Music Theory Quick Reference Handbook | 音乐理论速查手册

📚 Music Theory Quick Reference Handbook | 音乐理论速查手册

For Year 11 Cambridge IGCSE Music, a solid grasp of the 'formulas' behind intervals, scales, chords and structures is essential. This handbook compiles all the key theoretical rules, tables and patterns you need to memorise and apply quickly – whether you are sight‑reading a score, analysing a set work, or composing your own piece. Think of it as your maths‑formula sheet for music, with every concept expressed as a clear pattern or equation.

对剑桥 IGCSE Year 11 音乐课程而言，牢固掌握音程、音阶、和弦与结构背后的“公式”至关重要。本手册汇集了所有需要牢记并快速运用的核心理论规则、表格与模式——无论是视读总谱、分析指定作品，还是自己作曲，它都像音乐的“数学公式表”一样，将每一个概念清晰表达为规律或等式。

1. Intervals & Their Formulas | 音程及其公式

An interval is the distance between two pitches, measured in semitones. The quality (major, minor, perfect, augmented, diminished) follows a simple rule: perfect intervals (unison, 4th, 5th, octave) become augmented when enlarged by a semitone and diminished when reduced; major intervals (2nd, 3rd, 6th, 7th) become augmented when enlarged and minor when reduced by a semitone. Double augmentations or diminutions are possible but rare at IGCSE.

音程是两个音高之间的距离，以半音衡量。性质（大、小、纯、增、减）遵循简单规则：纯音程（同度、四度、五度、八度）扩大半音为增，缩小半音为减；大音程（二度、三度、六度、七度）扩大半音为增，缩小半音为小。双增或双减在 IGCSE 中可能遇到但少见。

Key formula: Number of semitones defines the interval size, but the letter names determine its quality. Always count the lower note to the higher note inclusive.

关键公式：半音数决定音程大小，但字母音名决定其性质。始终从下方音计数到上方音（含首尾）。

2. Major & Minor Scales Formula | 大调与小调音阶公式

. The relative natural minor scale uses the same key signature but starts on the 6th degree: A minor (relative to C major) gives the pattern T S T T S T T. The harmonic minor raises the 7th degree by a semitone, creating a distinctive augmented 2nd between the 6th and 7th degrees. Melodic minor ascending raises the 6th and 7th degrees; descending it reverts to the natural minor.

每个大调音阶遵循相同的全音（T）和半音（S）模式：T T S T T T S。例如 C 大调：C → D（全）→ E（全）→ F（半）→ G（全）→ A（全）→ B（全）→ C（半）。关系自然小调使用相同的调号，但以第 VI 级为主音：a 小调（C 大调的关系小调）模式为 T S T T S T T。和声小调升高第 VII 级半音，在第 VI 与 VII 级之间形成特征性的增二度。旋律小调上行升高第 VI 和第 VII 级，下行还原为自然小调。

Quick check: the harmonic minor always has a leap of three semitones between scale degrees 6 and 7; the melodic minor ascending sounds like a major scale with a lowered third.

速查：和声小调在 VI 级与 VII 级之间总有一个三个半音的跳跃；旋律小调上行听起来像降了 III 级的大调。

3. Key Signatures Quick Chart | 调号速查表

Key signatures are determined by the circle of fifths. For sharps, the order is F♯ C♯ G♯ D♯ A♯ E♯ B♯; the key is one semitone above the last sharp. For flats, the order is B♭ E♭ A♭ D♭ G♭ C♭ F♭; the key is the second‑to‑last flat in the signature (except F major with one flat, which is simply B♭). Use the mnemonic: Father Charles Goes Down And Ends Battle (sharps) / Battle Ends And Down Goes Charles’ Father (flats).

调号由五度圈决定。升号顺序为 F♯ C♯ G♯ D♯ A♯ E♯ B♯；调性为最后一个升号上方半音。降号顺序为 B♭ E♭ A♭ D♭ G♭ C♭ F♭；调性为倒数第二个降号（除 F 大调只有一个降号 B♭ 外）。记忆口诀：升号 — Father Charles Goes Down And Ends Battle；降号 — Battle Ends And Down Goes Charles’ Father。

Formula to find relative minor: go down a minor 3rd (3 semitones) from the major tonic.

寻找关系小调的公式：从大调主音向下小三度（3 个半音）。

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4. Triads & Chord Construction | 三和弦与和弦构成

A triad is a three‑note chord built by stacking two thirds on top of a root. The quality (major, minor, augmented, diminished) depends on the intervals between the notes. A major triad consists of a major third plus a perfect fifth; formula: root + 4 semitones + 3 semitones. A minor triad: root + 3 semitones + 4 semitones. Augmented: root + 4 + 4. Diminished: root + 3 + 3. Frequencies can also be expressed as ratios: major triad 4:5:6, minor triad 10:12:15.

三和弦是由根音上方叠加两个三度构成的三音和弦。性质（大、小、增、减）取决于音之间的音程。大三和弦 = 大三度 + 纯五度；公式：根音 + 4 个半音 + 3 个半音。小三和弦：根音 + 3 + 4。增三和弦：根音 + 4 + 4。减三和弦：根音 + 3 + 3。频率也可用比率表示：大三和弦 4:5:6，小三和弦 10:12:15。

Quick test: In a major key, chords built on I, IV, V are major; on ii, iii, vi are minor; vii° is diminished.

快速测试：大调中，I、IV、V 级和弦为大三和弦；ii、iii、vi 级为小三和弦；vii° 级为减三和弦。

5. Seventh Chords & Extensions | 七和弦与扩展音

Adding a seventh above the root creates a four‑note chord with extra colour. The dominant seventh (V⁷) is most common: major triad + minor 7th (root + 4 + 3 + 3 semitones). Major seventh: major triad + major 7th. Minor seventh: minor triad + minor 7th. Diminished seventh: diminished triad + diminished 7th. Half‑diminished seventh: diminished triad + minor 7th. Extensions (9th, 11th, 13th) are found in jazz and Romantic music, but IGCSE occasionally asks you to identify the chord type by ear or on a score.

在根音上方增加七度音构成四音和弦，增添色彩。属七和弦（V⁷）最常见：大三和弦 + 小七度（根音 + 4 + 3 + 3 半音）。大七和弦：大三和弦 + 大七度。小七和弦：小三和弦 + 小七度。减七和弦：减三和弦 + 减七度。半减七和弦：减三和弦 + 小七度。扩展音（9 音、11 音、13 音）出现在爵士和浪漫派音乐中，IGCSE 偶尔要求通过听觉或总谱辨认和弦类型。

Formula for dominant 7th resolution: the 7th (subdominant scale degree) resolves down by step, the leading note resolves up to tonic.

属七和弦解决的公式：七音（下属音级）下行级进解决，导音上行至主音。

6. Chord Inversions & Figured Bass | 和弦转位与数字低音

When the root is not the lowest note, the chord is inverted. First inversion has the 3rd in the bass (figured bass: ⁶₃ or simply ⁶). Second inversion has the 5th in the bass (⁶₄). Seventh chords add third inversion (7th in bass: ⁴₂). In IGCSE, you may need to write or recognise these symbols in Baroque‑style harmonisation. Remember that the numbers represent intervals above the bass note.

当根音不是最低音时，和弦即为转位。第一转位以三音为低音（数字低音：⁶₃ 或简写为 ⁶）。第二转位以五音为低音（⁶₄）。七和弦还有第三转位（七音为低音：⁴₂）。IGCSE 中，你可能需要在巴洛克风格的和声写作或辨认中运用这些符号。记住，数字表示低音上方的音程。

Common pattern: a ⁶₄ chord often functions as an appoggiatura (e.g. cadential ⁶₄) where the 6th and 4th above the bass resolve to 5th and 3rd over the same bass.

常见模式：⁶₄ 和弦常作为倚音使用（如终止式 ⁶₄），低音上方的六度和四度解决到同一低音上的五度和三度。

7. Common Chord Progressions | 常用和弦进行

cycle of fifths progression: iii → vi → ii → V → I. In the minor mode, II° (diminished supertonic) often substitutes for ii. The plagal cadence (IV → I) and the interrupted cadence (V → vi) are also stock progressions. In pop and rock, the I–V–vi–IV loop is ubiquitous.

功能性和声从主和弦（I）经过下属功能组（ii, IV）进行到属功能组（V, vii°），再回到主和弦。最可预测的公式是五度圈进行：iii → vi → ii → V → I。小调中，ii°（减上主和弦）常代替 ii。变格终止（IV → I）和阻碍终止（V → vi）也是标准进行。流行和摇滚中，I–V–vi–IV 循环无处不在。

Progression name	Chord sequence	Typical style / period
Perfect cadence	V(⁷) → I	Classical, Baroque
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