📚 Year 10 Edexcel Music: Formula & Theorem Quick Reference | 爱德思音乐：公式定理速查手册
This handbook distils the most important music theory 'formulae' and 'theorems' you will encounter in the Year 10 Edexcel Music course. From scale construction and interval counting to chord building and cadence patterns, these rules function like mathematical formulas – apply them correctly, and you can unlock accurate analysis and confident composition.
本手册浓缩了你在 Year 10 Edexcel 音乐课程中将遇到的最重要的音乐理论“公式”与“定理”。从音阶构建、音程计算到和弦构成和终止式模式，这些规则就像数学公式一样，只要正确运用，你就能解锁精准的分析和自信的创作。
1. Major Scale Formula | 大调音阶公式
A major scale follows a fixed pattern of whole tones (T) and semitones (S): T – T – S – T – T – T – S. Starting on any tonic note, apply this stepwise formula to determine the seven pitch classes of the major scale. For example, C major: C (T) D (T) E (S) F (T) G (T) A (T) B (S) C.
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。从任意主音开始，应用这个逐级公式即可确定大调的七个音级。例如 C 大调：C (T) D (T) E (S) F (T) G (T) A (T) B (S) C。
The formula can be expressed in semitones between adjacent degrees: 2 – 2 – 1 – 2 – 2 – 2 – 1. This numerical approach helps when working with a keyboard or fretboard.
该公式也可以用相邻级之间的半音数表示：2 – 2 – 1 – 2 – 2 – 2 – 1。这种数字化的方法在键盘或指板上操作时很有帮助。
2. 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. In semitones: 2 – 1 – 2 – 2 – 1 – 2 – 2. This is equivalent to playing a major scale from its sixth degree (Aeolian mode). For A natural minor: A (T) B (S) C (T) D (T) E (S) F (T) G (T) A.
自然小调音阶的模式为：T – S – T – T – S – T – T。半音数为：2 – 1 – 2 – 2 – 1 – 2 – 2。这相当于从大调第六级开始演奏（爱奥里亚调式）。以 A 自然小调为例：A (T) B (S) C (T) D (T) E (S) F (T) G (T) A。
3. Harmonic and Melodic Minor Formulae | 和声与旋律小调公式
Harmonic minor: T – S – T – T – S – 3 semitones (augmented 2nd) – S. In semitones: 2 – 1 – 2 – 2 – 1 – 3 – 1. This raises the 7th degree of the natural minor by a semitone, creating a distinctive gap between the 6th and 7th degrees.
和声小调：T – S – T – T – S – 3 个半音（增二度）– S。半音序列为：2 – 1 – 2 – 2 – 1 – 3 – 1。它将自然小调的第七级升高半音，从而使第六级与第七级之间产生鲜明的间隙。
Melodic minor (ascending): T – S – T – T – T – T – S. In semitones: 2 – 1 – 2 – 2 – 2 – 2 – 1. This raises both the 6th and 7th degrees from the natural minor, resembling a major scale with a lowered 3rd. Descending melodic minor typically reverts to the natural minor pattern.
旋律小调（上行）：T – S – T – T – T – T – S。半音数为：2 – 1 – 2 – 2 – 2 – 2 – 1。它将自然小调的第六级和第七级都升高半音，类似于降低了三级的大调音阶。下行旋律小调通常返回自然小调模式。
4. Interval 'Formula' – Semitone Counting | 音程“公式”——按半音数计算
Intervals are most reliably identified by counting the number of semitones between two notes. The basic mapping between interval quality and semitone count is shown below. Always check the letter-name distance first to determine the ordinal (2nd, 3rd, 4th, etc.).
通过计算两个音之间的半音数量可以最可靠地识别音程。音程性质与半音数的基本对应关系如下表。务必首先检查字母音名距离来确定序数（二度、三度、四度等）。
| Interval | Semitones | 中文音程 |
|---|---|---|
| Perfect Unison | 0 | 纯一度 |
| Minor 2nd | 1 | 小二度 |
| Major 2nd | 2 | 大二度 |
| Minor 3rd | 3 | 小三度 |
| Major 3rd | 4 | 大三度 |
| Perfect 4th | 5 | 纯四度 |
| Augmented 4th / Diminished 5th | 6 | 增四度 / 减五度 |
| Perfect 5th | 7 | 纯五度 |
| Minor 6th | 8 | 小六度 |
| Major 6th | 9 | 大六度 |
| Minor 7th | 10 | 小七度 |
| Major 7th | 11 | 大七度 |
| Perfect Octave | 12 | 纯八度 |
5. Triad Chord Formulae | 三和弦公式
A triad is built by stacking two thirds on top of a root. The quality of the triad depends on the combination of major 3rds (4 semitones) and minor 3rds (3 semitones). Learn these as fixed patterns.
三和弦是在根音之上叠加两个三度构建而成的。三和弦的性质取决于大三度（4 个半音）和小三度（3 个半音）的组合。请掌握这些固定模式。
- Major triad: Root + 4 semitones + 3 semitones. E.g., C–E–G.
- 大三和弦：根音 + 4 个半音 + 3 个半音。例如 C–E–G。
- Minor triad: Root + 3 semitones + 4 semitones. E.g., A–C–E.
- 小三和弦：根音 + 3 个半音 + 4 个半音。例如 A–C–E。
- Diminished triad: Root + 3 semitones + 3 semitones. E.g., B–D–F.
- 减三和弦：根音 + 3 个半音 + 3 个半音。例如 B–D–F。
- Augmented triad: Root + 4 semitones + 4 semitones. E.g., C–E–G♯.
- 增三和弦：根音 + 4 个半音 + 4 个半音。例如 C–E–G♯。
6. Seventh Chord Formulae | 七和弦公式
Adding a third on top of a triad creates a seventh chord. The most common combinations appear in the table below. Remember that a chord is named after its triad quality plus its seventh interval quality.
在三和弦上方再叠加一个三度就构成了七和弦。最常见的组合如下表。记住，七和弦的名称由下方的三和弦性质加上其七度音程性质决定。
| Chord type | Semitone pattern from root | 中文类型 |
|---|---|---|
| Major 7th | 0 – 4 – 7 – 11 | 大七和弦 |
| Dominant 7th | 0 – 4 – 7 – 10 | 属七和弦 |
| Minor 7th | 0 – 3 – 7 – 10 | 小七和弦 |
| Half-diminished 7th | 0 – 3 – 6 – 10 | 半减七和弦 |
| Diminished 7th | 0 – 3 – 6 – 9 | 减七和弦 |
Alternatively, you can think of a dominant 7th as a major triad + minor 7th; a major 7th as major triad + major 7th; and a minor 7th as minor triad + minor 7th.
或者也可以这样理解：属七和弦 = 大三和弦 + 小七度；大七和弦 = 大三和弦 + 大七度；小七和弦 = 小三和弦 + 小七度。
7. Key Signature 'Theorem' – Order of Sharps and Flats | 调号“定理”——升号和降号的次序
Key signatures follow immutable patterns. Sharps always appear in this order: F♯ C♯ G♯ D♯ A♯ E♯ B♯. Flats always appear in 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 flats: the second-to-last flat is the major key.
调号遵循不变的规律。升号总是按此顺序出现：F♯ C♯ G♯ D♯ A♯ E♯ B♯。降号则相反：B♭ E♭ A♭ D♭ G♭ C♭ F♭。由升号调号推大调的方法：取最后一个升号，再升高半音。由降号调号推大调：倒数第二个降号即为大调主音。
The relative minor is always a minor third (3 semitones) below the major tonic. This relationship is a theorem in itself: once you have the major key, subtract 3 semitones to obtain the relative minor.
关系小调总是比大调主音低小三度（3 个半音）。这个关系本身就像一条定理：一旦有了大调，减去 3 个半音即得到关系小调。
8. Circle of Fifths as a 'Formula Wheel' | 五度圈——公式转盘
The circle of fifths is a visual formula that organises all 12 pitches by perfect fifths. Moving clockwise adds a sharp (or removes a flat); moving anticlockwise adds a flat (or removes a sharp). Adjacent keys share six of their seven notes, which is why modulations often move to neighbouring keys on the circle.
五度圈是一个视觉化的公式，将 12 个音按纯五度关系组织起来。顺时针移动增加一个升号（或去掉一个降号）；逆时针移动增加一个降号（或去掉一个升号）。相邻的调共享七音中的六音，因此转调常常转向五度圈上相邻的调。
To construct the circle, start at C major (0 sharps/flats). Go up a perfect 5th to G major (1 sharp), then D (2 sharps), A (3 sharps), and so on. Going down a 5th takes you to F (1 flat), B♭ (2 flats), etc. This formula ensures you never get lost in key relationships.
构建五度圈：从 C 大调（0 升降号）开始。向上一个纯五度到 G 大调（1 升号），再到 D（2 升号），A（3 升号）等等。向下一个五度则到 F（1 降号），B♭（2 降号）等。这条公式确保你永远不会在调性关系中迷路。
9. Cadence 'Theorems' | 终止式“定理”
Cadences are chord progressions at phrase endings that function like musical punctuation. The four main cadences each have a fixed chord formula in a major key (using roman numerals).
终止式是乐句结尾的和弦进行，相当于音乐的标点符号。四种主要终止式在大调中各自遵循固定的和弦公式（使用罗马数字标记）。
| Cadence | Chord formula (major) | 中文 |
|---|---|---|
| Perfect (Authentic) | V – I | 正格终止 |
| Plagal | IV – I | 变格终止 |
| Imperfect | I – V, ii – V, IV – V (any to V) | 半终止 |
| Interrupted (Deceptive) | V – vi | 阻碍终止 |
In a minor key, the dominant chord is major (V) due to the raised leading note, so perfect and interrupted cadences still use the major V. Plagal cadences in minor use iv – i, and imperfect cadences frequently lead to the major V.
在小调中，导音升高使得属和弦为大三和弦（V），因此正格终止和阻碍终止仍然使用大三的 V。小调变格终止为 iv – i，半终止常常进行到大三的 V。
10. Time Signature and Rhythm Calculations | 拍号与节奏计算
Time signatures are not just conventions; they encode mathematical relationships. The top number indicates how many beats per bar, and the bottom number indicates the beat unit. For rhythmic arithmetic, think in terms of fractions of a whole note (semibreve).
拍号并不仅仅是习惯用法，它们编码了数学关系。上方数字代表每小节有几拍，下方数字代表以哪种音符为一拍。进行节奏运算时，可以理解为全音符的分数。
ets = 3 quavers. Triplet three-quaver group = 2 regular quavers in time value. These are essential formulae for accurate rhythmic dictation and score reading.
关键等值关系：一个全音符 = 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。附点增加音符时值的一半：附点四分音符 = 1.5 个四分音符 = 3 个八分音符。三连音三个八分音符 = 常规 2 个八分音符的时值。这些都是确保节奏听写和读谱准确的必要公式。
11. Inversion Symbols and Figured Bass Shorthand | 转位标记与数字低音速记
Chord inversions follow a systematic shorthand derived from figured bass. The intervals above the lowest bass note are expressed as numbers, forming a mini 'formula' for each inversion.
和弦转位遵循一套源自数字低音的系统化速记。最低音上方的音程用数字表示，构成了每种转位的小型“公式”。
| Position | Triad formula | Seventh chord formula | 中文 |
|---|---|---|---|
| Root | ⁵⁄₃ or nothing | ⁷ | 原位 |
| 1st inversion | ⁶⁄₃ or ⁶ | ⁶⁄₅ | 第一转位 |
| 2nd inversion | ⁶⁄₄ | ⁴⁄₃ | 第二转位 |
| 3rd inversion | N/A | ⁴⁄₂ or ² | 第三转位 |
In Roman numeral analysis, inversions are shown with a letter: 'a' for root, 'b' for first inversion, 'c' for second inversion (e.g., Ib, IVb). Relating these to figured bass numbers strengthens your understanding of voice leading.
在罗马数字分析中，转位用字母表示：'a' 原位，'b' 第一转位，'c' 第二转位（例如 Ib，IVb）。将这些与数字低音关联起来，可以加深你对声部进行的理解。
12. Modes as Rotations of the Major Scale | 调式——大调音阶的轮转
Each mode of the major scale is a simple rotational formula. By starting and ending the major scale on a different degree, you produce a distinct mode with its own quality. The table below lists the seven modes and their characteristic 'colour' tone.
大调音阶的每一种调式都是一个简单的轮转公式。在大调音阶中从不同的级数开始并结束，就会产生具有独特性质的调式。下表列出了七种调式及其特征音。
| Mode | Starts on degree | Semitone pattern (T/S) | 中文调式 |
|---|---|---|---|
| Ionian (Major) | 1 | T T S T T T S | 伊奥尼亚 |
| Dorian | 2 | T S T T T S T | 多利亚 |
| Phrygian | 3 | S T T T S T T | 弗里几亚 |
| Lydian | 4 | T T T S T T S | 利底亚 |
| Mixolydian | 5 | T T S T T S T | 混合利底亚 |
| Aeolian (Natural Minor) | 6 | T S T T S T T | 爱奥里亚 |
| Locrian | 7 | S T T S T T T | 洛克里亚 |
e its parent is C major. The theorem is simply: mode X = major scale starting on degree Y.
请记住，调号仍保持原大调的调号，但主音发生了转移。例如 D 多利亚没有升降号，因为它的母调是 C 大调。其“定理”很简单：X 调式 = 从 Y 级开始的大调音阶。
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