📚 Year 12 OCR Music: Formula & Theorem Quick-Reference Handbook | Year 12 OCR 音乐：公式定理速查手册
This quick-reference handbook collects the essential formulas, rules, and theoretical theorems you will need for Year 12 OCR Music. Whether you are analysing scores, completing harmony exercises, or preparing for the appraising paper, the patterns and tables below provide a rapid way to recall the building blocks of Western tonal music. Use this guide to lock in interval structures, chord constructions, cadence formulas, rhythmic mathematics, and much more.
这本速查手册汇集了 Year 12 OCR 音乐所需的核心公式、规则与理论定理。无论你是在分析乐谱、完成和声练习，还是在备考评鉴卷，下面的模式与表格都提供了快速回忆西方调性音乐基石的方法。用这本指南牢牢掌握音程结构、和弦构建、终止式公式、节奏数学以及其他重要知识。
1. Major Scale Formula | 大调音阶公式
A major scale is built from a rigid sequence of whole tones (W) and semitones (H): W – W – H – W – W – W – H. This pattern is identical for every major key. For instance, in C major the steps are C–D (W), D–E (W), E–F (H), F–G (W), G–A (W), A–B (W), B–C (H).
大调音阶由一个严格的全音（W）和半音（H）序列构成：W – W – H – W – W – W – H。这一模式适用于每一个大调。例如，在 C 大调中，各音级间的步进为 C–D（全音），D–E（全音），E–F（半音），F–G（全音），G–A（全音），A–B（全音），B–C（半音）。
The tonic (scale degree 1) names the key. To transpose the formula, simply start on the desired tonic and apply the W‑W‑H‑W‑W‑W‑H template. Degrees of the scale are often labelled with Roman numerals (I, II, III, IV, V, VI, VII).
主音（第 1 音级）决定了调的名称。若要移调，只需从目标主音出发并套用 W‑W‑H‑W‑W‑W‑H 的模板。音级常用罗马数字标记（I, II, III, IV, V, VI, VII）。
Formula: W – W – H – W – W – W – H
2. Minor Scales: Natural, Harmonic & Melodic | 小调音阶：自然、和声与旋律
The natural minor scale follows the pattern W – H – W – W – H – W – W. It can be derived by playing the major scale from its sixth degree (A is the relative minor of C major).
自然小调遵循 W – H – W – W – H – W – W 的模式。它可以通过从大调音阶的第六级开始演奏而得出（A 小调是 C 大调的关系小调）。
The harmonic minor scale raises the seventh degree by a semitone, creating a characteristic augmented second (A2) between degrees 6 and 7. Its step pattern becomes W – H – W – W – H – A2 – H (with A2 = 3 semitones).
和声小调将第七级升高半音，从而在第六级与第七级之间产生一个极具特色的增二度（A2）。其步进模式变为 W – H – W – W – H – A2 – H（增二度 = 3 个半音）。
The melodic minor scale alters both the sixth and seventh degrees when ascending (W – H – W – W – W – W – H), but reverts to the natural minor formula when descending.
旋律小调在上行时同时升高第六与第七级（W – H – W – W – W – W – H），下行时则恢复为自然小调模式。
Natural: W H W W H W W | Harmonic: W H W W H A2 H | Melodic (asc): W H W W W W H
3. Interval Calculation Table | 音程计算表
An interval is the distance between two pitches, measured in semitones. Quality (major, minor, perfect, augmented, diminished) depends on the number of letter names and the exact semitone count. The table below gives standard diatonic intervals within one octave.
音程是两个音高之间的距离，以半音为单位。音程的性质（大、小、纯、增、减）取决于音名字符数量和精确的半音数。下表列出了八度范围内的标准自然音程。
| Semitones | Interval Name | 中文名称 |
|---|---|---|
| 0 | Perfect Unison | 纯一度 |
| 1 | Minor 2nd | 小二度 |
| 2 | Major 2nd | 大二度 |
| 3 | Minor 3rd | 小三度 |
| 4 | Major 3rd | 大三度 |
| 5 | Perfect 4th | 纯四度 |
| 6 | Augmented 4th / Diminished 5th (tritone) | 增四度 / 减五度（三全音） |
| 7 | Perfect 5th | 纯五度 |
| 8 | Minor 6th | 小六度 |
| 9 | Major 6th | 大六度 |
| 10 | Minor 7th | 小七度 |
| 11 | Major 7th | 大七度 |
| 12 | Perfect Octave | 纯八度 |
To invert an interval, subtract the semitone number from 12 and swap major ↔ minor, augmented ↔ diminished, while perfect remains perfect. Example: a major 3rd (4 semitones) inverts to a minor 6th (8 semitones).
转位音程时，用 12 减去原半音数，并将大↔小、增↔减互换，纯音程保持不变。例如：大三度（4 个半音）转位后变为小六度（8 个半音）。
4. Triad Chord Construction | 三和弦构建
A triad consists of a root, a third, and a fifth. The quality is determined by the interval structure measured in semitones from the root. The four basic triads are summarised below.
三和弦由根音、三音和五音构成。其性质由从根音算起的音程半音结构决定。下面总结了四种基本三和弦。
| Triad Type | Semitone Formula | 中文名称 |
|---|---|---|
| Major | Root + 4 (major 3rd) + 3 (minor 3rd) | 大三和弦 |
| Minor | Root + 3 (minor 3rd) + 4 (major 3rd) | 小三和弦 |
| Diminished | Root + 3 + 3 (two minor 3rds) | 减三和弦 |
| Augmented | Root + 4 + 4 (two major 3rds) | 增三和弦 |
In Roman numeral analysis, triads built on scale degrees follow a fixed pattern in major keys: I (major), ii (minor), iii (minor), IV (major), V (major), vi (minor), vii° (diminished).
在罗马数字分析中，大调音阶各音级上构建的三和弦遵循固定模式：I（大），ii（小），iii（小），IV（大），V（大），vi（小），vii°（减）。
5. Seventh Chord Construction | 七和弦构建
Adding a seventh above the root extends a triad into a seventh chord. The quality depends on the triad type plus the interval of the seventh. Key seventh chords and their semitone formulas are shown below.
在根音上方加入七音可将三和弦扩展为七和弦。其性质取决于三和弦类型加上根音到七音的音程。以下是主要七和弦及其半音公式。
| Chord Type | Semitone Formula | 中文名称 |
|---|---|---|
| Major 7th | Root + 4 + 3 + 4 (major triad + major 7th) | 大七和弦 |
| Dominant 7th | Root + 4 + 3 + 3 (major triad + minor 7th) | 属七和弦 |
| Minor 7th | Root + 3 + 4 + 3 (minor triad + minor 7th) | 小七和弦 |
| Half‑diminished 7th | Root + 3 + 3 + 4 (diminished triad + major 7th? Wait: diminished triad + minor 7th? Actually half-diminished is diminished triad + minor 7th: 3+3+4. So formula: Root + 3 + 3 + 4. | 半减七和弦 |
| Full‑diminished 7th | Root + 3 + 3 + 3 (diminished triad + diminished 7th) | 减七和弦 |
Note: In the table above, the half-diminished seventh (m7♭5) is built: root + 3 semitones (minor 3rd) + 3 semitones (diminished 5th) + 4 semitones (minor 7th) = 3+3+4.
注意：上表中半减七和弦（小七降五）的构成：根音 + 3 半音（小三度）+ 3 半音（减五度）+ 4 半音（小七度），即 3+3+4。
6. Cadences and Their Formulae | 终止式及其公式
Cadences are two-chord formulas that punctuate musical phrases. Recognising and writing them involves specific chord movements, usually expressed with Roman numerals.
终止式是给乐句断句的两个和弦的公式。辨认与写作终止式需掌握特定的和弦进行，通常用罗马数字表示。
| Cadence | Formula | 中文名称 |
|---|---|---|
| Perfect (Authentic) | V (or V7) → I (both in root position, top voice resolves to tonic) | 完全终止 |
| Imperfect | I → V, ii → V, IV → V (any chord moving to V, ending on V) | 不完全终止 |
| Plagal | IV → I (the ‘Amen’ cadence) | 变格终止 |
| Interrupted (Deceptive) | V → vi (or occasionally V → IV/VI, surprising the listener) | 阻碍终止 |
A perfect cadence sounds final; a plagal cadence is softer. An imperfect cadence feels unfinished, while an interrupted cadence surprises with a non-tonic chord after V.
完全终止听上去充满结束感；变格终止较为柔和。不完全终止感觉未完待续，而阻碍终止在 V 后接非主和弦，令听者感到意外。
7. Time Signatures and Rhythmic Formulas | 拍号与节奏公式
Time signatures appear as two numbers. The top number indicates how many beats per bar; the bottom number shows the note value that equals one beat. The formula for simple time is straightforward: the beat note is the denominator as a power of 2 (e.g., 4 = crotchet, 8 = quaver). In compound time, each beat is a dotted note: the top number divided by 3 gives the number of dotted beats, while the denominator indicates the undotted note value that makes up the dotted beat.
拍号由两个数字组成。上方数字表示每小节的拍数；下方数字表示以哪种音符为一拍。简单拍子的公式直观明了：拍位音符是分母对应的 2 的幂次数值（例如 4 = 四分音符，8 = 八分音符）。在复合拍子中，每拍是一个附点音符：上方数字除以 3 得出附点拍的数量，分母则表示构成该附点拍的原音符。
Simple duple: 2/4 (2 crotchet beats), 2/2 (2 minim beats). Simple triple: 3/4, 3/2. Simple quadruple: 4/4. Compound duple: 6/8 (2 dotted
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