such as trumpet (B♭) or horn (F) are involved, the written pitch must be adjusted so the sounding pitch matches concert pitch. A B♭ trumpet sounds a major 2nd lower than written, so music for trumpet must be written a major 2nd higher than the desired concert sound.
当涉及到移调乐器如 B♭ 小号或 F 圆号时，记谱音高必须调整，以便实际音高与音乐会音高一致。B♭ 小号发出的音比记谱低大二度，因此小号谱必须比所需的音乐会音高大二度记写。
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