📚 Year 10 Eduqas Music: Quick Reference Formula & Theorem Handbook | Year 10 Eduqas 音乐：公式定理速查手册
Music is built on precise mathematical relationships, pattern-based structures, and repeatable formulas. From the construction of scales and chords to the calculation of intervals, time signatures, and cadences, a solid grasp of these "formulae and theorems" turns note-reading into deeper understanding. This handbook compiles the essential rules, patterns, and quick-reference tables needed for Year 10 Eduqas Music, presenting every concept in a clear, bilingual format so you can check facts at a glance.
音乐建立在精确的数学关系、基于模式的结构和可重复的公式之上。从音阶与和弦的构建，到音程、拍号和终止式的计算，扎实掌握这些“公式与定理”能将读谱转化为更深层次的理解。本手册汇编了 Year 10 Eduqas 音乐所需的基本规则、模式和速查表，以清晰的双语形式呈现，让你一目了然地查阅要点。
1. Understanding Semitones and Tones | 理解半音与全音
A semitone (half step) is the smallest interval used in Western tonal music. On a piano, it is the distance from any key to the very next key, whether white to black, black to white, or in the case of E–F and B–C, white to white.
半音（半音步）是西方调性音乐中使用的最小音程。在钢琴上，它是从任意一个琴键到下一个相邻琴键的距离，无论是白键到黑键、黑键到白键，还是像 E–F 和 B–C 那样的白键到白键。
A tone (whole step) consists of two semitones, skipping exactly one key on the keyboard. Semitones and tones are the fundamental building blocks of all scales and chords.
全音（全音步）由两个半音组成，在键盘上跳过一个琴键。半音和全音是所有音阶与和弦的基本构件。
2. The Major Scale Formula | 大调音阶公式
Every major scale follows an identical pattern of tones and semitones, regardless of starting note. This formula is one of the most important theorems in music theory and must be internalised for quick transposition and key signature work.
每个大调音阶无论从哪个音开始，都遵循完全相同的全音与半音模式。这个公式是音乐理论中最重要的定理之一，必须熟记以便快速移调和处理调号。
Major Scale Formula: W – W – H – W – W – W – H
大调音阶公式：全 – 全 – 半 – 全 – 全 – 全 – 半
In words: Whole, Whole, Half, Whole, Whole, Whole, Half. Starting on C, this gives C–D (W), D–E (W), E–F (H), F–G (W), G–A (W), A–B (W), B–C (H), producing the C major scale with no sharps or flats. Apply the same sequence to any tonic to generate its major scale.
也就是说：全音、全音、半音、全音、全音、全音、半音。从 C 开始，得到 C–D（全）、D–E（全）、E–F（半）、F–G（全）、G–A（全）、A–B（全）、B–C（半），构成没有升降号的 C 大调音阶。将相同的序列应用于任何主音即可生成其大调音阶。
3. The Natural Minor Scale Formula | 自然小调音阶公式
The natural minor scale uses a different tone–semitone pattern. It can also be derived from the major scale by lowering the 3rd, 6th, and 7th degrees by one semitone.
自然小调音阶使用不同的全音–半音模式。它也可以通过将大调音阶的第 3、6、7 级音降低半音而得到。
Natural Minor Scale Formula: W – H – W – W – H – W – W
自然小调音阶公式：全 – 半 – 全 – 全 – 半 – 全 – 全
Starting on A, this yields A–B (W), B–C (H), C–D (W), D–E (W), E–F (H), F–G (W), G–A (W), giving A natural minor with no sharps or flats. The pattern is also the same as the Aeolian mode.
从 A 开始，产生 A–B（全）、B–C（半）、C–D（全）、D–E（全）、E–F（半）、F–G（全）、G–A（全），得到没有升降号的 A 自然小调。这一模式也等同于爱奥尼亚调式之外的艾奥里亚调式。
4. Harmonic and Melodic Minor Adjustments | 和声与旋律小调的调整
The harmonic minor scale raises the 7th degree of the natural minor by a semitone, creating a distinctive augmented 2nd interval between the 6th and 7th degrees. The formula becomes: W – H – W – W – H – (W+H) – H, where (W+H) represents an augmented 2nd of three semitones.
和声小调音阶将自然小调的第 7 级音升高半音，在第 6 级和第 7 级之间产生一个特有的增二度音程。其公式变为：全 – 半 – 全 – 全 – 半 – （全+半） – 半，其中（全+半）代表三个半音的增二度。
The melodic minor scale raises both the 6th and 7th degrees when ascending (to avoid the augmented 2nd) and reverts to the natural minor when descending. Ascending formula: W – H – W – W – W – W – H. Descending: W – W – H – W – W – H – W.
旋律小调音阶在上行时升高第 6 和第 7 级音（以避免增二度），下行时恢复为自然小调。上行公式：全 – 半 – 全 – 全 – 全 – 全 – 半。下行公式：全 – 全 – 半 – 全 – 全 – 半 – 全。
5. Interval Construction and Qualities | 音程的构建与性质
An interval is defined by its number (2nd, 3rd, 4th, etc.) and its quality (major, minor, perfect, augmented, diminished). The core rule: the number counts letter names inclusive, and the quality depends on the exact number of semitones between the two pitches.
音程由其度数（二度、三度、四度等）和性质（大、小、纯、增、减）来定义。核心规则是：度数在字母名上包含两端计算，而性质取决于两个音高之间确切的半音数量。
The table below gives the semitone count for common intervals under the standard tuning system. Use it as a quick reference when identifying or building intervals.
下表列出了标准律制下常见音程的半音数。用于识别或构建音程时的快速参考。
| Interval Name / 音程名称 | Semitones / 半音数 |
|---|---|
| Perfect Unison / 纯一度 | 0 |
| Minor 2nd / 小二度 | 1 |
| Major 2nd / 大二度 | 2 |
| Minor 3rd / 小三度 | 3 |
| Major 3rd / 大三度 | 4 |
| Perfect 4th / 纯四度 | 5 |
| Augmented 4th / Diminished 5th / 增四度 / 减五度 | 6 |
| Perfect 5th / 纯五度 | 7 |
| Minor 6th / 小六度 | 8 |
| Major 6th / 大六度 | 9 |
| Minor 7th / 小七度 | 10 |
| Major 7th / 大七度 | 11 |
| Perfect Octave / 纯八度 | 12 |
To find an interval from a given note, count the letter names for the number, then adjust by semitones to match the quality. For example, C to E spans three letters (C-D-E), so it is a 3rd; four semitones make it a major 3rd.
从给定的音找出音程时，先按字母名数出度数，再根据半音数调整性质。例如 C 到 E 跨越三个字母名（C-D-E），所以是三度；四个半音使其成为大三度。
6. Triad Chord Formulas | 三和弦公式
A triad is a three-note chord stacked in thirds. The quality of the triad is determined by the exact arrangement of major and minor thirds, measured in semitones from the root upward. The following formulas are essential for Eduqas listening, composing, and score-reading tasks.
三和弦是由三个按三度叠置的音构成的和弦。三和弦的性质由大三度和小三度的具体排列决定，并从根音向上用半音衡量。以下的公式对于 Eduqas 的听力、作曲和读谱任务至关重要。
| Chord Type / 和弦类型 | Formula from Root / 自根音起的公式 | Example on C / C 音示例 |
|---|---|---|
| Major / 大三和弦 | 4 semitones + 3 semitones | C–E–G |
| Minor / 小三和弦 | 3 semitones + 4 semitones | C–E♭–G |
| Diminished / 减三和弦 | 3 semitones + 3 semitones | C–E♭–G♭ |
| Augmented / 增三和弦 | 4 semitones + 4 semitones | C–E–G♯ |
To build a major triad: root + major 3rd (4 semitones) + perfect 5th (7 semitones from root). The minor triad replaces the major 3rd with a minor 3rd (3 semitones). The diminished triad uses a minor 3rd and a diminished 5th (6 semitones), while the augmented triad uses a major 3rd and an augmented 5th (8 semitones).
构建大三和弦：根音 + 大三度（4 个半音）+ 纯五度（自根音起 7 个半音）。小三和弦将大三度换成小三度（3 个半音）。减三和弦使用小三度和减五度（6 个半音），而增三和弦使用大三度和增五度（8 个半音）。
7. Seventh Chord Construction | 七和弦的构建
Adding a 7th above the root to a triad creates a seventh chord, which introduces richer harmonic colour. The type of 7th is defined by the interval it makes with the root, and its combination with the underlying triad follows fixed formulas.
在三和弦根音上方添加七度音便构成七和弦，带来更丰富的和声色彩。七度音的类型由它与根音构成的音程决定，它与下方三和弦的组合遵循固定公式。
| Seventh Chord / 七和弦 | Triad + 7th from Root / 三和弦 + 根音上方的七度音 | C Root Example / C 根音示例 |
|---|---|---|
| Major 7th / 大七和弦 | Major triad + Major 7th (11 semitones) | C–E–G–B |
| Dominant 7th / 属七和弦 | Major triad + Minor 7th (10 semitones) | C–E–G–B♭ |
| Minor 7th / 小七和弦 | Minor triad + Minor 7th (10 semitones) | C–E♭–G–B♭ |
| Half-diminished 7th / 半减七和弦 | Diminished triad + Minor 7th (10 semitones) | C–E♭–G♭–B♭ |
| Diminished 7th / 减七和弦 | Diminished triad + Diminished 7th (9 semitones) | C–E♭–G♭–B𝄫 (A) |
The dominant 7th is particularly important in functional harmony because it contains a tritone between the 3rd and 7th of the chord, creating a strong pull towards the tonic. These formulas allow you to spell any seventh chord quickly.
属七和弦在功能和声中尤为重要，因为它在和弦的三音与七音之间包含一个三全音，对主音产生强烈的倾向。这些公式让你能迅速拼出任何七和弦。
8. Circle of Fifths and Key Signatures | 五度圈与调号体系
The Circle of Fifths arranges keys so that each step clockwise adds one sharp (or removes one flat), and each step anticlockwise adds one flat (or removes one sharp). This is the central theorem for understanding key relationships and accidentals.
五度圈将各调排列，顺时针每走一步增加一个升号（或减少一个降号），逆时针每走一步增加一个降号（或减少一个升号）。这是理解调性关系及变音记号的核心定理。
Sharp keys order of addition: F♯ C♯ G♯ D♯ A♯ E♯ B♯ (mnemonic: Father Charles Goes Down And Ends Battle). Flat keys order: B♭ E♭ A♭ D♭ G♭ C♭ F♭ (Battle Ends And Down Goes Charles' Father).
升号调增加的顺序：F♯ C♯ G♯ D♯ A♯ E♯ B♯（记忆口诀：Father Charles Goes Down And Ends Battle）。降号调的顺序：B♭ E♭ A♭ D♭ G♭ C♭ F♭（Battle Ends And Down Goes Charles' Father）。
| Major Key / 大调 | Sharps / 升号数 | Sharps Names / 升号音名 |
|---|---|---|
| C | 0 | – |
| G | 1 | F♯ |
| D | 2 | F♯, C♯ |
| A | 3 | F♯, C♯, G♯ |
| E | 4 | F♯, C♯, G♯, D♯ |
| B | 5 | F♯, C♯, G♯, D♯, A♯ |
| F♯ | 6 | F♯, C♯, G♯, D♯, A♯, E♯ |
| C♯ | 7 | F♯, C♯, G♯, D♯, A♯, E♯, B♯ |
For flat keys, the table is mirrored: F major has 1 flat (B♭), B♭ major has 2 flats (B♭, E♭), and so on. The last flat in the key signature is always the subdominant, while the last sharp is the leading note.
降号调的表与之镜像：F 大调有 1 个降号（B♭），B♭ 大调有 2 个降号（B♭, E♭），依此类推。调号中的最后一个降号总是下属音，而最后一个升号总是导音。
9. Time Signatures and Meter Basics | 拍号与节拍基础
A time signature states how many beats are in each bar (top number) and what note value counts as one beat (bottom number). Simple time signatures have beats that divide naturally into two; compound time signatures divide the beat into three equal parts.
拍号标明每小节有多少拍（上方数字）以及以什么音符为一拍（下方数字）。单拍子的每一拍自然分为二等分；复拍子则将一拍分为三等分。
Simple Duple/Triple/Quadruple: 2/4, 3/4, 4/4; Compound Duple/Triple/Quadruple: 6/8, 9/8, 12/8
单二拍子/单三拍子/单四拍子：2/4、3/4、4/4；复二拍子/复三拍子/复四拍子：6/8、9/8、12/8
In compound time, the beat is a dotted note. For example, in 6/8 there are two dotted-crotchet beats per bar. The note values add up as follows: 3 quavers = 1 dotted crotchet beat. This "three-quavers-per-beat" rule is a core theorem for rhythmic grouping.
在复拍子中，拍是附
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