Year 12 OCR Music: Formulae & Theorems Quick Reference Handbook

📚 Year 12 OCR Music: Formulae & Theorems Quick Reference Handbook | 公式定理速查手册

The Year 12 OCR Music course requires a thorough understanding of music theory ‘formulae’ and compositional ‘theorems’. This reference condenses interval logic, chord construction, cadential patterns, voice leading rules, and developmental techniques into a compact, exam-ready handbook. Every entry is presented as a clear statement followed by its immediate application, helping you move confidently from recognition to creative use in analysis and composing tasks.

Year 12 OCR 音乐课程需要透彻掌握音乐理论中的“公式”和作曲“定理”。本速查手册将音程逻辑、和弦构成、终止式模式、声部进行法则以及发展手法浓缩为备考手册。每个条目都先给出清晰陈述，再立即给出应用说明，帮助你在分析和创作任务中从辨认自信过渡到创造性运用。

1. Interval Formulae | 音程计算公式

Every interval is defined by the number of semitones between two pitches and the staff degree (second, third, etc.). Use the following semitone counts as a quick reference for perfect, major and minor intervals.

每个音程由两个音高之间的半音数量与谱面度数（二度、三度等）共同定义。以半音数为准快速判定纯、大、小音程。

Major 2nd = 2 semitones; Major 3rd = 4 semitones; Perfect 4th = 5 semitones; Perfect 5th = 7 semitones; Major 6th = 9 semitones; Major 7th = 11 semitones; Octave = 12 semitones. The corresponding minor intervals are one semitone smaller.

大二度 = 2 半音；大三度 = 4 半音；纯四度 = 5 半音；纯五度 = 7 半音；大六度 = 9 半音；大七度 = 11 半音；纯八度 = 12 半音。对应的小音程少一个半音。

Augmented intervals expand a perfect or major interval by one semitone; diminished intervals contract a perfect or minor interval by one semitone. For example, C to F♯ is an augmented 4th (6 semitones), while C to G♭ is a diminished 5th (also 6 semitones) – enharmonically identical but functionally different.

增音程将纯或大音程扩张一个半音；减音程将纯或小音程收缩一个半音。例如 C 到 F♯ 为增四度（6 半音），C 到 G♭ 为减五度（6 半音）——等音相同但功能不同。

2. Triad Construction Theorems | 三和弦构成定理

A triad is a stack of two thirds. The quality is determined by the exact semitone spacing between root, third and fifth. Memorise these four fundamental ‘theorems’ to build any triad from a given root.

三和弦是两个三度的堆叠。其性质由根音、三音和五音之间的半音间隔决定。记住下面四个基本“定理”，可以从任意根音构建和弦。

Major triad formula: Root + 4 semitones (major 3rd) + 3 semitones (minor 3rd). Total: 7 semitones between outer voices.	大三和弦公式：根音 + 4 半音（大三度）+ 3 半音（小三度）。外声部间隔共 7 半音。
Minor triad formula: Root + 3 semitones (minor 3rd) + 4 semitones (major 3rd).	小三和弦公式：根音 + 3 半音（小三度）+ 4 半音（大三度）。
Diminished triad formula: Root + 3 semitones + 3 semitones. Outer fifth is diminished (6 semitones).	减三和弦公式：根音 + 3 半音 + 3 半音。外声部五度是减五度（6 半音）。
Augmented triad formula: Root + 4 semitones + 4 semitones. Outer fifth is augmented (8 semitones).	增三和弦公式：根音 + 4 半音 + 4 半音。外声部五度是增五度（8 半音）。

When inverting a triad, the chord quality remains unchanged; only the bass note changes. In first inversion the third is in the bass, in second inversion the fifth is in the bass. Apply the same semitone mapping from the new bass note to check voicing.

转换转位时，和弦性质不变，只有低音改变。第一转位三音在低音，第二转位五音在低音。用同样的半音关系从新低音出发检查排列。

3. Seventh Chord Formulae | 七和弦结构公式

Seventh chords add a third above the fifth, creating a four-note sonority. The combination of the triadic quality and the type of seventh yields distinct formulae.

七和弦在五音上方再加一个三度，构成四音音响。三和弦性质与七度类型的组合给出明确公式。

Major seventh (Maj7): Major triad + major 3rd (4 semitones) above 5th → Root+4+3+4. Common in tonic I⁷ and subdominant IV⁷.	大七和弦：大三和弦 + 五音上方大三度（4 半音）→ 根+4+3+4。常见于主七和弦 I⁷ 与下属七和弦 IV⁷。
Dominant seventh (V⁷): Major triad + minor 3rd (3 semitones) above 5th → Root+4+3+3. Uniquely a major triad with a minor seventh.	属七和弦 (V⁷)：大三和弦 + 五音上方小三度（3 半音）→ 根+4+3+3。唯一一个包含大三和弦和小七度的组合。
Minor seventh (m7): Minor triad + minor 3rd above 5th → Root+3+4+3. Found on ii, iii, vi.	小七和弦：小三和弦 + 五音上方小三度 → 根+3+4+3。出现在 ii, iii, vi 级。
Half-diminished seventh (ø⁷): Diminished triad + major 3rd above 5th → Root+3+3+4. Occurring on vii in major keys.	半减七和弦 (ø⁷)：减三和弦 + 五音上方大三度 → 根+3+3+4。在大调的 vii 级出现。
Diminished seventh (dim⁷): Diminished triad + minor 3rd above 5th → Root+3+3+3. All intervals between adjacent notes are minor thirds; symmetrical chord.	减七和弦 (dim⁷)：减三和弦 + 五音上方小三度 → 根+3+3+3。所有相邻音程均为小三度；对称和弦。

In analysis, the seventh must resolve down by step in common-practice style. The upper voice leading of seventh chords often treats the seventh as a suspension-like dissonance that resolves to a consonance in the next chord.

在分析中，七音在共性实践时期须级进下行解决。七和弦的上方声部进行常将七音视为类似延留音的不协和音，解决到下一和弦的协和音。

4. Cadence Recognition Rules | 终止式识别规则

Cadences are punctuation marks in tonal music. Use these formulae to identify them instantly by chord pair and metrical placement.

终止式是调性音乐中的标点符号。通过和弦对和节拍位置，使用以下公式迅速识别它们。

Perfect cadence V–I: Both chords in root position; the tonic I must arrive on a strong beat. The leading note rises to the tonic, creating the strongest close. Plagal cadence IV–I: Subdominant to tonic, often used for ‘Amen’ endings. No leading-note resolution required.

正格终止 V–I：两和弦均为原位；主和弦 I 必须在强拍出现。导音上行至主音，构成最强收束。变格终止 IV–I：下属到主和弦，常构成“阿门”结尾，无需导音解决。

Imperfect cadence I–V (or ii–V, IV–V): Ends on V in root position. Sounds incomplete and requires continuation. Interrupted cadence V–vi: V moves to the submediant (vi) instead of the expected I, creating a deceptive surprise. In minor keys, V–VI is also common.

不完全终止 I–V（或 ii–V、IV–V）：以原位 V 结尾，音响未完成，需要继续。阻碍终止 V–vi：V 进行到下中音和弦 vi 而非预期的 I，造成意外。小调中 V–VI 也很常见。

When analysing a score, always note the key first, then check the bass line and the chord above it. The cadence type is determined purely by the last two chords of the phrase and their metrical strength.

分析乐谱时，先确定调性，再检查低音线条及其上方和弦。终止式类型完全由乐句最后两个和弦及其节拍强弱决定。

5. The Circle of Fifths Theorem | 五度圈定理

The circle of fifths organises all 12 major and minor keys in a closed loop of perfect fifths. Moving clockwise from C, each step adds one sharp; moving anticlockwise, each step adds one flat.

五度圈以纯五度闭环排列所有12个大调和小调。从C顺时针每步增加一个升号，逆时针每步增加一个降号。

Sharp keys: C (0♯) → G (1♯) → D (2♯) → A (3♯) → E (4♯) → B (5♯) → F♯ (6♯) → C♯ (7♯). The new sharp is always the leading tone (7th degree) of the new key. Flat keys: C (0♭) → F (1♭) → B♭ (2♭) → E♭ (3♭) → A♭ (4♭) → D♭ (5♭) → G♭ (6♭) → C♭ (7♭). The new flat is always the subdominant (4th degree) of the new key.

升号调：C (0♯) → G (1♯) → D (2♯) → A (3♯) → E (4♯) → B (5♯) → F♯ (6♯) → C♯ (7♯)。新增升号总是新调的导音（第Ⅶ级）。降号调：C (0♭) → F (1♭) → B♭ (2♭) → E♭ (3♭) → A♭ (4♭) → D♭ (5♭) → G♭ (6♭) → C♭ (7♭)。新增降号总是新调的下属音（第Ⅳ级）。

The relative minor of any major key shares the same key signature and lies a minor third below the major tonic. For example, A minor is the relative of C major, E minor of G major. The pattern forms a nested inner circle for effortless relative key identification.

任何大调的关系小调使用相同调号，且位于大调主音下方小三度。例如 A 小调是 C 大调的关系调，E 小调是 G 大调的关系调。这种模式形成嵌套的内圈，快速识别关系大小调。

6. Voice Leading Principles | 声部进行法则

In four-part SATB (Soprano, Alto, Tenor, Bass) writing, smooth voice leading is governed by a set of strict rules derived from common-practice style. Treat these as ‘axioms’ that must not be broken.

在四声部 SATB（女高音、女低音、男高音、男低音）写作中，流畅的声部进行受共性实践时期的一套严格法则约束。将这些法则视为不可违背的“公理”。

Forbidden parallels: Consecutive perfect fifths and octaves between any two voices are prohibited. They destroy voice independence. Hidden (direct) fifths and octaves: Approach a perfect fifth or octave by similar motion when the upper voice leaps; this is usually avoided in outer voices unless the soprano moves by step.

禁止平行：任何两声部之间不得出现连续纯五度和纯八度，它们破坏声部独立性。隐伏五八度：当上方声部跳进并以同向运动到达纯五度或纯八度时通常应避免，除非女高音级进。

Spacing: An interval of more than an octave between adjacent upper voices (S–A, A–T) is avoided; tenor and bass may exceed an octave in keyboard style but not in strict vocal style. Voice crossing: Voices should not cross above or below their neighbouring voice. Keep each voice within its comfortable range.

间距：相邻上方声部（S–A、A–T）之间避免超过八度；键盘风格中男高音与男低音可超过八度，但严格声乐风格不可。声部交叉：声部不应交叉到相邻声部的上方或下方，保持各声部在舒适音区。

Leading-note resolution: In V–I progressions, the leading note (7th degree) must rise by step to the tonic, especially when it is in the soprano or bass. In inner voices, it may occasionally fall to the 5th of I if a full chord cannot be achieved.

导音解决：在 V–I 进行中，导音（Ⅶ级）必须级进上行到主音，尤其是当它处于女高音或男低音时。在内声部中，若无法构成完整和弦，可偶尔下行至 I 的五音。

7. Harmonic Progression Formulae | 和弦进行公式

Tonal harmony follows circular motions rooted in functional categories: tonic (I, vi), pre-dominant (ii, IV), and dominant (V, vii°). The ‘progression theorem’ can be summarised as T – PD – D – T.

调性和声遵循功能分类的循环运动：主功能 (I, vi)、前主功能 (ii, IV) 和属功能 (V, vii°)。和声进行定理可概括为 T – PD – D – T。

Common progressions: I–IV–V–I is the strongest cadential formula. I–vi–IV–V–I is the extended ‘doo-wop’ pattern. The descending-fifth sequence: iii–vi–ii–V–I moves by root motion down a perfect fifth each time, creating a powerful sense of direction.

常见进行：I–IV–V–I 为最强终止公式。I–vi–IV–V–I 是扩展的 50 年代和声模式。下行五度循环：iii–vi–ii–V–I 每次根音下行纯五度，产生强烈方向感。

In a minor key, the chord palette changes: i – ii° – III – iv – V – VI – VII (or vii°⁷). Harmonic minor raises the leading note, giving V and vii° their usual dominant function. The tune dictates whether melodic minor inflections affect the chord choice.

在小调中，和弦色彩发生变化：i – ii° – III – iv – V – VI – VII（或 vii°⁷）。和声小调升高导音，赋予 V 和 vii° 惯常的属功能。旋律形态决定旋律小调变化音是否影响和弦选择。

8. Non-Chord Tones Formulae | 和弦外音处理公式

Non-chord tones (NCTs) create melodic tension against the underlying harmony. Each type follows a formula of approach, dissonance, and resolution. Memorise the approach-resolution pattern to identify them in scores or use them in composition.

和弦外音 (NCTs) 在和声背景上制造旋律张力。每种和弦外音都有固定的进入、协和一不协和、解决的公式。记住这些进入—解决模式，便于在乐谱中识别或在创作中运用。

Passing tone (PT): approached by step, left by step in the same direction. It fills the gap between two chord tones. Neighbour note (NT): approached by step, returns to the original chord tone. It creates an upper or lower ornament.Published by TutorHao | Year 12 音乐 Revision Series | aleveler.com

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Year 12 OCR Music: Formulae & Theorems Quick Reference Handbook | 公式定理速查手册