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KS3 OCR Music: Quick Reference Handbook of Formulas and Theorems | KS3 OCR 音乐：公式定理速查手册

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📚 KS3 OCR Music: Quick Reference Handbook of Formulas and Theorems | KS3 OCR 音乐：公式定理速查手册

This concise reference guide brings together the essential patterns, rules, and formulas that underpin KS3 OCR Music. From scale construction to chord building, from interval counting to time signatures, you can treat these as your musical theorems—ready to be applied in listening, composing, and performing.

这本速查手册汇集了支撑 KS3 OCR 音乐课程的核心模式、规则和公式。从音阶构建到和弦构成，从音程计算到拍号设置，你可以把它们当作音乐定理——随时在聆听、作曲和演奏中运用。

1. The Major Scale Formula | 大调音阶公式

Every major scale follows the same interval pattern of whole steps (W) and half steps (H): W – W – H – W – W – W – H. In terms of semitones, this is 2 – 2 – 1 – 2 – 2 – 2 – 1. Starting on any note and applying this sequence will produce a correct major scale, provided you use each letter name once and only once.

每个大调音阶都遵循相同的全音（W）与半音（H）模式：全 – 全 – 半 – 全 – 全 – 全 – 半。用半音数表达即为 2 – 2 – 1 – 2 – 2 – 2 – 1。从任意音开始，按照此顺序构建，并确保每个音名字母恰好使用一次，就能得到正确的大调音阶。

Step Movement Semitones Example (C Major)
1 to 2 Tone 2 C → D
2 to 3 Tone 2 D → E
3 to 4 Semitone 1 E → F
4 to 5 Tone 2 F → G
5 to 6 Tone 2 G → A
6 to 7 Tone 2 A → B
7 to 8 Semitone 1 B → C

Formula: W-W-H-W-W-W-H (2-2-1-2-2-2-1 semitones)

2. Natural Minor Scale Formula | 自然小调音阶公式

The natural minor scale uses the pattern W – H – W – W – H – W – W (semitones: 2 – 1 – 2 – 2 – 1 – 2 – 2). If you play a major scale but lower the 3rd, 6th, and 7th degrees by a semitone, you obtain the relative natural minor starting on the 6th degree of the major scale.

自然小调使用模式 全 – 半 – 全 – 全 – 半 – 全 – 全（半音数：2 – 1 – 2 – 2 – 1 – 2 – 2）。如果你将一个大调音阶的第3、第6和第7级音降低半音，就会得到以该大调第6级为主音的自然小调。

For example, A natural minor uses all white keys on the piano: A–B–C–D–E–F–G–A, matching the pattern exactly. The relative major is C major.

例如，A 自然小调使用钢琴的全部白键：A–B–C–D–E–F–G–A，完全符合该模式。其关系大调是 C 大调。

Natural Minor Formula: W-H-W-W-H-W-W

3. Harmonic and Melodic Minor Scales | 和声小调与旋律小调

The harmonic minor scale raises the 7th degree of the natural minor by a semitone, giving the pattern: W – H – W – W – H – A2 – H (A2 = augmented 2nd, three semitones). In semitones: 2 – 1 – 2 – 2 – 1 – 3 – 1. The melodic minor scale raises the 6th and 7th degrees when ascending: W – H – W – W – W – W – H (2–1–2–2–2–2–1) and typically reverts to the natural minor pattern when descending.

和声小调将自然小调的第7级升高半音，模式为：全 – 半 – 全 – 全 – 半 – 增二度 – 半（增二度为三个半音）。半音数：2 – 1 – 2 – 2 – 1 – 3 – 1。旋律小调在上行时升高第6、第7级：全 – 半 – 全 – 全 – 全 – 全 – 半（2–1–2–2–2–2–1），下行时通常还原为自然小调模式。

These altered minors create distinctive moods—harmonic minor sounding dramatic, and melodic minor balancing smoothness with a leading tone.

这些变化小调创造出独特的色彩——和声小调听感戏剧化，旋律小调则在导音与平滑旋律间取得平衡。

4. Interval Formulas: Measuring Distance | 音程计算公式：测量距离

An interval is the distance in semitones between two notes. Each interval name has a fixed semitone count:

音程是两音之间的半音距离。每个音程名称对应固定的半音数：

  • Minor 2nd: 1 semitone (e.g., E–F) / 小二度：1 个半音
  • Major 2nd: 2 semitones (C–D) / 大二度：2 个半音
  • Minor 3rd: 3 semitones (A–C) / 小三度：3 个半音
  • Major 3rd: 4 semitones (C–E) / 大三度：4 个半音
  • Perfect 4th: 5 semitones (G–C) / 纯四度：5 个半音
  • Tritone (augmented 4th/diminished 5th): 6 semitones / 三全音（增四度/减五度）：6 个半音
  • Perfect 5th: 7 semitones (C–G) / 纯五度：7 个半音
  • Minor 6th: 8 semitones (E–C) / 小六度：8 个半音
  • Major 6th: 9 semitones (C–A) / 大六度：9 个半音
  • Minor 7th: 10 semitones (G–F) / 小七度：10 个半音
  • Major 7th: 11 semitones (C–B) / 大七度：11 个半音
  • Perfect Octave: 12 semitones / 纯八度：12 个半音

Always count the lower note as 0 when working with semitones, then add the number of steps upward.

计算半音时总是从下方音符开始数 0，然后逐步向上加。

5. Triad Construction Formulas | 三和弦构成公式

A triad is built by stacking two thirds on top of a root note. The quality is determined by the pattern of those thirds (in semitones):

三和弦是在根音上叠置两个三度构成的。其性质由这两个三度的半音数模式决定：

  • Major triad: root + 4 semitones (major 3rd) + 3 semitones (minor 3rd) → e.g., C–E–G / 大三和弦：根音 + 4 半音 + 3 半音
  • Minor triad: root + 3 semitones + 4 semitones → e.g., C–E♭–G / 小三和弦：根音 + 3 半音 + 4 半音
  • Diminished triad: root + 3 semitones + 3 semitones → e.g., C–E♭–G♭ / 减三和弦：根音 + 3 半音 + 3 半音
  • Augmented triad: root + 4 semitones + 4 semitones → e.g., C–E–G♯ / 增三和弦：根音 + 4 半音 + 4 半音

Triad Semitone Formulas: Major (4+3), Minor (3+4), Diminished (3+3), Augmented (4+4)

Apply these formulas from any starting note, remembering to use the correct letter names according to the scale.

从任意根音应用这些公式时，记得要使用符合音阶规律的正确音名。

6. Seventh Chord Formulas | 七和弦构成公式

Seventh chords add a fourth note—the interval of a 7th above the root. The semitone stack common in KS3 work includes:

七和弦在根音上方增加了第四个音——七度音。KS3 学习中常见的半音叠置包括：

  • Major 7th: root + 4 + 3 + 4 semitones (e.g., Cmaj7: C–E–G–B) / 大七和弦：4+3+4
  • Dominant 7th: root + 4 + 3 + 3 semitones (e.g., C7: C–E–G–B♭) / 属七和弦：4+3+3
  • Minor 7th: root + 3 + 4 + 3 semitones (e.g., Cm7: C–E♭–G–B♭) / 小七和弦：3+4+3
  • Half-diminished 7th: root + 3 + 3 + 4 semitones (e.g., Cm7♭5: C–E♭–G♭–B♭) / 半减七和弦：3+3+4
  • Diminished 7th: root + 3 + 3 + 3 semitones (e.g., Cdim7: C–E♭–G♭–A) / 减七和弦：3+3+3

Notice how the top interval of the dominant 7th is a minor 7th (10 semitones above the root), which gives it a characteristic tension seeking resolution.

注意属七和弦最上方的七度音是一个小七度（距根音10个半音），这赋予了它寻求解决的独特张力。

7. Chord Inversions and Figured Bass Shortcut | 和弦转位与数字低音速记

An inversion results when a note other than the root is the lowest sounding pitch. Triads have three positions:

当和弦的最低音不是根音时，就产生了转位。三和弦有三种位置：

  • Root position: root – 3rd – 5th (bass = root). Figured bass shorthand: 5/3 or simply nothing. / 原位：根音–三音–五音，数字低音：5/3
  • First inversion: 3rd – 5th – root (bass = 3rd). Figured bass: 6 (or 6/3). / 第一转位：三音在低音，数字低音：6
  • Second inversion: 5th – root – 3rd (bass = 5th). Figured bass: 6/4. / 第二转位：五音在低音，数字低音：6/4

The spacing can change, but the lowest note defines the inversion. Seventh chords also have third inversions with the 7th in the bass.

音与音之间的距离可以变化，但最低音决定了转位。七和弦还有以七音为低音的第三转位。

Recognising inversions helps with bass line writing and harmonic analysis at KS3.

识别转位有助于 KS3 阶段编写低音线条与和声分析。

8. Simple and Compound Time Signatures | 简单拍子与复合拍子

Simple time: each beat divides into two equal notes. The top number indicates beats per bar, and the bottom number gives the beat unit: 2/4, 3/4, 4/4.

简单拍子：每个节拍均分为两个均等的音符。上方数字表示每小节拍数，下方数字表示以何种音符为一拍：2/4、3/4、4/4。

Compound time: each beat divides into three. The top number divided by 3 gives the number of dotted beats per bar; the bottom number shows the note value that makes up each beat subdivision. 6/8 means two dotted-crotchet beats per bar (6 ÷ 3 = 2).

复合拍子：每个节拍均分为三个音符。上方数字除以3得到每小节附点节拍数；下方数字指示节拍细分音符的时值。6/8 表示每小节两拍，每拍为附点四分音符（6÷3=2）。

Time Signature Type Beats per bar Beat division
2/4 Simple 2 crotchet beats 2 quavers per beat
4/4 Simple 4 crotchet beats 2 quavers per beat
6/8 Compound 2 dotted-crotchet beats 3 quavers per beat
9/8 Compound 3 dotted-crotchet beats 3 quavers per beat

Simple: top number = beats; Compound: (top number / 3) = beats

9. Dotted Notes, Ties, and Triplets | 附点音符、延音线与三连音

A dot placed after a note increases its duration by half of its original value. Thus a dotted crotchet equals a crotchet plus a quaver: dotted value = original × 1.5.

音符后的附点使该音符的时值增加原有时值的一半。因此附点四分音符等于一个四分音符加一个八分音符：附点时值 = 原有时值 × 1.5。

A tie joins two notes of the same pitch, adding their durations together without re-articulating the second note. Triplets compress three notes into the time of two of the same kind, indicated by a ‘3’ bracket; each triplet quaver group equals one crotchet beat.

延音线连接两个相同音高的音符，将其时值相加且不重新演奏第二个音。三连音将三个音符压缩到原本两个同类音符的时值中，用数字“3”标记；一组三连音八分音符等于一个四分音符拍。

  • Dotted minim = 3 crotchet beats / 附点二分音符 = 3 拍
  • Triplet quavers = 1 crotchet beat / 三连音八分音符 = 1 拍
  • Tied notes sustain without re-striking / 延音线连接后持续发声，不重新发音

10. The Circle of Fifths as a Key-Signature Formula | 五度圈作为调号公式

The circle of fifths is a pattern that reveals how many sharps or flats are in a given major key. Starting from C major (0 sharps/flats), each step clockwise (up a perfect 5th) adds one sharp; each step anticlockwise (up a perfect 4th / down a perfect 5th) adds one flat.

五度圈是一个揭示大调调号中升、降号数量的模式。从 C 大调（无升降号）开始，顺时针每一步（上行纯五度）增加一个升号；逆时针每一步（上行纯四度/下行纯五度）增加一个降号。

Sharp keys: G (1♯), D (2♯), A (3♯), E (4♯), B (5♯), F♯ (6♯). The order of sharps is F♯–C♯–G♯–D♯–A♯–E♯. The last sharp is always the leading note (7th degree) of the major key.

升号调：G（1♯）、D（2♯）、A（3♯）、E（4♯）、B（5♯）、F♯（6♯）。升记号顺序为 F♯–C♯–G♯–D♯–A♯–E♯。最后一个升号总是该大调的导音（第7级音）。

Flat keys: F (1♭), B♭ (2♭), E♭ (3♭), A♭ (4♭), D♭ (5♭), G♭ (6♭). The order of flats is B♭–E♭–A♭–D♭–G♭–C♭. The penultimate flat in the key signature is the name of the major key.

降号调：F（1♭）、B♭（2♭）、E♭（3♭）、A♭（4♭）、D♭（5♭）、G♭（6♭）。降记号顺序为 B♭–E♭–A♭–D♭–G♭–C♭。调号中倒数第二个降号即为该大调调名。

Order of sharps: F♯ C♯ G♯ D♯ A♯ E♯   Order of flats: B♭ E♭ A♭ D♭ G♭ C♭

11. Transposition Shortcut | 移调速算法

Transposition means moving every note by the same interval. To transpose up a perfect 5th, move each note 7 semitones higher; to transpose down a minor 3rd, move 3 semitones lower. Keep the new key signature in mind—adjust accidentals accordingly.

移调意味着将每个音符按相同音程移动。向上移纯五度，即将每个音升高7个半音；向下移小三度，则降低3个半音。要记住新调号，并相应调整临时变音记号。

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