📚 Year 8 OCR Music: Formula & Theorem Quick Reference Handbook | Year 8 OCR 音乐：公式定理速查手册
In Year 8 OCR Music, understanding the essential formulas and rules that underpin notation, scales, chords, and structure is key to becoming a confident musician. This quick reference handbook gathers all the fundamental 'equations' of music theory into one place, from note values and intervals to cadence patterns and transposition, helping you memorise and apply them with ease.
在 Year 8 OCR 音乐课程中，理解支撑记谱法、音阶、和弦及曲式结构的基本公式与规则，是建立自信演奏能力的关键。这本速查手册将音乐理论中所有的基本“方程式”汇集一处——从音符时值和音程到终止式模式与移调方法，帮助你轻松记忆并灵活运用。
1. Note Duration Formulas | 音符时值公式
Every rhythm starts with a mathematical relationship between note values. In 4/4 time, the semibreve (whole note) is the longest standard duration, and each shorter note divides the beat by powers of two.
所有节奏都始于音符时值之间的数学关系。在 4/4 拍中，全音符是标准的最长时值，每个更短的音符都以 2 的幂次方划分拍子。
Dotted notes add half the value again: Dotted Minim = Minim + Crotchet = 3 crotchet beats.
核心公式为：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。附点音符增加原时值的一半：附点二分音符 = 二分音符 + 四分音符 = 3 个四分音符拍。
| Note | Rest | Duration (beats) | Dotted Duration |
|---|---|---|---|
| Semibreve | Whole rest | 4 | 6 |
| Minim | Half rest | 2 | 3 |
| Crotchet | Quarter rest | 1 | 1½ |
| Quaver | Eighth rest | ½ | ¾ |
These note value relationships are the foundation of rhythm dictation and score reading in the Year 8 OCR syllabus.
这些音符时值关系是 Year 8 OCR 音乐大纲中节奏听写与乐谱阅读的基础。
2. Time Signature Rules | 拍号规则
A time signature is like a fraction: the top number tells you how many beats are in each bar, and the bottom number tells you which note value gets one beat. For example, 3/4 means three crotchet beats per bar.
拍号就像分数：上方数字表示每小节有几拍，下方数字表示以哪种音符为一拍。例如，3/4 表示每小节有三个四分音符拍。
Simple time signatures have beats that divide naturally into two equal parts (e.g. 2/4, 3/4, 4/4). Compound time signatures have beats that divide into three equal parts (e.g. 6/8 has two dotted-crotchet beats, each split into three quavers).
单拍子的每一拍可以自然地分成两个等份（如 2/4、3/4、4/4）。复拍子的每一拍则可以分成三个等份（如 6/8 有两个附点四分音符拍，每拍分为三个八分音符）。
Simple metre: beat = ♩ ; Compound metre: beat = ♩.
When identifying time signatures in OCR listening questions, clap the pulse and count the quaver groupings to distinguish between 3/4 and 6/8.
在 OCR 听力考试中辨别拍号时，用手指拍出律动并数八分音符的分组方式，可以区分 3/4 和 6/8 拍。
3. Major Scale Formula | 大调音阶公式
Every major scale is built from the same sequence of tones (T) and semitones (S). The formula is: T – T – S – T – T – T – S. Semitones occur naturally between the 3rd–4th and 7th–8th degrees.
每一个大调音阶都遵循相同的全音（T）和半音（S）序列。公式为：T – T – S – T – T – T – S。半音自然出现在第 3–4 级和第 7–8 级之间。
Major Scale Formula: T – T – S – T – T – T – S
Starting on C, you get C-D (T), D-E (T), E-F (S), F-G (T), G-A (T), A-B (T), B-C (S). Applying this formula to any tonic note generates all major scales, and explains why key signatures have sharps or flats.
从 C 音开始，得到 C-D（T），D-E（T），E-F（S），F-G（T），G-A（T），A-B（T），B-C（S）。将此公式应用于任何一个主音，就能生成所有大调音阶，并解释了为什么调号会有升号或降号。
Use the formula to check your scale writing: if the interval between the 3rd and 4th notes is not a semitone, you have made a mistake.
用此公式检查你的音阶写作：如果第 3 和第 4 音之间的音程不是半音，就说明写错了。
4. Minor Scale Formulas | 小调音阶公式
There are three main forms of the minor scale, each with its own interval formula. The natural minor uses: T – S – T – T – S – T – T. This is the same set of notes as its relative major, starting on the 6th degree.
小调音阶主要有三种形式，每种都有自己的音程公式。自然小调公式为：T – S – T – T – S – T – T。它的音符组合与其关系大调完全相同，只不过从第 6 级开始。
The harmonic minor raises the 7th degree by a semitone, creating an augmented 2nd (3 semitones) between the 6th and 7th: T – S – T – T – S – T+S – S. For example, A harmonic minor contains G♯.
和声小调将第 7 级音升高半音，从而在第 6 级与第 7 级之间产生一个增二度（3 个半音），公式为：T – S – T – T – S – T+S – S。例如 a 和声小调中含有 G♯。
The melodic minor ascends with raised 6th and 7th (T – S – T – T – T – T – S) and descends like the natural minor. OCR Year 8 students should recognise the characteristic sound of each minor form.
旋律小调上行时升高第 6 和第 7 级（T – S – T – T – T – T – S），下行时还原为自然小调。Year 8 OCR 学生需要能听辨每种小调形式的独特音响效果。
5. Interval Calculation Theorems | 音程计算定理
An interval is the distance between two notes, measured in semitones. The table below shows the semitone count for all intervals within an octave.
音程是两个音之间的距离，以半音为单位测量。下表展示了一个八度以内所有音程的半音数。
| Interval | Semitones | Example (from C) |
|---|---|---|
| Perfect Unison | 0 | C-C |
| Minor 2nd | 1 | C-D♭ |
| Major 2nd | 2 | C-D |
| Minor 3rd | 3 | C-E♭ |
| Major 3rd | 4 | C-E |
| Perfect 4th | 5 | C-F |
| Tritone (Aug 4th / Dim 5th) | 6 | C-F♯ |
| Perfect 5th | 7 | C-G |
| Minor 6th | 8 | C-A♭ |
| Major 6th | 9 | C-A |
| Minor 7th | 10 | C-B♭ |
| Major 7th | 11 | C-B |
| Perfect Octave | 12 | C-C' |
Inversion theorem: To invert an interval, subtract the number from 9 and reverse the quality. A major 3rd (e.g. C-E) becomes a minor 6th (E-C). Perfect intervals remain perfect; major becomes minor, and vice versa.
音程转位定理：将音程度数从 9 中减去，并将性质反转。大三度（如 C-E）转位后变为小六度（E-C）。纯音程转位后仍为纯音程；大音程变为小音程，反之亦然。
6. Chord Building Formulas | 和弦构建公式
Triads are three-note chords built by stacking intervals above a root note. The formula depends on the number of semitones between the root and the third, and between the root and the fifth.
三和弦是由根音上方叠置音程构成的三音和弦。构建公式取决于根音与三音、根音与五音之间的半音数量。
Major triad: Root + 4 semitones + 7 semitones
Minor triad: Root + 3 semitones + 7 semitones
Diminished triad: Root + 3 semitones + 6 semitones
Augmented triad: Root + 4 semitones + 8 semitones
itones up). A minor = A, C (3), E (7). The primary triads in any major key are I, IV and V – a minor key, i and iv are minor, while V is often major (using the harmonic minor scale).
例如，C 大调和弦 = C（0），E（上升 4 个半音），G（上升 7 个半音）。a 小调和弦 = A，C（3），E（7）。任何大调中的正三和弦为 I、IV、V 级，均为大和弦；在小调中，i 和 iv 为小和弦，而 V 级常为大和弦（使用和声小音阶）。
Seventh chords add a fourth note: a dominant 7th consists of a major triad plus a minor 7th (10 semitones from the root). The formula: Root + 4 + 7 + 10.
七和弦再增加一个音：属七和弦由一个大三和弦加一个小七度（距根音 10 个半音）构成。公式为：根音 + 4 + 7 + 10。
7. Circle of Fifths & Key Signatures Theorem | 五度圈与调号定理
The circle of fifths organises all major and minor keys by the number of sharps or flats. Moving clockwise adds a sharp (or removes a flat); each step is a perfect 5th up.
五度圈通过升号或降号的数量将所有大小调组织起来。顺时针方向每步上行纯五度，增加一个升号（或减少一个降号）。
Sharp keys: C (0♯), G (1♯ F♯), D (2♯ F♯ C♯), A (3♯), E (4♯), B (5♯), F♯ (6♯), C♯ (7♯). To find the major key name from a sharp key signature, go one semitone above the last sharp.
升号调：C（0 升），G（1 升 F♯），D（2 升 F♯、C♯），A（3 升），E（4 升），B（5 升），F♯（6 升），C♯（7 升）。从升号调号推断大调名称：取最后一个升号上方半音即可。
Flat keys: C (0♭), F (1♭ B♭), B♭ (2♭), E♭ (3♭), A♭ (4♭), D♭ (5♭), G♭ (6♭), C♭ (7♭). For flat keys, the penultimate flat in the key signature is the tonic major key (except F major).
降号调：C（0 降），F（1 降 B♭），B♭（2 降），E♭（3 降），A♭（4 降），D♭（5 降），G♭（6 降），C♭（7 降）。对于降号调，调号中倒数第二个降号音即为主音大调名称（F 大调除外）。
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