📚 Year 12 SQA Music: Quick Reference Formula & Theorem Handbook | 苏格兰 SQA Year 12 音乐：公式定理速查手册
A solid grasp of the fundamental ‘formulas’ in music theory can transform how you read, perform, and create music. This handbook distils the essential rules and patterns you need for SQA Year 12 Music — from interval calculations and scale structures to chord spellings and cadential progressions. Keep it by your side as a quick-reference companion for both written papers and aural analysis.
扎实掌握音乐理论中的基本“公式”，能彻底改变你读谱、演奏和创作音乐的方式。本手册提炼了 SQA Year 12 音乐课程所需的核心规则与模式——从音程计算、音阶结构到和弦拼写与终止进行。无论是书面试卷还是听力分析，它都是你身边的速查伴侣。
1. Interval Formulas in Semitones | 用半音计算音程的公式
Intervals are the building blocks of melody and harmony. The table below gives the semitone count for each simple interval within one octave; adding or subtracting octaves shifts the interval class accordingly. Learn these like multiplication tables.
音程是旋律与和声的基石。下表列出了八度内每个单音程的半音数；加上或减去八度会相应改变音程类别。像背乘法口诀一样掌握它们。
| Interval Name (English) | 音程名称 (中文) | Semitones |
|---|---|---|
| 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 (Tritone) | 增四度/减五度 (三全音) | 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 |
The core rule: a major interval reduced by one semitone becomes minor; a perfect interval reduced becomes diminished; augmented intervals are one semitone wider than perfect or major. When spelling intervals, use the letter names first — the number of staff positions determines the number (2nd, 3rd, etc.).
核心规则：大音程降低一个半音变为小音程；纯音程降低变为减音程；增音程比纯或大音程宽一个半音。拼写音程时，先看字母名称——五线谱上的位置数量决定度数（二度、三度等）。
2. Major Scale Construction Formula | 大调音阶构建公式
Every major scale follows an unbreakable pattern of tones (T) and semitones (S). Starting from the tonic, the sequence is: T – T – S – T – T – T – S. This can also be expressed in semitones: 2 – 2 – 1 – 2 – 2 – 2 – 1.
每条大调音阶都遵循不可改变的全音 (T) 与半音 (S) 模式。从主音开始，序列为：全–全–半–全–全–全–半。用半音表示即为：2 – 2 – 1 – 2 – 2 – 2 – 1。
Formula: T T S T T T S or 2 2 1 2 2 2 1
To spell any major scale, start at the chosen tonic and apply this interval pattern step by step. For example, G major: G (T→) A (T→) B (S→) C (T→) D (T→) E (T→) F♯ (S→) G. Remember that each letter name must appear exactly once; accidentals are adjusted to maintain the formula.
要拼写任何大调音阶，从选定的主音开始，逐步套用此音程模式。例如 G 大调：G (全→) A (全→) B (半→) C (全→) D (全→) E (全→) F♯ (半→) G。记住每个字母名称必须恰好出现一次；临时记号需调整以维持公式。
3. Minor Scale Patterns: Natural, Harmonic, Melodic | 小调音阶模式：自然、和声、旋律
Minor keys have three main forms, each with a distinct formula. The natural minor uses the key signature alone and follows the pattern T – S – T – T – S – T – T (semitone formula: 2–1–2–2–1–2–2). It is the Aeolian mode.
小调有三种主要形式，每种都有独特的公式。自然小调仅使用调号，遵循全–半–全–全–半–全–全的模式（半音公式：2–1–2–2–1–2–2）。即爱奥利亚调式。
The harmonic minor raises the 7th degree by a semitone to create a leading tone, producing a distinctive augmented 2nd between degrees 6 and 7. Its semitone sequence: 2–1–2–2–1–3–1.
和声小调将第 VII 级升高半音以制造导音，在第 VI 与 VII 级之间产生特有的增二度。其半音序列为：2–1–2–2–1–3–1。
The melodic minor raises both the 6th and 7th degrees when ascending (to bridge the gap smoothly) and reverts to natural minor when descending. Ascending semitone pattern: 2–1–2–2–2–2–1.
旋律小调上行时升高第 VI 和第 VII 级（以便平滑过渡），下行时恢复为自然小调。上行半音模式：2–1–2–2–2–2–1。
Quick comparison of A minor scale forms:
A 小调各形式的快速对比：
- Natural: A B C D E F G A
- Harmonic: A B C D E F G♯ A
- Melodic ascending: A B C D E F♯ G♯ A Descending: A G F E D C B A
4. Triad Chord Building Rules | 三和弦构建规则
A triad is a three-note chord stacked in thirds. The quality (major, minor, diminished, augmented) is determined by the types of thirds between the notes. Use the semitone patterns below to build any triad from its root.
三和弦是由三度叠置而成的三个音构成的和弦。其性质（大、小、减、增）取决于音与音之间的三度类型。使用下面的半音模式即可从根音构建任何三和弦。
| Triad Type | 和弦类型 | Interval Stack (from root) | Semitone Pattern |
|---|---|---|---|
| Major | 大三和弦 | Major 3rd + Minor 3rd | 4 + 3 |
| Minor | 小三和弦 | Minor 3rd + Major 3rd | 3 + 4 |
| Diminished | 减三和弦 | Minor 3rd + Minor 3rd | 3 + 3 |
| Augmented | 增三和弦 | Major 3rd + Major 3rd | 4 + 4 |
The formula for root position always yields a chord with the root as the lowest note, the third in the middle, and the fifth on top. Inversions are covered later.
原位公式始终产生以根音为最低音、三音居中、五音在上的和弦。转位将在后面介绍。
5. Key Signatures & the Circle of Fifths | 调号与五度循环
The circle of fifths is a visual formula for key signatures. Moving clockwise adds one sharp each time (or removes a flat); moving anticlockwise adds one flat (or removes a sharp). The order of sharps is F♯ C♯ G♯ D♯ A♯ E♯ B♯; the order of flats is B♭ E♭ A♭ D♭ G♭ C♭ F♭.
五度循环是调号的视觉公式。顺时针移动每次增加一个升号（或减少一个降号）；逆时针移动每次增加一个降号（或减少一个升号）。升号顺序为 F♯ C♯ G♯ D♯ A♯ E♯ B♯；降号顺序为 B♭ E♭ A♭ D♭ G♭ C♭ F♭。
To find the major key from a sharp key signature, go one semitone above the last sharp. For flats, the penultimate flat in the sequence is the major key. Relative minor keys share the same key signature but start on the 6th degree of the major scale.
要从升号调号找出大调，取最后一个升号上方半音。对于降号，序列中倒数第二个降号即该大调。关系小调共用同一调号，但起始于大调音阶的第六级。
Relative minor tonic = Major tonic – 3 semitones (minor 3rd down)
6. Time Signatures & Rhythm Equations | 拍号与节奏公式
A time signature is a fraction that tells you how many beats are in each bar (top number) and what note value equals one beat (bottom number). Common values: 4 = crotchet, 8 = quaver, 2 = minim. Simple time beats divide naturally into two; compound time beats divide into three.
拍号是一个分数，告诉你每小节有多少拍（上方数字）以及何种音符时值等于一拍（下方数字）。常见时值：4 = 四分音符，8 = 八分音符，2 = 二分音符。单拍子的拍子自然地二等分；复拍子的拍子则三等分。
| Type | 类型 | Top Number Rule | Beat Division |
|---|---|---|---|
| Simple Duple | 单二拍 | 2 | Each beat splits into 2 |
| Simple Triple | 单三拍 | 3 | Each beat splits into 2 |
| Simple Quadruple | 单四拍 | 4 | Each beat splits into 2 |
| Compound Duple | 复二拍 | 6 | Each beat splits into 3 (two dotted-crotchet beats) |
| Compound Triple | 复三拍 | 9 | Each beat splits into 3 (three beats) |
| Compound Quadruple | 复四拍 | 12 | Each beat splits into 3 (four beats) |
Rhythm equations: 1 semibreve = 2 minims = 4 crotchets = 8 quavers = 16 semiquavers. Dotted notes add half their value; a dotted crotchet = crotchet + quaver = 3 quavers. Triplets fit three notes into the time normally taken by two.
节奏等式：1 全音符 = 2 二分音符 = 4 四分音符 = 8 八分音符 = 16 十六分音符。附点音符增加自身时值的一半；附点四分音符 = 四分音符 + 八分音符 = 3 个八分音符。三连音则把三个音挤入通常两个音所占的时值。
7. Harmonic Progressions & Cadence Formulas | 和声进行与终止式公式
In SQA Music, recognising standard chord progressions is vital. Roman numerals indicate chords built on scale degrees: I is the tonic, IV the subdominant, V the dominant. The plagal cadence moves IV → I; the perfect cadence moves V → I; an interrupted cadence goes V → vi; and the imperfect cadence ends on V (e.g. I – V, ii – V).
在 SQA 音乐中，识别标准和弦进行至关重要。罗马数字表示音阶上建立的和弦：I 是主和弦，IV 是下属和弦，V 是属和弦。变格终止为 IV → I；正格终止为 V → I；阻碍终止走向 V → vi；半终止则结束在 V 上（如 I–V，ii–V）。
Common progressions often follow the circle of fifths root movement: vi – ii – V – I. In a major key, primary triads I, IV, V are major; ii, iii, vi are minor; vii° is diminished. Always check that the leading note (7th degree) resolves up by step in a V–I cadence.
常见进行常遵循五度循环的根音运动：vi – ii – V – I。在大调中，正三和弦 I、IV、V 为大三和弦；ii、iii、vi 为小三和弦；vii° 为减三和弦。始终检查在 V–I 终止中导音（第七级）是否以级进上行解决。
8. Triad Inversion Formulas & Figured Bass | 三和弦转位公式与数字低音
Inversions change the bass note without altering the chord’s pitches. Root position has the root in the bass; first inversion places the third in the bass; second inversion places the fifth in the bass. The intervallic structure above the bass determines the figuring.
转位改变低音而不改变和弦内的音高。原位以根音为低音；第一转位以三音为低音；第二转位以五音为低音。低音上方的音程结构决定了数字标记。
| Position | 位置 | Bass Note | Intervals above bass | Figured Bass |
|---|---|---|---|---|
| Root | 原位 | Root | 3rd, 5th | (none) or ⁵₃ |
| 1st inversion | 第一转位 | 3rd | 3rd, 6th | ⁶₃ (often ⁶) |
| 2nd inversion | 第二转位 | 5th | 4th, 6th | ⁶₄ |
Second inversion triads are typically used in cadential patterns (I⁶₄ – V – I) or as passing chords. Remember: the chord symbol remains the same regardless of inversion; only the bass note changes.
第二转位三和弦通常用于终止模式（I⁶₄ – V – I）或作为经过和弦。记住：无论转位如何，和弦符号保持不变；只有低音改变。
9. Seventh Chords & Extended Harmony Rules | 七和弦与延伸和声规则
Seventh chords add a fourth note, a seventh above the root, to a triad. The most common is the dominant 7th (V⁷), built on the fifth degree of a major or harmonic minor scale. Its formula: major triad + minor 7th.
七和弦在三和弦上增加第四个音——根音上方的七度音。最常见的是属七和弦 (V⁷)，建立在大调或和声小调的第五级上。其公式为：大三和弦 + 小七度。
| Seventh Chord Type | 七和弦类型 | Triad Base | Added 7th | Example (C) |
|---|---|---|---|---|
| Major 7th | 大七和弦 | Major | Major 7th (11 semitones) | C E G B |
| Dominant 7th | 属七和弦 | Major | Minor 7th (10 semitones) | C E G B♭ |
| Minor 7th | 小七和弦 | Minor | Minor 7th | C E♭ G B♭ |
| Half-diminished (m7♭5) | 半减七（小七降五） | Diminished | Minor 7th | C E♭ G♭ B♭ |
| Diminished 7th | 减七和弦 | Diminished | Diminished 7th (9 semitones) | C E♭ G♭ B♭♭ (A) |
In functional harmony, the 7th of a V⁷ resolves down by step, while the leading tone (3rd of the chord) resolves up. Dominant 7ths are often inverted; third inversion (7th in bass) is figured as ⁴₂.
在功能性和声中，V⁷ 的七音向下级进解决，而导音（和弦的三音）向上解决。属七和弦常使用转位；第三转位（七音在低音）数字标记为 ⁴₂。
10. Modes of the Major Scale | 大调调式
Modes are scales created by starting on different degrees of a parent major scale. Each mode has a distinct pattern of tones and semitones. Recognising modes is essential for aural analysis and composition questions.
调式是从原始大调音阶的不同音级开始所形成的音阶。每种调式都有独特的全音、半音模式。识别调式对于听力分析和作曲题至关重要。
| Mode | 调式 | Starting Degree | Characteristic Tone | Semitone Pattern |
|---|---|---|---|---|
| Ionian | 伊奥尼亚 | I | Major 7th | 2 2 1 2 2 2 1 |
| Dorian | 多利亚 | II | Natural 6th (minor scale) | 2 1 2 2 2 1 2 |
| Phrygian | 弗里几亚 | III | Minor 2nd | 1 2 2 2 1 2 2 |
| Lydian | 利底亚 | IV | Augmented 4th | 2 2 2 1 2 2 1 |
| Mixolydian | 混合利底亚 | 更多咨询请联系16621398022（同微信）
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